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March 2007
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March 29, 2007

Paul Cohen, emeritus professor and winner of world's top math prize, dies at 72

news-service.stanford.edu
Stanford Report, March 28, 2007
BY DAWN LEVY
Paul Joseph Cohen, an emeritus professor of mathematics famed for work on set theory and 1966 winner of the world's top math prize, died March 23 at Stanford Hospital of a rare lung disease. He was 72.
Cohen won two of the most prestigious awards in mathematics—in completely different fields. He won the American Mathematical Society's Bôcher Prize in 1964 for analysis and the Fields Medal, considered the "Nobel Prize" of mathematics, in 1966 for logic.
"Paul Cohen was one of the most brilliant mathematicians of the 20th century," said Princeton Math Professor Peter Sarnak, who received his doctorate from Stanford in 1980 under Cohen's direction. "Like many great mathematicians, his mathematical interests and contributions were very broad, ranging from mathematical analysis and differential equations to mathematical logic and number theory. This breadth was highlighted in a conference held at Stanford last September celebrating Cohen's work and his 72nd birthday. The gathering consisted of leading experts in different fields who normally would not find themselves listening to the same set of lectures."
Stanford Mathematics Chair Yasha Eliashberg, the Herald L. and Caroline L. Ritch Professor in the School of Humanities and Sciences, was among many mathematicians who recalled Cohen's passion for tackling extremely difficult, longstanding mathematical problems—and solving them. "His solution of the Continuum Hypothesis will be remembered as one of the crown achievements of mathematics in the last 50 years, along with Andrew Wiles's proof of Fermat's Last Theorem and the recent proof of the Poincaré conjecture by Grigori Perelman," Eliashberg said.
"He is best known for his solution of the first of the 23 problems that the German mathematician David Hilbert posed in his very influential address to the International Mathematical Union in 1900," Sarnak said. "By the 1950s, after the work of Gödel, this problem, known as the 'Continuum Hypothesis,' had become the central one in the set theory."
In the late 1870s, German mathematician Georg Cantor put forth a hypothesis that said any infinite subset of the set of all real numbers can be put into one-to-one correspondence either with the set of integers or with the set of all real numbers. All attempts to prove or disprove this conjecture failed until 1938, when Kurt Gödel showed it was impossible to disprove the continuum hypothesis.
Despite having never worked in set theory, Cohen proved the extremely surprising result that both the Continuum Hypothesis and the Axiom of Choice—two of the most basic ideas in mathematics—were actually undecidable using the axioms of set theory. This result, which meant that conventional mathematics could neither prove nor disprove concrete and well known mathematical assertions, caused healthy turbulence among philosophers, logicians and mathematicians concerned with the concept of truth.
"Kurt Gödel, whose work in the 1930s on the consistency of the continuum hypothesis was completed by Cohen's proof of its independence from the usual axioms of set theory, lauded Cohen's work as 'no doubt...the greatest advance in the foundations of set theory since its axiomatization,'" wrote Solomon Feferman, an emeritus professor of mathematics and philosophy famed for work in logic, in an e-mail interview.
Alexander S. Kechris, a descriptive set theorist at Caltech, said Cohen invented and used in his independence proofs a fundamental mathematical technique called forcing. "It has since become a major tool in modern mathematical logic," Kechris said. Feferman, the Patrick Suppes Family Professor of Humanities and Sciences, Emeritus, explained that forcing is used to construct unusual models of the axioms of set theory, whereby statements are made true in stages and forced to remain so in all further stages.
Angus MacIntyre, a professor of applied logic at Queen Mary, University of London, said Cohen "had done work that should long outlast our times. For mathematical logic, and the broader culture that surrounds it, his name belongs with that of Gödel. Nothing more dramatic than their work has happened in the history of the subject."
Life path
Cohen was born April 2, 1934, in Long Branch, N.J., to parents Abraham and Minnie, both Jewish immigrants from Poland. According to a 1968 article from the Trenton Evening Times, Cohen, the youngest of four children, was only nine years old when his sister Sylvia checked out a book about calculus from a New York library for him. Librarians were reluctant to let her have the book, much less for her younger brother, arguing that even some college professors didn't understand calculus.
Cohen grew up in Brooklyn and graduated from Stuyvesant High School in New York City in 1950. He attended Brooklyn College from 1950 to 1953 but left before receiving a bachelor's degree when he learned he could pursue graduate studies in Chicago with just two years of college under his belt. From the University of Chicago's Mathematics Department, he received a master's degree in 1954 and a doctorate in 1958. He wrote his thesis, "Topics in the Theory of Uniqueness of Trigonometric Series," under the supervision of Antoni Zygmund.
Before the award of his doctorate, Cohen taught math at the University of Rochester from 1957 to 1958. He also taught at the Massachusetts Institute of Technology during the 1958-59 academic year. From 1959 to 1961, he was a fellow at Princeton's Institute for Advanced Study.
Cohen joined Stanford's faculty in 1961 as an assistant professor of mathematics, becoming an associate professor in 1962, the year he received an Alfred P. Sloan research fellowship. In 1963, he won a Research Corp. Award for "his proof of the independence of the continuum hypothesis and of the axiom of choice, and initiating a whole series of advances in the field." He became a full professor in 1964.
"He inspired me when I was a young mathematician," said MacIntyre, a graduate student at Stanford from 1964 to 1967. "I never heard him lecture on set theory, but rather on algebraic geometry and p-adic fields. He had a very special style, full of enthusiasm and very 'hands on.' He used as little general theory as possible and always conveyed a sense that he got to the heart of things. His techniques, even in something as abstract as set theory, were very constructive. He was dauntingly clever, and one would have had to be naïve or exceptionally altruistic to put one's 'hardest problem' to the Paul I knew in the '60s."
Sarnak agreed: "Cohen was a dynamic and enthusiastic lecturer and teacher. He made mathematics look simple and unified. He was always eager to share his many ideas and insights in diverse fields. His passion for mathematics never waned."
At a White House ceremony on Feb. 13, 1968, President Johnson presented him with the 1967 National Medal of Science for "epoch-making results in mathematical logic which have enlivened and broadened investigations in the foundation of mathematics." Calling Cohen "one of the most brilliant of mathematical logicians," Johnson said: "His work has greatly influenced the foundation and development of mathematics."
In 1972, Cohen became the first holder of the Marjorie Mhoon Fair Professorship in Quantitative Science. Author of the book Set Theory and the Continuum Hypothesis, he was a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the American Mathematical Society and the American Philosophical Society. He retired in 2004 but continued to teach until this quarter.
"In recent years, Cohen continued to work on notoriously difficult problems and in particular the Riemann Hypothesis, which is problem eight on Hilbert's list," Sarnak said. "As of today this problem remains unsolved."
Cohen played piano and violin and sang in a Stanford chorus and in a Swedish folk group, according to his son Charles. He spoke Swedish, French, Spanish, German and Yiddish and traveled widely, taking sabbaticals in England, Sweden, France and Hawaii. He met his wife, Christina, from the Swedish town of Malung, during a cruise from Stockholm to Leningrad in the summer of 1962. They married on Oct. 10, 1963.
Cohen is survived by wife Christina Cohen of Stanford; sister Tobel Cosiol of San Jose, Costa Rica; brother Ruby Cassel of Brooklyn, N.Y.; twin sons Eric and Steven Cohen of Los Angeles, Calif., and son Charles Cohen and his wife, Andreea, of Boston, Mass.
In lieu of flowers, the family would prefer donations in Cohen's memory to the Peninsula Open Space Trust (POST). Donations can be made online at www.openspacetrust.org. Condolences may be sent to the Cohen Family at 755 Santa Ynez St., Stanford, CA 94305 or condolences@paulcohen.org. Arrangements for a memorial service are pending. For updated information, go to www.paulcohen.org.
Paul Cohen, emeritus professor and winner of world's top math prize, dies at 72
March 29, 2007

Mathematician helps crack conundrum

Peter Trapa
Peter Trapa
deseretnews.com
By Joe Bauman
Deseret Morning News
Peter Trapa has been caught up in what may be the world's biggest Lie.
Before anyone gets exercised, it should be understood that the word is pronounced Lee (after a Norwegian mathematical named Sophus Lie), that Lie groups are mathematical constructs describing a special kind of symmetry, and that the achievement by Trapa and 17 colleagues ranks as a major breakthrough in math and physics.
Using a supercomputer at the University of Washington in Seattle, they devised a mathematical description of a Lie group called E8, which Trapa said is one of the most difficult and complex of what is called the exceptional series of Lie groups.
(The formal way to print the name of this group is a capital E and a subscript 8, which doesn't reproduce in newspaper print. It is pronounced E-eight.)
To print out its solution using small type would require "a calculation the size of Manhattan," says the American Institute of Mathematics in a press release.
Trapa, associate professor of mathematics at the University of Utah, is part of a far-flung team compiling an atlas of Lie groups, which are constructs that "encode continuous symmetries."
A snowflake has sixfold symmetry because its crystal grows along hexagonal patterns. A circle has continuous symmetry. More complex figures do, too, such as a cube and certain everyday objects, as well as theoretical constructs that would exist in higher dimensions than those we experience. Lie groups are valuable to math and physics.
Members of the atlas team also worked on describing E8, which Trapa said is one of the most interesting Lie groups that humans can reasonably hope to tackle. This theoretical construct of 248 dimensions was discovered in the 19th century.
"It makes sense to take a closer look at it," Trapa said. He and his partners studied ways to make a supercomputer do the work of describing it.
The result is a matrix, a table written in square form, made of polynomials. "The size of the square table is something like 450,000 by 450,000" units, Trapa said. "So there's a lot of entries."
Commented the institute, "If each entry was written in a one inch square, then the entire matrix would measure more than 7 miles on each side."
Sage, the supercomputer that ran the calculations, produced an answer amounting to 60 gigabytes of information, the institute noted.
What good is it? The description is like a high-definition photograph of a galaxy, according to Trapa. If an astronomer wants to know more about a particular part of the galaxy, it's not hard to zoom in on that section of the photo.
With the E8 description, researchers can do the same thing, zoom in to work on new problems.
"This object E8 does appear in string theory, but whether or not these results will lead to any application, that's pretty speculative," he said.
"The most interesting places to look" for new insights are parts of E8 that have connections with other areas of mathematics, Trapa added. Meanwhile, "everything is freely available" to other researchers.
A software package can be downloaded that deals with E8 and all other Lie groups.
The work was possible because of software devised by one of the team's members, Fokko du Cloux of Lyon, France. Du Cloux was diagnosed with ALS after he finished the software program in November 2005, and he continued working on the project until he died that November, according to an account by another team member, David Vogan, mathematics professor at MIT.
Originally, mathematicians believed no supercomputer could tackle the problem of describing E8, said Trapa. But when the group thought about it further, "well, it looked right on the cusp of what supercomputers could do," he said.
"The computer actually ran for two weeks, but several of us were working more or less for a year" on the problem, with issues like how to set it up so the computer could address it.
The calculation "took several starts and restarts" of the supercomputer, but the gigantic answer was finished in January.
Mathematician helps crack conundrum
March 29, 2007

His mind is on the eighth dimension

www.boston.com
By Billy Baker, Globe Correspondent
March 26, 2007
Several years ago, David Vogan was having lunch in Paris with a fellow American mathematician. At a nearby table, some American tourists were having trouble communicating with the waiter, so his friend, who spoke French, stepped in to assist.
The two groups began chatting, and the conversation got to the "What do you do?" phase.
"My friend said, 'I'm an English teacher,' " Vogan remembered. "Telling someone you're a mathematician is a conversation-killer. I usually tell people that I play with computers."
It's understandable that Vogan, a 52-year-old math professor at MIT with shoulder-length hair and a salt-and-pepper beard, is reluctant to get into what he does. His recent work is "frightening to think of geometrically," he said, and so complex that it has left a trail of crashed computers -- very powerful computers, mind you -- all over the world.
Vogan and an international team from the American Institute of Mathematics announced last Monday that after four years of work, they had mapped something called E{-8}, one of the largest and most complicated structures in mathematics. If printed on paper, the calculation would cover 49 square miles, according to Vogan, which is more than twice the size of Manhattan. While the data for the Human Genome Project would fill less than one gigabyte of space on a computer, E{-8}, would fill 60.
OK. But what is it? When asked the question recently in a conference room on the MIT campus, Vogan let out a smile that implied, "You're not going to follow this, but since you asked . . ." Then, rather than reach for a supercomputer, he picked up a piece of chalk and drew a cube on a blackboard.
"Now, a cube has three dimensions and eight corners," he said. "To draw a picture of E{-8}, it would have eight dimensions and 240 corners."
We're sort of following you, but how does an eight- dimensional object factor into a three-dimensional world?
"A lot of people ask that question," Vogan said, before reaching for another concept that a layman might understand. "Try and think of it like the movement of the planets around the sun. Each planet has a position that's three-dimensional and a velocity that has three dimensions, so you would need 54 dimensions to map the position of the planets. For E{-8}, you would need 248 numbers to describe where you are instead of just two numbers to find where you are in a city."
Vogan has been a math superstar since his undergraduate days at the University of Chicago, according to Paul Sally, 74, a Roslindale native who was his mentor there. "His progress was just phenomenal. He's one of the top two students I've had in my 42 years teaching undergraduates. He quickly became one of the truly bright young mathematicians in the world. He's not young and bright anymore; he's just one of the best."
But math superstars are not above a bit of geek criticism. A reader on Slashdot, a website that bills itself as "news for nerds," compared Vogan to the Vogons, who are responsible for destroying the earth in Douglas Adams's "The Hitchhiker's Guide to the Galaxy." The book describes Vogon poetry as the third worst in the universe.
"The title of my talk" announcing the findings was "The Character Table for E{-8}, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness,' " Vogan says. "Someone called it the second-worst poetry in the universe.
"So I was elevated one level above that, which is nice."

FACT SHEET
Hometown: Grew up in Bellefonte, Pa.; lives in Arlington.
Education: After receiving his bachelor's degree in mathematics at the University of Chicago in 1974, he earned a PhD at MIT in 1976.
Family: Wife, Lois Corman, is a church administrator; son, Jonathan Vogan, 27, works with Doctors Without Borders; daughter, Allison Corman-Vogan, 18, is a senior at Arlington High School and will attend Brandeis in the fall.
Hobbies: Hiking in the White Mountains; reading mystery and science-fiction novels. What draws him to difficult math: "It's like crossword puzzles or mountain climbing. It's something that's possible to do, but just barely."
Where to find him on Sunday mornings: Ringing the bell atop the Old South Church at exactly 10:45 a.m.

© Copyright 2007 Globe Newspaper Company.
His mind is on the eighth dimension

March 29, 2007

Feature on 18th Century Elmton maths genius

www.worksoptoday.co.uk
HE could neither read nor write, he had no idea of how to spell his own name and he spent his entire working life as a farm labourer.

Yet Jedidiah Buxton was recognised throughout the length and breadth of England as a mathematical genius – and he was born in Elmton 300 years ago.
The son of a village schoolmaster and the grandson of the local vicar, Jedidiah had been born into an educated family background on 20th March 1707.
But despite efforts to teach him, he always remained illiterate in the extreme with a mental age of a 10-year-old.
As a child he had learned up to his 10 times table but he had always showed a decided distaste for orthodox school and any kind of mathematical training.
By 18th century standards he was classed as stupid and unteachable even though his calculations were astounding – and they were all mental.
But because of his lack of formal education he was forced to spend all his working life as a farm labourer.
Jedidiah had no idea why numbers came to mean so much to him, but by the age of 17 he could perform complex calculations without the aid of a pen, paper or chalk.
Using his own complex methods he was able to quickly complete problems set by local people.
And because he lacked proper training he was unaware of arithmetical short-cuts familiar to today's students, making his mathematical achievements even more remarkable.
His life was totally dominated by numbers. A regular church attender, he was unable to recall church sermons but knew exactly how many words each hymn or psalm contained.
And if he was presented with a series of problems he would resolve them all at the same time.
Difficult problems took their own particular toll on him. He would withdraw into himself and when it was all over he would more often than not need a good sleep to recover from the strain.
If a time was mentioned he would straight away convert it into minutes and seconds. While distances were changed into alternative units of measurement.
On one memorable occasion, when he was asked by his employer to calculate the size of his estate, he strode it out, giving the answer in acres, roods, perches and eventually into square hair's breadths, astounding the experts.
In addition to numbers, Jedidiah's other interest was the Royal Family, and in 1754 he decided to walk to London to see the king – a distance of 204 miles.
Unfortunately, George II was away at the time, but while he was in London Jedidiah was invited to appear before the Royal Society, where his talents were put under the spotlight.
Members were so satisfied by his answers that they gave him a gratuity aknowledging that he really was a genius.
While he was in London he was taken to the Drury Lane Theatre to see the renowned David Garrick in Richard III.
However, the grandeur of the occasion meant little to him and rather than watch the play he preferred instead to count the actor's words and add up the dancers' steps.
After the excitement of London Jedidiah resumed his life in the country.
Over the years his talent attracted several visitors – one of them a well-known mathematician, Mr T.Holliday.
He said: "When I met him he was a man of middle age."
"He was almost in rags and was working with a spade as a farm labourer. "His wife and daughter and their home reflected their poor circumstances."
The first question put to Jedidiah was a complex cubical problem
Mr Holliday set about finding the answer using a pen and paper, but Jedidiah came up with the right answer long before him and it had all been worked out in his head.
And when he was asked if he could tell what acreage 3,584 broccoli plants would need if the rows were four feet apart and seven feet separated them he came up with an answer within 30 minutes.
He was always calculating – it was said that he could multiply numbers of 20 to 30 figures easily in his head and repeat the figures of his answer backwards while holding a conversation at the same time.
In January 1764 he agreed to have his portrait painted.
He was so unmoved by the experience that while he was sitting for the artist he calculated his age from the point when the portrait was started at 3.38pm and 43 seconds in the afternoon to be 56 years, 10 months, one week, two days, nine hours, 53 minutes and 43 seconds or 20,743 days, 497, 841 hours, 29 870, 513 minutes or 1,792,230,823 seconds.
The manner of Jedidiah's death was equally as memorable as his remarkable life had been.
While visiting the Duke of Portland at Welbeck Abbey one day he told the duke that they would not be meeting again, saying he would die the following Thursday.
The Duke thought he was out of sorts and told his servants not to give him too much beer, but Jedidiah was insistent and bade his farewells to his friends and neighbours oblivious of the fact that they thought it amusing.
When Thursday came he went about his business as usual. But after he had eaten his dinner he sat down and died at the very time he had predicted. A fitting end for an enigmatic genius.
Jedidiah was finally buried in Elmton on 5th March 1772.
Although his descendants can still be found in the area, others made their way to Australia and North America.
His grandson Henry Buxton was a pioneer in Canada and later in the United States.
The town of Buxton in Oregon still bears the family name.

The Guardian would like to thank Elmton with Creswell Local History Group for their help with this feature. Contact them on 01909 720943 or 01909 721695.
27 March 2007
Feature on 18th Century Elmton maths genius

March 29, 2007

Predicting the evolution of superbugs

communications.uwo.ca
Lindi Wahl
Lindi Wahl
By Mitchell Zimmer
Mar 27th, 2007
Lindi Wahl's ability to form mathematical models that predict the evolution of drug resistance in microbes has earned her this year's Florence Bucke prize.
In celebration of the recognition, Wahl presents the annual Bucke lecture on April 2 at 7:30 p.m. in Room 3250 of the 3M Building.
Wahl, from the Department of Applied Mathematics, says her investigations into the probability that a mutation could confer some benefit to a population started with some "beautiful mathematics from the 1920s-30s addressing these sorts of problems."
For a mathematician, biology can present so many interesting questions and possibilities.
"What's the probability that this gene gets off the ground once the mutation has happened? What's the probability that the mutation can spread through the population?"
"The mathematics that was done then (1920s and 1930s) was all for a constant population size and for a fixed generation time so everybody reproduces in the spring and then all of the surviving offspring reproduce again in the spring. The generation time is always one year long and then everybody has ... the most basic discrete offspring distribution that mathematically you might think of using."
But that's not how real life works.
When it comes to bacteria and viruses, the reproduction strategies are vastly different from the model described above.
"The population size might fluctuate hugely, there's no season, so generation times are asynchronous as well as overlapping and they are also of different lengths," says Wahl.
"Especially for viral populations the virus has to first bump into a cell and infect it and then once it's in the infected cell, the generation time is roughly fixed, but that bumping in time can depend on a lot of factors so generation times vary a lot ... randomly and then the offspring distribution for bacteria -- it's not a distribution which can be anywhere between zero and five offspring, it's two or one or zero. A lot of my work is taking these beautiful mathematical results and doing the same thing but trying to add some more realistic assumptions for microbes."
As an example of applying her work, Wahl points to modern drug treatment of AIDS.
"For HIV, just a single base pair mutation can confer tremendous resistance to a single drug, the drug can be 50 times less effective."
Now suppose the rate of the mutation is one in a million. At first that sounds like slim odds for a mutation. However, when you consider that an infected person can carry a virus load of millions upon millions, the odds of developing resistance doesn't seem that unlikely.
If, however, you started a drug regimen simultaneously with three drugs, then the odds of resistance decrease dramatically. As Wahl explains, when "triple-drug cocktails are prescribed for HIV, then you need three mutations simultaneously to be resistant to three different drugs."
In other words, if one mutation confers resistance at a rate of one in a million, then the chance of another mutation occurring at the same time for resistance to two drugs would be one in one thousand billion. The odds are even less for three mutations happening at the same time (the rate becomes a number with 18 zeroes after it).
Part of building a mathematical model of microbes depends on your starting point.
"We try to put in just the very most basic assumptions about the life history of the organism and that already complicates things so much, it's unbelievable... that's why it's research."
Following the Bucke Lecture, a complimentary reception will be held at Michael's, Room 3340, Somerville House.
Predicting the evolution of superbugs
March 29, 2007

Mathematical mystery in Escher's art examined, April 3

www.princeton.edu
A mathematical puzzle in the work of Dutch graphic artist M.C. Escher is the subject of a lecture by mathematician Hendrik Lenstra at 8 p.m. Tuesday, April 3, in McCosh 10.

Lenstra, a professor of mathematics at the University of Leiden in the Netherlands, will speak on "Escher and the Droste Effect," which refers to the infinite reproduction of an image within an image.
Lenstra has been fascinated with Escher and the mathematical concepts that many of his lithographs illustrated. In 2000, Lenstra focused on Escher's "Print Gallery," which features a man looking at a distorted picture of seaside buildings drawn on a twisted grid, with a mysterious blank patch in the center.
Using elliptic curve theory to describe the distortion necessary to create the Droste effect in Escher's lithograph, Lenstra arrived at an exact mathematical formulation of the artist's process. With colleague Bart de Smit and students, he was able to fill in the patch and generate a complete, mathematically precise version of the drawing. Lenstra's lecture will describe this two-year project and show his team's computer variations on Escher's idea.
The talk is designated as the Louis Clark Vanuxem lecture and is sponsored by the Department of Mathematics and the University Public Lecture series.
Mathematical mystery in Escher's art examined, April 3

March 29, 2007

The Tangle of Turbulence Revealed: Could Lead To Better Car Design

www.sciencedaily.com
Science Daily — Picture the flow of water over a rock. At very low speeds, the water looks like a smooth sheet skimming the rock's surface. As the water rushes faster, the flow turns into turbulent, roiling whitewater that can overturn your raft.
Turbulence is important in virtually all phenomena involving fluid flow, such as air and gas mixing in an engine, ocean waves breaking on a cliff and air whipping across the surface of a vehicle. However, a comprehensive description of turbulent fluid motion remains one of physics' major unsolved problems.
Now, in a paper to be published in an upcoming issue of Physical Review Letters, MIT researchers report that they have visualized for the first time a convoluted tangle underlying turbulence. This work may ultimately help engineers design better planes, cars, submarines and engines.
Researchers have long suspected that there's a hidden but coherent structure underlying turbulence's messy complexity, but there has been no objective way of identifying it, said MIT research group leader George Haller, professor of mechanical engineering, who also heads Morgan Stanley's Mathematical Modeling Center in Hungary.
"The fluid mechanics community has not reached a consensus even on an objective definition of a vortex, or whirlpool effect, let alone the definition of structures forming turbulence. The mathematical techniques we have developed give a systematic way to identify the material building blocks of a turbulent flow," Haller said. To picture the skeleton of turbulence, the MIT researchers analyzed experimental data obtained from co-authors Jori Ruppert-Felsot and Harry Swinney of the University of Texas at Austin. The Texas group used water jets to force water from below into a rotating tank of fluid. They seeded the resulting complicated flow with luminescent buoyant particles. When illuminated with a laser, the miniscule polystyrene spheres were visible as they raced around the vortices and jets.
While the particles looked cool, "most important to our analysis were the particles' velocities, which our collaborators obtained by recording the particles' motion with a high-resolution camera, then using a software tool to figure out which particle moved where in a split second," Haller said. "This gave us a high-quality map of the whole velocity field of the turbulent flow at each time instance."
The technical analysis of the velocity field was carried out by MIT mechanical engineering graduate student Manikandan Mathur, whose work is jointly supervised by Haller and co-author Thomas Peacock, assistant professor of mechanical engineering at MIT.
Using involved mathematical tools, Mathur uncovered a convoluted tangle embedded in the flow. "With this approach, we isolated the very source of turbulent mixing, not just its effect on dye or smoke as earlier studies did," said Mathur.
The complexity they found surprised the MIT team. They knew that in turbulent flow, unsteady vortices appear on many scales and interact with each other. What they didn't know was that the complicated, constantly evolving flow patterns are driven by two competing armies of particles constantly being pulled together and pushed apart.
The researchers identified a complex network of two types of curves formed by two distinct groups of particles. The first type of curve, which the researchers colored red, attracts other fluid particles. At the same time, the second type, colored blue, repels other fluid particles. Both sets of curves evolve with the flow. Imagine that the particles visible in the turbulent water are like an army of ants being chased through a bowl of mixed-up red and blue spaghetti. "The ants love red spaghetti and want to stay close to it, but they hate blue spaghetti and won't touch it. And they have to keep running in the bowl under these constraints, stuck in an endless maze forever," said Haller.
The resulting images, which look like dense, tangled masses of blue and red fibers, are snapshots of this stunning, constantly deforming structure. "The chaotic tangle forms the skeleton of turbulence as fluid is simultaneously attracted to, and repelled by, its different components," Haller said.
The MIT researchers call their discovery the "Lagrangian skeleton" of turbulence because their particle-based approach is motivated by the work of 19th-century mathematician Joseph-Louis Lagrange. "Lagrange developed mathematical tools still used today for calculating mechanical and fluid motion," said Peacock.
Among many applications, the new results promise to aid the early detection of clear air turbulence that causes those unexpected jolts in airplanes; they may also help control the spread of oceanic pollution. "Most certainly, they will lead to a better appreciation of ants running in a bowl of spaghetti," said Haller.
This work was supported by the National Science Foundation, the Air Force Office for Scientific Research and the Office of Naval Research.

Note: This story has been adapted from a news release issued by Massachusetts Institute of Technology.
The Tangle of Turbulence Revealed: Could Lead To Better Car Design

March 29, 2007

Math Tutors Celebrate Math Education Month

digital50.com
LOS ANGELES-(Business Wire)-March 28, 2007 - How long will it take to get to grandma's house if traffic is moving at 40 miles per hour? How much tip should be left for the waiter if the bill is $17.63? In honor of Mathematics Education Month, Mathnasium reminds its neighbors that all kids can learn to love math, and challenges you to test your math IQ online at www.mathnasium.com/mathiq.htm.
"Our philosophy is based on the idea that children don't hate math - they hate being confused and intimidated by math," said Larry Martinek, chief instructional officer for Mathnasium. "By teaching children math in a way that makes sense to them, we eliminate those negative feelings."
According to Martinek, the key to understanding math is "Number Sense," a deep mathematical understanding developed over time through instruction and materials that make sense to the learner.
The Mathnasium Method was developed by a math teacher and his students over the past 30 years. It is a time-tested, personalized program that employs diagnostics, instruction, worksheets, manipulatives, and games to build Number Sense, and with it, "confidence and a deep understanding and lifelong love of mathematics," Martinek said.
To get residents started, Martinek offers the following tips for parents to help their children build Number Sense.
— Just as you read with your kids, try "mathing" with your kids. Have your kids make change at the store, or figure out how long it will take to get to grandma's house.
— Challenge children with problems both orally and visually, with little or no writing. This will enhance their ability to "see" the problems without getting frustrated with mathematical rules.
— The most basic skills in mathematics are counting and grouping ("seeing" numbers in groups). To develop counting skills, help children learn to count from any number, to any number, by any number (e.g., count by 5s starting at 4). To expand children's thinking processes and help them "see" groups, ask questions like: "7 and how much more make 10?" "How far is it from 89 to 100?"
To receive a booklet, or for more information on how to boost your child's math skills, please call 1-877-MATHNASIUM or visit the company's Web site at www.mathnasium.com.

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Math Tutors Celebrate Math Education Month

March 29, 2007

Regional mathematics faculty converge on campus

www.mercyhurst.edu
What do a square-wheeled bicycle, a 17th-century French painting, and the Indiana legislature have in common?
That query is one that will be explored when the Allegheny Mountain Section of the Mathematical Association of America (MAA) holds its annual spring meeting at Mercyhurst College April 13-14.
Dr. Donald Platte, chair of the Mercyhurst College Mathematics and Computer Systems Department and past governor of the Allegheny Mountain Section of the MAA, said Mercyhurst is eager to host the more than 125 mathematics faculty from institutions throughout western Pennsylvania and West Virginia who will converge on the Erie campus. The group will hear a number of invited speakers and share research through a contributed paper session for faculty and students.
Dr. Deanna Haunsperger, professor of mathematics at Carleton College in Minnesota and former co-editor of the MAA's undergraduate magazine, Math Horizons, will talk about the magazine's mission of introducing students to the world of mathematics outside the classroom, using a square-wheeled bicycle, French painting and Indiana legislature as examples.
Also speaking will be Dr. Fred Roberts, mathematics professor at Rutgers University, and director of DIMACS, a National Science Foundation "science and technology center" that includes Rutgers and Princeton universities, AT&T Labs, Bell Labs and numerous other academic and industry partners. In recent years Roberts briefed members of Congress on contributions of the mathematical sciences to emergency preparedness, disaster prevention, and related security matters. Dr. James Sellers, director of undergraduate mathematics at Penn State and 2006 Allegheny Mountain Section Teaching Award Winner, is also slated to address the group on integer partitions. Sellers research area is combinatorics and partition functions.

Released on Wednesday, March 28, 2007
Regional mathematics faculty converge on campus

March 29, 2007

Math + Rock = Mathematicians

media.www.theorion.com
Math-centered indie rock band obsesses over fractions, trinomials and theorems in song
By: Maxwell Rowe
Issue date: 3/28/07 Section: Entertainment
The Mathematicians, the band based on numbers, will be dividing the stage 8 p.m. Tuesday at Monstro's Pizza in a show that is sure to add up to an explosive night of music.
"They fucking rock," said Rachel Loveless, singer for Gruk, which will also be playing at the show. "One of the best live bands I've ever seen, and I've seen a lot of live bands."
The Mathematicians base their music on math and their lyrics on math metaphors. The band is made up of three former mathematicians, Dewi Decimal, vocals, keyboard and vocoder; Albert Gorithm, vocals, drums and sampler; and Pete Pythagoras, vocals and bass. The three fulfill their obsession with math through their music, Pythagoras said.
"Pretty much, we're mathematicians," he said. "We thought, 'What better way to portray that then composing music?'"
The band dresses in "nerd attire" when on stage and maintains the persona throughout the show, Loveless said.
"They dress up like nerds with pocket protectors," she said. "When they put on the clothes, they become the people, super high energy."
Pythagoras disagrees.
"I hear all these people say that we put on a persona when we get on stage," he said. "I've never really seen it like that."
The band, from upstate New York, is on a national tour tapping into the West Coast at the end of March. The Mathematicians released their second album, "Level Two," in 2006. The show will be focused around that album and a few new songs, Pythagoras said.
"We don't play old songs too much," he said. "We're feeling the 'Level Two' vibe right now."
The Mathematicians have incorporated video sequences produced by Jonathan Phelps into their live sets. Phelps also produced the band's music video for "Weapons of Math Instruction."
"It's live video mixing, a DJ, but visual," Pythagoras said.
Phelps locked himself in his room and put together things on film he felt when he listened to the band's music, Pythagoras said.
The concept of math and music may seem elementary, such as in the movie "School House Rock," but the Mathematicians are anything but.
"It's a mix of punk, rock, hip-hop, electronic, dance - any music that we can wrap our brains around," Pythagoras said. "Originally, it was to make some fun music, but with 'Level Two,' it got a little darker and a little more serious."
The band members have incorporated their past band experiences to create something unique. The music is catchy and poppy, but there are serious issues vocalized through numbers.
"The music came from the total sum trace of all the elements of older bands we were in," Pythagoras said. "I met Albert on a bus in Portland, and we came to the East Coast, met Dewi, who had a lot of good ideas and said, 'Let's start a band and try to solve this equation.'"
The band has been playing together since 2003, and Tuesday's show marks its second trip to Chico. Gruk and the Mathematicians met in Redding at a house show in May 2004. Since then, Gruk has made the trip to the Mathematicians' hometown and vice versa.
Gruk starts a national tour in July, and the Mathematicians are wrapping up their tour at the end of April. Both bands have plans for future releases. Gruk will be releasing a 7-inch discography and a split 7-inch with the Wobblies. As for the Mathematicians, they are working on their third album, "Level Three."
"The tour is going pretty well," Pythagoras said. "It always starts to pick up in the western part of the country, pretty good to finally be here."
Also included in Tuesday's lineup are Kids with Headlice and Baghdad Batteries. There is a $3 to $5 donation, and education will be provided while you rock out.
"It's serious rock," Loveless said. "But it's funny seeing these guys get up on stage and sing about math."

Maxwell Rowe can be reached at mrowe@theorion.com
--
The Scoop
Who: The Mathematicians, Gruk, Kids with Headlice and Baghdad Batteries
Where: Monstro's Pizza
When: 8 p.m. Tuesday
Cost: $3 to $5 donations
More information: www.chicolist.com Math + Rock = Mathematicians

March 23, 2007

Varadhan wins Abel Prize

www.aftenposten.no
Srinivasa S. R. Varadhan
Indian-born American mathematician Srinivasa S. R. Varadhan
has been awarded the 2007 Abel Prize.

Indian-born New York University professor Srinivasa S. R. Varadhan was awarded the 2007 Abel Prize for mathematics on Thursday.
Varadhan, 67, received the NOK 6 million (USD 975,000) prize for "his fundamental contributions to probability theory."
Varadhan teaches at NYU's Courant Institute of Mathematical Sciences, and the award said his theories are useful in a broad range of fields, including quantum field theory, statistical physics, population dynamics, econometrics and finance, and traffic engineering.
In a popularized presentation of Varadhan's work, University of Oslo professor Tom Louis Lindstrøm said large deviations are those results that appear to defy normal odds. For example, if a normal coin were tossed 1,000 times, about half the tosses would be expected to turn up as 'heads.'
"But this need not happen," he wrote. "There is a small - extremely small - probability that the coin will show 'heads' every time. ... The art of large deviations is to calculate the probability of such rare events."
Varadhan's Large Deviation Principle sums up how to apply the techniques to the chances of such unlikely outcomes.
The Abel Prize, first awarded in 2003, was created by the Norwegian government and named after 19th Century Norwegian mathematician Niels Henrik Abel.
Varadhan wins Abel Prize
March 23, 2007

It All Adds Up to a Big Prize For Math Professor at NYU

www.nysun.com
BY GARY SHAPIRO - Staff Reporter of the Sun
Champagne corks popped at New York University's Courant Institute of Mathematical Sciences yesterday as one of its professors, Srinivasa Varadhan, won the Abel Prize, considered the Nobel of mathematics.
It is awarded by the Norwegian Academy of Science and Letters.
"I was shocked," Mr. Varadhan, who won the $850,000 prize, said. His work has become a cornerstone for a great deal of modern probability theory.
He has made key contributions to the theory of large deviations, which explores the precise ways of calculating probabilities of very unlikely conjunctions of events, such as a long string of winning hands at blackjack. His research has implications for quantum theory, statistical physics, population dynamics, econometrics, and traffic engineering, and the way in which the large-scale structure of the universe emerges from the sea of chance small events.
"He has to be considered the leading figure in probability in the second half of the 20th century," a professor at the Massachusetts Institute of Technology, Daniel Stroock, said. His work has involved so-called ruin problems, such as what reserves an insurance company should keep if it encounters a terrible year.
"There are a lot of events with small probability," Mr. Varadhan said. "Sooner or later, one of them will occur. You want to know which one of them will occur first." In a telephone interview, Mr. Stroock gave the example of an asteroid hitting the Earth and wiping out the planet. He said the chances are very small, but the consequences are so calamitous that one is interested in knowing its probability.
A professor at SUNY New Paltz, Krishnamurthi Ravishankar, stressed Mr. Varadhan's generosity, as did a mathematician at New York University, Gerard Ben Arous, who said Mr. Varadhan is so full of ideas that he can share his knowledge with those who know less.
On this topic, his colleagues roared when the director of the Courant Institute, Leslie Greengard, told the following anecdote: Mr. Stroock recalled a friend once saying that working with the theory of large deviations consisted of two steps. "The first step requires you to prove either the upper or lower bound yourself. The second step requires you to get on the telephone and ask Varadhan how to prove the other bound."
A professor of mathematics at NYU, Sylvain Cappell, quipped that members of the Courant Institute winning the Abel Prize for the second time in three years is an example of the large deviation in probability for which Mr. Varadhan is getting the award.
Born in India, Mr. Varadhan came to NYU in 1963 as a post-doctoral fellow. His son, Gopal, was killed in the terror attacks of September 11, 2001.
It All Adds Up to a Big Prize For Math Professor at NYU
March 23, 2007

International team solves E8: 248-dimensional math puzzle

www.itwire.com.au
By William Atkins
Tuesday, 20 March 2007
E8 is a complex structure with 248 dimensions. It took 4 years of prep work by 18 mathematicians and computer scientists and 3 full days of computer time to solve a matrix with over 205 billion parts that contained 60 times more data than the Human Genome Project.
Professor of mathematics Peter Sarnak at Princeton University said of the team's result: "This is exciting. Understanding and classifying the representations of Lie Groups has been critical to understanding phenomena in many different areas of mathematics and science including algebra, geometry, number theory, Physics and Chemistry. This project will be valuable for future mathematicians and scientists." [See below: http://aimath.org/E8/.]
After four years of theorizing, designing, and developing equations, a team of nineteen mathematicians and computer scientists from the United States and Europe finally input everything into a SAGE supercomputer at the University of Washington, which spent three continuous days to turn out a final answer.
E8 is also called the exceptional Lie group E8. In mathematics, E8 is the name of a root system (a vector group in a Euclidean space) and of several associated Lie groups (which describe the symmetry of structures) and also their Lie algebras (algebraic structures that are used to study geometric objects such as Lie groups). E8 has a rank of 8 and a dimension of 248. It contains a 453,060 by 453,060 matrix, which is a rectangular table with 453,060 columns and 453,060 rows with a total of 205,263,363,600 entries.
E8 was mapped by the team of mathematicians and computer scientists in early 2007 at the American Institute of Mathematics. Over 60 gigabytes of storage space was required for the resulting data.
The project is known as the Atlas of Lie Groups and Representations. The goal of the Atlas project is to determine the unitary representations of all the Lie groups. The Atlas team consists of numerous researchers from the United States and Europe. The core group consists of Jeffrey Adams (University of Maryland), Dan Barbasch (Cornell University), John Stembridge (University of Michigan), Peter Trapa (University of Utah), Marc van Leeuwen (University of Poitiers, France), David Vogan (MIT), and (until his 2006 death) Fokko du Cloux (University of Lyon, France).
David Vogan, from the Massachusetts Institute of Technology (MIT), in Cambridge, is one of the team of mathematicians that worked on E8. He described their work as: "…as complicated as symmetry can get." [BBC News: http://news.bbc.co.uk/1/hi/sci/tech/6466129.stm]
Vogan presented the team's result at a MIT lecture on Monday, March 19, 2007. His article is called "The Character Table for E8, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness".
The Atlas team believes that their results will help various fields of physics understand structures and designs with more than three dimensions such as string theory in cosmology and quantum gravity in quantum mechanics.
The American Institute of Mathematics (AIM) is a nonprofit organization that was founded in 1994 by John Fry and Steve Sorenson. Its goals are to expand the scope of mathematical knowledge through research projects, sponsored conferences, and the development of an on-line mathematics library. The home Web page of AIM is http://www.aimath.org/.
A brief mathematical description of E8 appears at: http://en.wikipedia.org/wiki/E8_%28mathematics%29.
More information about E8 appears at the article "Mathematicians Map E8": http://aimath.org/E8/
International team solves E8: 248-dimensional math puzzle
March 23, 2007

Truth and Lies

www.economist.com
Mar 22nd 2007
From The Economist print edition
Mapping the most complex known mathematical object
FOR more than a century mathematicians have known about Lie groups. These are families of shapes named after Sophus Lie, a Norwegian mathematician who discovered them. There are four "simple" families of Lie groups and five others—this being mathematics—that are not quite so simple.
The simplest member of the simplest Lie group is the circle, which looks the same however it is rotated. Its higher-dimensional cousin, the sphere, has the same properties, only more so, and is thus the second-simplest of the same family. The five non-simple groups—dubbed "exceptional" in their complexity and symmetry—are harder to envisage and, for almost 120 years, the details of the most intricate of these have lain beyond reach. This week a group of mathematicians led by Jeffrey Adams of the University of Maryland announced that they had completed a map of the largest and most complicated one, a structure known to mathematicians as E{-8}.
Lie groups have two defining features: surface and symmetry. A sphere has two surface dimensions. In other words, any place on its surface is defined by just two numbers, the longitude and the latitude. But it has three dimensions when it comes to symmetries. A sphere can spin on an axis that runs, say, from north to south, or on each of two axes placed at right angles to this. E{-8} is rather more difficult to visualise. Its "surface" has 57 dimensions—that is, it takes 57 co-ordinates to define a point on it, and it has 248 axes of symmetry.
Grappling with such a structure is as tricky as it sounds. But Dr Adams's team decided to have a go. They want to create an atlas of maps of the Lie groups. This involves making a description in the form of a matrix for each structure. (A matrix is a multi-dimensional array of numbers, such as that found in a sudoku puzzle.) Dr Adams and his colleagues began by writing a computer program that would generate such matrices, a task that took them more than three years. It transpired that they needed 453,060 points to describe E{-8} but that they also needed to express the relationship between each of these points. That meant they had to devise a matrix with 453,060 rows and the same number of columns. In total this gives 205 billion entries. To complicate things further, many of these entries were not merely numbers but polynomials—sequences in which a given number is raised to a series of different powers, for example its square and its cube.
Processing such a vast quantity of data was beyond the capacity of even modern supercomputers, so the team were forced to tinker with the problem to make it tractable. This tinkering led them to a piece of ancient maths known as the Chinese remainder theorem.
This theorem is contained in a book written in the late third-century AD by a mathematician called Sun Tzu (not to be confused with the military strategist of the same name). It is used to simplify large calculations by breaking them down into many smaller ones, the results of which can then be recombined to generate the answer to the original question.
One problem addressed in the original book concerns counting soldiers. Sun Tzu's solution was that the soldiers should first split into groups of three, then groups of five, then groups of seven, with the number unable to join a group (in other words, the remainder) being noted each time. The three remainders can then be used to calculate how many soldiers are present. For example, if two were left over from the groups of three, three left over from the groups of five and two left over from the groups of seven, there would have been 23 soldiers in the unit (or possibly 233, but the difference should be obvious to even the stupidest commanding officer). The researchers worked out how to use the remainder theorem to bring their calculation within the capacity of a supercomputer called Sage, which spent more than three days crunching the numbers to generate the map of E{-8}. Not content with letting the supercomputer do all the arithmetic, the mathematicians simultaneously jotted down some calculations of their own on the back of an envelope. They worked out that if each entry in the matrix were written on paper that was one inch square, the answer would cover an area the size of Manhattan.
And the point is
Apart from the satisfaction of mapping E{-8} at long last, mathematicians are pleased because the structure keeps popping up in another branch of intellectual endeavour: string theory. This purports to be the best explanation of the universe beyond the Standard Model of physics that describes all known particles and forces, but which is generally acknowledged to be incomplete. String theory requires that the universe has many more dimensions than those that are obvious, but that most of these extra dimensions are too small to be discerned with today's equipment. One of the ways in which they can be hidden involves E{-8}, so having a mathematical map of its structure could be handy. Cheaper, too, than building a particle accelerator the size of the solar system.
Truth and Lies
March 23, 2007

Polynomials Everywhere

www.fordham.edu
Robert H. Lewis
Photo by Ken Levinson
Robert H. Lewis
Associate Professor of Mathematics
For about twenty years, I have worked on the borderline between mathematics and computer science. I've become an applied mathematician, but in a sense that didn't exist thirty years ago.
I think the general public does not have a very good idea of what mathematicians do, so let me start with some generalities. Before roughly 1985, almost all mathematicians in academic positions in the United States and Europe were pure mathematicians. They spent their careers discovering and proving theorems with no regard to potential applications. Most people will recall the Pythagorean Theorem from geometry, which states that a2 + b2 - c2 = 0 for the sides of a right triangle. To a mathematician, there is no interest in working out numerical examples; the interest is in proving that the theorem is always correct. The proof is a rigorous logical argument; arithmetic is irrelevant. Mathematics encompasses far more than geometry, but nonetheless, virtually all mathematicians in academia were engaged in discovery and proof of new theorems. Their results often did turn out to be of interest to others. For example, the recent movie A Beautiful Mind concerns John Nash, whose work influenced economists.
There were (and are) also applied mathematicians, but they tended to work in industry or the military. They used advanced mathematics to help engineers develop better products.
These traditional categories were seriously challenged around 1977 by the proof of the Four Color Theorem. It says that no matter how complicated your map (think of a map of the United States), four colors is enough to shade the regions (states) so that any two that border have different colors. The proof was not just the expected kind of logical argument. They designed an algorithm that could be run by a computer to check several thousand complex cases that no person could possibly do. It took the computer hundreds of hours. To some, this was heresy; to others, the opening of a new realm.
Everyone sensed that something new was happening in the mathematical world. The computer was not just doing a lot of arithmetic. The software encoded a mathematical structure called a graph and checked certain symbolic properties of it.
About that time, I started out as a pure mathematician working in algebraic topology. But I was soon attracted to computer science and obtained a degree in it. I am not interested in proving theorems with software, but rather solving problems that involve algebraic symbolic manipulation (as opposed to mere arithmetic). I have written a cutting-edge computer algebra system to do this, called Fermat (on the Web at: www.bway.net/~lewis). In doing so I didn't prove any theorems, but designed some pretty complex algorithms.
Here of late, I mostly work with systems of polynomials. Most people probably remember polynomials from high school mathematics. We encountered above a2 + b2 - c2, which is a polynomial in three variables with three terms (or pieces) of degree two (the exponents). For another example, x2y3 + z2 – 3xyz - x2 has four terms, three variables, and is degree five because that is the sum of the exponents in the first term. An amazing number and variety of "real world" problems can be reduced to systems of polynomials. I have worked on problems arising in pure mathematics, computer vision and robotics, medical research and other topics.
My latest project results from the convergence of computational chemistry, flexibility of three-dimensional objects, and systems of polynomials.
Basically, living things are made of proteins, and proteins work because they can fold up. Molecules can fold because they are flexible. Simple examples are easily built from a few plastic balls and rods, as in Chemistry 101. In 1812, the French mathematician Augustin-Louis Cauchy considered flexibility of three-dimensional structures (think of a geodesic dome) where each joint can pivot or hinge. He proved that if the structure is convex (no indentations) it must be rigid. People came to believe that there were no flexible structures at all. Astonishingly, in 1978 a non-convex one was found. It is very enlightening to hold a model of one of these and feel it move.
My colleagues and I have a new approach to understanding flexibility, using symbolic computation instead of numerical calculation. We describe the geometry of a certain object with six polynomial equations. We solve this system of six to derive what is called a resultant, which turns out to be one polynomial in about two hundred thousand terms, in twelve variables, of degree thirty-one. As an ordinary text file, it occupies three megabytes of storage space on a computer hard drive (by comparison, the plain text version of the entire King James Bible occupies just four megabytes of storage space). Of course, there is no interest whatever in actually looking at all these terms. Furthermore, it's not enough just to have this monster polynomial. I developed an algorithm to detect flexibility in the object by examining the resultant. We hope to extend this to more situations.
The concepts here are not beyond the grasp of undergraduate mathematics majors, and we hope to increase their participation in research at Fordham.
Readers can find my essay on mathematics education at: www.fordham.edu/mathematics/whatmath.html



The "Sapientia et Doctrina" section of Inside Fordham features first-person columns written by members of the Fordham Jesuit community and University faculty. Our Jesuit correspondents offer essays on teaching and learning from a Jesuit perspective, or focus on some aspect of scholarship as seen through the lens of Jesuit tradition. Faculty correspondents write on an academic topic: their own academic specialty or current research; or an aspect of scholarship, written for the lay person. The two types of columns alternate by issue.

For more information please contact the editor, Bob Howe, at (212) 636-6538, howe@fordham.edu.
Polynomials Everywhere

March 23, 2007

Programming language pioneer passes away

www.theage.com.au
John Backus
John Backus
March 21, 2007 - 11:06AM
John Backus, whose development of the Fortran programming language in the 1950s changed how people interacted with computers and paved the way for modern software, has died. He was 82.
Backus died Saturday in Ashland, Oregon, according to IBM, where he spent his career.
Prior to Fortran, computers had to be meticulously "hand-coded" - programmed in the raw strings of digits that triggered actions inside the machine.
Fortran was a "high-level" programming language because it abstracted that work - it let programmers enter commands in a more intuitive system, which the computer would translate into machine code on its own.
The breakthrough earned Backus the 1977 Turing Award from the Association for Computing Machinery, one of the industry's highest accolades. The citation praised Backus' "profound, influential, and lasting contributions."
Backus also won a National Medal of Science in 1975 and got the 1993 Charles Stark Draper Prize, the top honour from the National Academy of Engineering. "Much of my work has come from being lazy," Backus told Think, the IBM employee magazine, in 1979.
"I didn't like writing programs, and so, when I was working on the IBM 701 (an early computer), writing programs for computing missile trajectories, I started work on a programming system to make it easier to write programs."
John Warner Backus was born in Wilmington, Delaware, in 1924. His father was a chemist who became a stockbroker. Backus had what he would later describe as a "checkered educational career" in prep school and the University of Virginia, which he left after six months.
After being drafted into the army, Backus studied medicine but dropped it when he found radio engineering more compelling.
Backus finally found his calling in math, and he pursued a master's degree at Columbia University in New York.
Shortly before graduating, Backus toured the IBM offices in midtown Manhattan and came across the company's Selective Sequence Electronic Calculator, an early computer stuffed with 13,000 vacuum tubes.
Backus met one of the machine's inventors, Rex Seeber - who "gave me a little homemade test and hired me on the spot," Backus recalled in 1979.
Backus' early work at IBM included computing lunar positions on the balky, bulky computers that were state of the art in the 1950s.
But he tired of hand-coding the hardware, and in 1954 he got his bosses to let him assemble a team that could design an easier system.
The result, Fortran, short for Formula Translation, reduced the number of programming statements necessary to operate a machine by a factor of 20.
It showed sceptics that machines could run just as efficiently without hand-coding.
A wide range of programming languages and software approaches proliferated, although Fortran also evolved over the years and remains in use.
Backus remained with IBM until his retirement in 1991. Among his other important contributions was a method for describing the particular grammar of computer languages. The system is known as Backus-Naur Form.
AP
Programming language pioneer passes away
March 23, 2007

St. John's Hosts International Logic Conference,
Uniting Students with Preeminent Mathematicians

www.stjohns.edu
March 20, 2007
Though most of us consider the computer to be a 20th century invention, the concept of computer software distilled throughout the 19th century, as a rise of mathematicians began grappling with modern theories of mathematical logic.
Last weekend, the youngest generation of this small and supremely gifted group of thinkers gathered for the second international New York Graduate Student Logic Conference, co-sponsored by the St. John's Department of Mathematics and hosted on the University's Manhattan campus, in the heart of TriBeCa. The two-day conference, co-organized by Rehana Patel, Ph.D., Assistant Professor of Mathematics and Computer Science, debuted two years ago at St. Francis College in Brooklyn.
Participants at the event broached such heavily esoteric subjects such as epistemology, isomorphic structures, transfinite set theories and algorithmic randomness. Confusing subjects, yes, but according to conference leaders, their applications impact the lives of every Average Joe who's ever done online banking.
"Logic is a subject with an Ancient pedigree — it dates back to the Greeks — but it's got this whole new dimension to it thanks to computer science," said Patel, who specializes in a branch of mathematical logic called model theory. "So, suddenly, this very theoretical subject has come to have these incredible applications." "All the software applications you could possibly imagine are done by logic," added Mirna Dzamonja, Reader of Math for the University of East Anglia (England) and an Advanced Fellow for the Engineering and Physical Sciences Research Council, during the conference. "There is no programming without it."
Student Spotlight
Unlike traditional academic conferences, which typically spotlight tenured professors and other veteran scholars, last weekend's event focused primarily on a select group of accomplished Ph.D. students. The student-centered approach was intentionally crafted by Patel and her co-organizer Erez Shochat, Assistant Professor of Mathematics at St. Francis, who both emphasized how important it was in the early stages of their own mathematical careers to receive feedback from higher-level peers.
"We think it's important that graduate students receive proper exposure in the field," said Patel, noting that the St. John's mission has always demanded a student-first approach. "We in the field of logic are a very small community, and people tend to be very encouraging to young researchers. So we invited a handful of eminent scholars — some of the best people in the subject from around the world — to these talks and make a point of introducing these senior faculty to students who study within similar areas."
The scholars to which Patel referred are indeed some of the highest ranking in their respective fields. They include Dzamonja, Martin Davis, Professor Emeritus at New York University, famed for his contributions to solving one of the "Hilbert problems"; Edward Nelson, Professor of Mathematics at Princeton University and inventor of a special approach to math logic called "Internal Set Theory"; Gregory Cherlin, Professor of Mathematics at Rutgers University who has published about 90 papers and books and lectured to the International Congress of Mathematicians; and Joseph Dauben, Distinguished Professor of History and History of Science and head of the Ph.D. history program for The City University of New York.
But despite their extraordinary accomplishments, this prodigious group of scholars all seemed to agree that the conference, much like the future of math logic, was not about them; it was about their younger colleagues.
"The students presenting their work [at this conference] represent the next generation of logicians," said Dauben before the conference opened. "[Thus], the chances of finding the next great contributors to the field are very high."
"Much of the state-of-the-art knowledge transfer in mathematical logic happens at conferences, [but] it's not very often that graduate students actually get to present their research at any length," added Dzamonja, lauding the efforts of conference organizers.
Rodrigo Peláz, a doctoral student from the Universitat de Barcelona who delivered a lecture on a mathematical approach called G-Compact Theory, echoed the praise of his senior peers. "It's a very enriching opportunity for us Ph.D. students to exchange ideas," he said, adding, "This is a really good conference compared to others, because we students can practice giving talks to a very high-level audience, which is very important for us."
The idea of a New York logic conference sprouted in 2003, during the weekly mathematical logic seminars that Patel and Shochat attended at the CUNY Graduate Center. Inspired by the large number of logicians in the New York area, the two professors enlisted the co-sponsorship of the Mid-Atlantic Mathematical Logic Seminar (a traveling conference funded by the National Science Foundation), and organized the inaugural conference at St. Francis in 2004.
"New York has such a vibrant group of people in logic," said Patel, emphasizing the proud metropolitan identity of St. John's. "So a conference like this is just good for the future of logic in the city."
St. John's Hosts International Logic Conference, Uniting Students with Preeminent Mathematicians
March 23, 2007

Mathematics Awareness Week Held at UVSC

newsnet.byu.edu
By Brittanie Morris - 19 Mar 2007
Utah Valley State College will host its second annual Mathematics Awareness Week this week in preparation for annual nationwide Mathematics Awareness Month in April.
According to a new release, the week is designed to promote awareness among faculty and students of the importance and role of mathematics in everyday life. "It's something we've wanted to do for a long time," said Kathryn Van Wagoner, manager of Math Tutorial Services at UVSC. "Math Awareness Week is held on college campuses across the country."
UVSC's Math Awareness Week will feature keynote speaker Roland Steadham, chief meteorologist at KUTV. He will speak Tuesday on "Boots? Or Flip Flops? Discovering the Wacky World of TV Weather Forecasting and its Connection to Math."
The week will also feature a power-testing workshop, which will teach success strategies for math tests, a factoring bee for those who have never taken calculus, a speed chess tournament, puzzles, games and a speed Sudoku competition. Participants in the various competitions will compete for UVSC Bookstore gift certificates, as well as other prizes.
The theme for this year's Mathematics Awareness Month is "Mathematics and the Brain," a theme announced by the American Mathematical Society, the American Statistical Association, the Mathematical Association of America and the Society for Industrial and Applied Mathematics.
According to mathaware.org, the month had its beginnings in 1986 with Mathematics Awareness Week. The week was inspired by U.S. President Ronald Reagan's declaration of mathematics application as indispensable in many business and government fields. Reagan encouraged Americans to be aware of the importance of mathematic applications in their daily lives.
"There's a lot more to math than just algebra," Van Wagoner said.
Activities will be all week. Stop by the UVSC campus or contact the UVSC mathematics department for more information.
Mathematics Awareness Week Held at UVSC
March 23, 2007

Willamette Professors Receive National Mathematics Grant

www.salem-news.com
Salem-News.com
(SALEM) - Two Willamette University math professors have received a $491,400 grant from the National Science Foundation to provide an eight-week summer research experience for math students and teachers. The grant was recently awarded to Willamette assistant math Professors Inga Johnson and Colin Starr, who are the leaders of the Willamette Valley Consortium for Mathematics Research. The consortium is made up of four Oregon schools: Willamette University, Linfield College, Lewis & Clark College and the University of Portland. Each of the four schools will host a summer research team of four undergraduates, two faculty members and one teacher from the K-12 or community college level. Each team will focus on a project from faculty research interests in number theory, probability and statistics, geometry, computer science or applied analysis. All four teams will gather once a week for talks about their projects, presentations by invited speakers and social activities. Participants at Willamette will work with Johnson and Starr to study the Frobenius Problem, also known as the "postage stamp problem," a topic in number theory. The summer program is open to teachers and students nationwide. The final application deadline is April 6th, although preference will be given to applications received by March 30. To apply or learn more about the consortium, go to willamette.edu/cla/math/REU-RET.
Willamette Professors Receive National Mathematics Grant
March 23, 2007

Patterns in nature discussed

www.unlvrebelyell.com
Speaker links mathematics with nature in poetic way
By Cameron Asgarian
Last Monday, UNLV's Barrick Museum of Natural History hosted professor John A. Adam from Old Dominion University entitled, "Patterns in Nature," the lecture and slide show exhibited the numerous instances in nature where mathematical patterns appear.
From breast-shaped clouds to hexagonal shapes formed by cracks in pavement, mathematical formulae were shown to be ever-present in organic matter. The auditorium of the Barrick Museum was filled before the 7:30 p.m. start time, composed mainly of an older crowd but sprinkled with students from a wide range of majors. As Modest Mouse's "Never Ending Math Equation" played softly through the sound system before the lecture began, and Professor Adam explained he had "Monty Python in his blood," it was soon apparent that this wasn't going to be an equation-filled crash course in super-physics.
In fact, for all the natural phenomena that showed mathematical properties, the lecture was very light on concrete math explanations and heavier on poems about the beauty of nature and melodrama.
Adam opened his speech with numerous quotes from the likes of William Blake and Henri Poincaré. Already there were sniffles and cackles echoing throughout the lecture hall. Hailing from Reading, England, Adam was, from the start, not the average guest lecturer. His strategy of frequent quips and British slang kept the crowd from falling asleep but might have left the scientifically hungry unsatisfied.
The numerous slides focused mainly on rainbows and other effects caused by light passing through various forms of condensation, like the 22 degree radius ice halo, the most commonly found image, along with massive tangential arcs and "sun dogs" which form on a parallel line on the circumference of the ring. Some of the most impressive pictures featured superior mirages, and the rare-but-terrifying instances of Alexander's Dark Band, a phenomenon that occurs when there is a double rainbow and the space in between is much darker than the rest of the sky.
Light images weren't the only place where math showed its ominous head, Adam said. As a card-carrying member of the Cloud Appreciation Society, numerous slides showed several patterns in cloud-forms that exemplified mathematical theorems.
Many of the photos he had personally taken were quite beautiful. One of the major themes of Adam's unorthodox performance was that nature always uses the least amount of energy necessary, and this fact is indicative in natural patterns such as rivers meandering rather than taking a straight, harder course and the cracking patterns found in dry lake beds. This fact most completely exemplifies the existence of math in nature.
The paradoxical nature of the lecture was perhaps its finest quality. One might think that reducing the beauty of nature to mere mathematical equations, or seeing a giant multi-colored ring in the sky as just a 46 degree or 22 degree circular image, would be blasphemy. However, the fact that such beauty comprises so much concrete math only adds to the beauty and makes it more real. The beauty of nature which the opening poem by Henri Poincaré described was what inspired Adam to do his line of work, he said.
"I love my job, and to me math and nature are one and the same," Adam said.
Students attending apparently felt the same way about the subject. "I thought the lecture was interesting, and I have no doubt that patterns are present in nature," said Julia, a sophomore art major who only provided her first name. Julia said she heard of the lecture from a flyer at the Student Information Desk. "It really makes you think about intelligent design and also the cold harsh reality that is math," she added.
Patterns in nature discussed
March 23, 2007

Is Beauty Truth and Truth Beauty?

www.sciam.com
How Keats's famous line applies to math and science
By Martin Gardner

WHY BEAUTY IS TRUTH: A HISTORY OF SYMMETRY
by Ian Stewart
Basic Books, 2007

The title of Ian Stewart's book (he has written more than 60 others) is, of course, taken from the enigmatic last two lines of John Keats's "Ode on a Grecian Urn": "Beauty is truth, truth beauty,"--that is all Ye know on earth, and all ye need to know.
But what on earth did Keats mean? T. S. Eliot called the lines "meaningless" and "a serious blemish on a beautiful poem." John Simon opened a movie review with "one of the greatest problems of art--perhaps the greatest--is that truth is not beauty, beauty not truth. Nor is it all we need to know." Stewart, a distinguished mathematician at the University of Warwick in England and a former author of this magazine's Mathematical Recreations column, is concerned with how Keats's lines apply to mathematics. "Euclid alone has looked on Beauty bare," Edna St. Vincent Millay wrote. To mathematicians, great theorems and great proofs, such as Euclid's elegant proof of the infinity of primes, have about them what Bertrand Russell described as "a beauty cold and austere," akin to the beauty of great works of sculpture.
Stewart's first 10 chapters, written in his usual easygoing style, constitute a veritable history of mathematics, with an emphasis on the concept of symmetry. When you perform an operation on a mathematical object, such that after the operation it looks the same, you have uncovered a symmetry. A simple operation is rotation. No matter how you turn a tennis ball, it does not alter the ball's appearance. It is said to have rotational symmetry. Capital "H" has 180-degree rotational symmetry because it is unchanged when turned upside down. It also has mirror reflection symmetry because it looks the same in a mirror. A swastika has 90-degree rotational symmetry but lacks mirror reflection symmetry because its mirror image whirls the other way.
Associated with every kind of symmetry is a "group." Stewart explains the group concept in a simple way by considering operations on an equilateral triangle. Rotate it 60 degrees in either direction, and it looks the same. Every operation has an "inverse," that cancels the operation. Imagine the corners of the triangle labeled A, B and C. A 60-degree clockwise rotation alters the corners' positions. If this is followed by a similar rotation the other way, the original positions are restored. If you do nothing to the triangle, this is called the "identity" operation. The set of all symmetry transformations of the triangle constitutes its group.
Stewart's history begins with Babylonian and Greek mathematics, introducing their basic concepts in ways a junior high school student can understand. As his history proceeds, the math slowly becomes more technical, especially when he gets to complex numbers and their offspring, the quaternions and octonions. The history ends with the discoveries of Sophus Lie, for whom Lie groups are named, and the work of a little-known German mathematician, Joseph Killing, who classified Lie groups. Through this historical section, Stewart skillfully interweaves the math with colorful sketches of the lives of the mathematicians involved.
Not until the book's second half does Stewart turn to physics and explain how symmetry and group theory became necessary tools. A chapter on Albert Einstein is a wonderful blend of elementary relativity and details of Einstein's life. Next comes quantum mechanics and particle theory, with several pages on superstrings, the hottest topic in today's theoretical physics. Stewart is a bit skeptical of string theory, which sees all fundamental particles as inconceivably tiny filaments of vibrating energy that can be open-ended or closed like a rubber band. He does not mention two recent books (reviewed in the September 2006 issue of Scientific American) that give string theory a severe bashing. Lee Smolin's The Trouble with Physics denounces string theory as "not a theory at all," only a mishmash of bizarre speculations in search of a viable theory. Peter Woit's book is entitled Not Even Wrong, a quote from the great Austrian physicist Wolfgang Pauli. He once described a theory as so bad it was "not even wrong."
Is string theory beautiful? Its promoters think so. Smolin and Woit believe that its recent absorption into a richer conjecture called M-theory has turned the former beauty of strings into mathematical structures as ugly as the epicycles Ptolemy invented to explain the orbits of planets as they circle the earth.
We are back to the mystery of Keats's notorious lines. In my opinion, John Simon is right. Even beautiful mathematical proofs can be wrong. In 1879 Sir Alfred Kempe published a proof of the four-color map theorem. It was so elegant that for 10 years it was accepted as sound. Alas, it was not. Henry Dude­ney, England's great puzzle maker, published a much shorter and even prettier false proof.
In The New Ambidextrous Universe I write about the vortex theory of atoms. This popular 19th-century conjecture had an uncanny resemblance to superstrings. It maintained that atoms are not pointlike but are incredibly tiny loops of energy that vibrate at different frequencies. They are minute whirlpools in the ether, a rigid, frictionless substance then believed to permeate all space. The atoms have the structure of knots and links, their shapes and vibrations generating the properties of all the elements. Once created by the Almighty, they last forever.
In researching vortex theory, I came across many statements by eminent physicists, including Lord Kelvin and James Clerk Maxwell, suggesting that vortex theory was far too beautiful not to be true. Papers on the topic proliferated, books about it were published. Scottish mathematician Peter Tait's work on vortex atoms led to advances in knot theory. Tait predicted it would take several generations to develop the theory's mathematical foundations. Beautiful though it seemed, the vortex theory proved to be a glorious road that led nowhere.
Stewart concludes his book with two maxims. The first: "In physics, beauty does not automatically ensure truth, but it helps." The second: "In mathematics beauty must be true--because anything false is ugly." I agree with the first statement, but not the second. We have seen how lovely proofs by Kempe and Dudeney were flawed. Moreover, there are simply stated theorems for which ugly proofs may be the only ones possible.
Let me cite two recent examples. Proof of the four-color map theorem required a computer printout so vast and dense that it could be checked only by other computer programs. Although there may be a beautiful proof recorded in what Paul Erdös called "God's book"--a book that, he suggested, included all the theorems of mathematics and their most beautiful proofs--it is possible that God's book contains no such proof. The same goes for Andrew Wiles's proof of Fermat's last theorem. It is not computer-based, but it is much too long and complicated to be called beautiful. There may be no beautiful proof for this theorem. Of course, mathematicians can always hope and believe otherwise.
Because symmetry is the glue and tape that binds the pages of Stewart's admirable history, a stanza from Lewis Carroll's immortal nonsense ballad The Hunting of the Snark could serve as an epigraph for the book:
You boil it in sawdust: you salt it in glue:
You condense it with locusts and tape:
Still keeping one principal object in view--
To preserve its symmetrical shape.

Martin Gardner wrote Scientific American's Mathematical Games column for 25 years. His latest book, The Annotated Hunting of the Snark, was published last year by W. W. Norton.
Is Beauty Truth and Truth Beauty?

March 23, 2007

Brits expose warming con

www.contracostatimes.com
THOMAS SOWELL: SYNDICATED COLUMNIST
BRITAIN'S CHANNEL 4 has produced a devastating documentary titled "The Great Global Warming Swindle." It has not been broadcast by any U.S. networks. But fortunately it is available on the Internet.
Distinguished scientists specializing in climate and climate-related fields talk in plain English and present readily understood graphs showing what a crock the global warming hysteria is.
These include scientists from MIT and top-tier universities in a number of countries. Some of these are scientists whose names were paraded on some of the global warming publications that are being promoted in the media -- but who state plainly that they neither wrote nor approved them. One threatened to sue unless his name was removed.
Although the public has been led to believe that "all" the leading scientists buy the global warming hysteria and the political agenda that goes with it, in fact the official reports from the United Nations or the National Academy of Sciences are written by bureaucrats -- and then garnished with the names of leading scientists who were "consulted" but whose contrary conclusions have been ignored.
There is no question that the globe is warming but it has warmed and cooled before and is not as warm today as it was centuries ago, before there were any automobiles and before there was as much burning of fossil fuels as today.
None of today's dire predictions happened then.
The British documentary goes into some of the many factors that have caused the Earth to warm and cool for centuries, including changes in activities on the sun, 93 million miles away.
According to these climate scientists, human activities have little effect on the climate compared with many other factors, from volcanoes to clouds.
These climate scientists debunk the mathematical models that have been used to hype global warming hysteria, even though hard evidence stretching back over centuries contradicts these models.
What is even scarier than seeing how easily the public, the media and politicians have been manipulated and stampeded is discovering how much effort has been put into silencing scientists who dare to say that the emperor has no clothes.
Academics who jump on the bandwagon are far more likely to get big research grants than those who express doubts -- and research is the lifeblood of an academic career.
Environmental movements around the world are committed to global warming hysteria, and nowhere more so than on college and university campuses, where they can harass those who say otherwise. One of the scientists interviewed on the British documentary reported getting death threats.
Even conservative Republicans seem to have taken the view that if you can't lick 'em, join 'em. So have big corporations, which have joined the stampede. This enables green crusaders to declare that "everybody" believes the global warming scenario, except for a scattered few "deniers" who are likened to Holocaust deniers.
The difference is that we have the hardest and most painful evidence that there was a Holocaust. But for the global warming scenario, we have only a movie made by a politician and mathematical models whose results change drastically when you change a few of the arbitrary variables.
No one denies that temperatures are a degree warmer than a century ago. What the scientists in this documentary deny is that you can mindlessly extrapolate that, or that we are headed for a climate catastrophe if we don't take drastic steps that could cause an economic one.
"Global warming" is just the latest hysterical crusade to which we seem to be increasingly susceptible.

Sowell is a senior fellow at the Hoover Institution, Stanford University.
Brits expose warming con

March 16, 2007

Mathematician, alumnus Wilkins honored for inspirational, scientific achievements

chronicle.uchicago.edu
Ernest Wilkins
Members of the University community recently honored alumnus J. Ernest Wilkins Jr. (above) at a reception,
where Dean Robert Fefferman, Deputy Provost Kenneth Warren,
the Fairfax M. Cone Distinguished Service Professor in English Language & Literature and the College,
and University Trustee Walter Massey
spoke about Wilkins' accomplishments as a mathematician and scientist.
Wilkins completed his Ph.D. at Chicago in Mathematics in 1942 at age 19.
By Steve Koppes
News Office
On a recent snowy March afternoon in the Eckhart Hall Tea Room, J. Ernest Wilkins Jr. officially took his place among the University's pantheon of legendary scientists and mathematicians. Wilkins' portrait and a plaque in his honor were officially unveiled at a reception on Friday, March 2.
"Growing up reading about your achievements was an inspiration," University Trustee Walter Massey told Wilkins at the ceremony. Wilkins' diverse body of work means that researchers in multiple fields can lay claim to it, added Massey, a physicist and the president of Morehouse College in Atlanta.
Wilkins enrolled at the University at the age of 13 in 1936. At age 17, he received his A.B. in mathematics and ranked in the top 10 in the Putnam Competition, a national undergraduate mathematics contest. Wilkins remained at the University for graduate study in mathematics, receiving his Ph.D. as a 19-year-old in 1942. "The University of Chicago Mathematics Department has extremely high standards. It's been an outstanding department for quite some time," said Robert Fefferman, Dean of the Physical Sciences Division and the Max Mason Distinguished Service Professor in Mathematics and the College. "It's extraordinary for someone 19 years old to get a Ph.D. from a department of that quality in a very rigorous subject."
Wilkins, 83, was born in Chicago to J. Ernest Wilkins Sr., a lawyer who served as U.S. Assistant Secretary of Labor from 1954 to 1958, and Lucile Robinson Wilkins, a teacher. Among his many achievements, the younger Wilkins in 1976 became the second African American to be elected to the National Academy of Engineering, one of the highest honors an engineer can receive.
Early in his career, Wilkins worked at Chicago on the Manhattan Project, the U.S. effort to build the atomic bomb. While here, he worked with future Nobel laureate Eugene Wigner and made contributions to nuclear-reactor physics, including what is now known as the Wilkins effect and the Wigner-Wilkins spectrum.
Wilkins also attained distinction in the private sector. Following the Manhattan Project, he worked as a mathematician for the American Optical Company in Buffalo, N.Y., designing lenses for microscopes and ophthalmologic uses. He held a variety of positions at the United Nuclear Corporation from 1950 to 1960. As manager of United Nuclear's Research and Development Division, Wilkins oversaw a staff of approximately 30 scientists who did contract work for the Atomic Energy Commission.
During this time, he entered New York University to obtain formal training as a mechanical engineer. There he earned a B.S., with magna cum laude honors, in 1957 and another master's degree in 1960. For the next 10 years, he managed additional nuclear-reactor projects for the General Atomic Company in San Diego.
He took a sabbatical leave in 1976 to become a visiting scientist at Argonne National Laboratory. From there, he became a vice president at EG and G Idaho Inc., in Idaho. Wilkins returned to Argonne as a Distinguished Fellow in 1984.
At various stages of his career, Wilkins taught at the Tuskegee Institute in Alabama, Howard University in Washington, D.C., and Clark Atlanta University in Georgia.
"He is such a fabulous role model that his example should encourage brilliant African-American mathematics and science faculty members and students to choose Chicago as their academic home," Fefferman said.
The history of the physical sciences at the University is rife with significant contributions from individuals of widely diverse backgrounds. Just two examples include Alberto Calderón of Argentina and theoretical astrophysicist Subrahmanyan Chandrasekhar of India. They were two of the most influential thinkers in their fields during the 20th century, Fefferman said.
Without such people, "this would be a very different university in math and science," Fefferman said.
"We would probably be lucky to be in the top hundred science universities in the United States, maybe even in the top 200. It's just so absurd not to welcome everyone who wants to participate in what I consider a very compelling and noble adventure, discovering great science."
Mathematician, alumnus Wilkins honored for inspirational, scientific achievements
March 16, 2007

Pi Day celebrated

www.nature.com
Mathematophiles of all ages enjoyed this year's ode to pi.
Heidi Ledford
What is it that draws hundreds of visitors to San Francisco's Exploratorium every March to celebrate Pi Day? The allure of the unknowable? The draw of a mathematical mystery? Sure, all of that, said several participants at yesterday's event, but also the free pie.
Pi Day is celebrated on 14 March — written in the United States as 3-14, the first three digits of pi — at locales around the world. But the celebration at the Exploratorium, a hands-on science museum a stone's throw away from the Golden Gate Bridge, was the first. Maybe.
Pi Day started in 1987 or 1988, but even the originators can't quite remember when. "The origins of Pi Day are shrouded in the mystery of the 1980s," says Ron Hipschman, physicist and Exploratorium exhibit designer, who has helped design the Pi Day celebrations from year one... whenever that was.
And was the Exploratorium the first to celebrate Pi Day? Hipschman shrugs. "That's what it said in Wikipedia," he says, "so it must be true, right?"
Larry Shaw, the wild-haired official Exploratorium Pi Day founder, says the adventure began at a staff retreat, when Shaw started chatting to his co-workers about the mysteries of mathematical constants. "There are anomalies that are just curious, and pi and e are two of those," he says (with 'e' roughly equal to 2.7, Nature suggests 2 July for e-day, although there is no obvious snack to partake in).
"Nobody has a universal view of these numbers, and that leaves an opening for the imagination." Kids are good for that, Shaw notes, as he nods his head towards the dazzling brownian motion of children bouncing around the exhibit hall.
Pie and pi-ku
The first Pi Day was straightforward — the staff of the Exploratorium ordered pies; the staff of the Exploratorium ate pies. The other embellishments came later. The Pi Shrine, for example — a round disk with digits winding around its edge embedded into the carpet on the second floor — didn't exist until 1989. This year's Pi Day included: pi poetry readings, pi-kus (haikus about pi) and pi limericks; a pizza-dough tossing lesson; a demonstration of Pi Day in the virtual-reality game, Second Life; and, an unofficial prerequisite for Pi Days nearly everywhere, free pizza (as in 'pizza pie') and pie.
Promptly at 1:59 — that is, 3-14 1:59, the first six digits of pi — Shaw turns on a recording of a sing-songy computerized voice reading the digits of pi, and leads a march of Pi Day celebrants past the steam-engine display, with a left turn past the soap film exhibit, a swing around the corner at the coloured shadows demonstration, and a final ascent up the stairs to the Pi Shrine. There, celebrants sang Happy Birthday to Albert Einstein, who, incidentally, turned 128 on this year's Pi Day.
Not just for kids
First in line after Shaw is 13-year-old Paul Rapoport, who spent years needling his mother before she finally agreed to let him make the trip from New York to San Francisco just to attend Pi Day. "She didn't want to come," he says. "I had to drag her." Rapoport is in the eighth grade but teaches himself a little calculus on the side, just for kicks. When asked whether Paul is likely to want to return to the Pi Day celebration next year, his mother rolls her eyes and winces. "I think he wants to run it," she says.
After circling the shrine, many of the celebrants return to their position in the line for free pizza. "My favourite part of Pi Day hasn't yet begun," says one, with a longing glance across the hall to where Exploratorium workers are racing to set up the free pie line.
Others stopped by a downstairs theatre to watch students from Bridge College Prep School in nearby Oakland, California, recount as many digits of pi as they could remember. Eighth grader Dakarai Lewis, who can recite 134 digits, rattles off the first few dozen digits, pauses, rattles off another couple of dozen, pauses, and finally completes his run to a round of wild applause and whoops from the audience.
Standing in the audience is 91-year-old James Stichka. Stichka, who graduated with a degree in maths from the University of California, Berkeley, in 1938, heard about Pi Day on Monday and immediately made plans to attend. "I want to meet all these kooks like me," he says with a smile. He's wearing a cardboard sign around his neck entitled "The sequence of pi" that lists a series of pie flavours, beginning with lemon meringue.
Onwards to July
A little while later, there's a performance of a surprisingly good Einstein rap, performed by an Einstein puppet and two Exploratorium workers in white lab coats. Then the show's over, and the crowd begins to wander away while "When the Moon hits your eye / like a big pizza pie / that's amore" plays over the sound system and film clips of people getting pied continues to loop on the monitors. The Exploratorium settles back down to the normal background buzz of the museum: the pop and whir of the bicycle simulator, the occasional child's yelp or squeal. Pi Day is over.
"We'll be back again next year," says Dennis Vozaitis of Milano Pizzeria, who ran dough-tossing demonstrations during the afternoon. "Everybody had so much fun."
Before then, of course, there is Pi Approximation Day to look forward to: 22 July (as Pi can be closely approximated by dividing 22 by 7). It may not be serious, but it is a good excuse for a party.
Pi Day celebrated
March 16, 2007

Noted Mathematicians from Top Universities Across the Nation and Europe to Lecture

www.stjohns.edu
The St. John's University Manhattan Campus (101 Murray Street) will be the host site for the Second New York Graduate Student Logic Conference, March 17-18, 2007. The conference is organized by Rehana Patel, Assistant Professor of Mathematics and Computer Science at St. John's University and Erez Shochat, Assistant Professor of Mathematics at St. Francis College.
Conference participants are also invited to a special pre-conference event on Friday, March 16 at the CUNY Graduate Center in midtown Manhattan (365 Fifth Avenue at 34th Street). There is no pre-registration for the conference. However, participants are advised that they will need to show photo ID to enter both St. John's University and the CUNY Graduate Center.
The goal of the conference is to promote graduate education in logic by bringing together the best graduate students working in the field of mathematical logic today. The event is sponsored by the National Science Foundation through the Mid-Atlantic Mathematical Logic Seminar (MAMLS), St. John's University and by the City University of New York through a Collaborative Incentive Grant.
The conference has assembled the brightest minds in mathematical logic and gives working graduate students in the field a chance to interact and share ideas with top senior logicians in the country. A timeline of lectures, biographies of all guest speakers and subject matter to be discussed during the two-day event can be found by visiting the conference web site at http://nylogic.org/GradStudentConference/StJohns2007. Open to all students free of charge, MAMLS offers a $35 flat reimbursement to all students that participate at its conferences. Additional funding may also be available for those students coming from outside the New York Metropolitan Area.
For information contact Rehana Patel at (718) 990-2021 or e-mail inquiries to patelr@stjohns.edu. Interested Media representatives can contact Dominic Scianna, Director of Media Relations at (718) 990-6185 or e-mail requests to sciannad@stjohns.edu.
Noted Mathematicians from Top Universities Across the Nation and Europe to Lecture
March 13, 2007

Journeys to the Distant Fields of Prime

www.nytimes.com
Terence Tao
Terence Tao, 31, is one of the world's top mathematicians.
By KENNETH CHANG
Published: March 13, 2007
LOS ANGELES —Four hundred people packed into an auditorium at U.C.L.A. in January to listen to a public lecture on prime numbers, one of the rare occasions that the topic has drawn a standing-room-only audience.
Another 35 people watched on a video screen in a classroom next door. Eighty people were turned away.
The speaker, Terence Tao, a professor of mathematics at the university, promised "a whirlwind tour, the equivalent to going through Paris and just seeing the Eiffel Tower and the Arc de Triomphe."
His words were polite, unassuming and tinged with the accent of Australia, his homeland. Even though prime numbers have been studied for 2,000 years, "There's still a lot that needs to be done," Dr. Tao said. "And it's still a very exciting field."
After Dr. Tao finished his one-hour talk, which was broadcast live on the Internet, several students came down to the front and asked for autographs.
Dr. Tao has drawn attention and curiosity throughout his life for his prodigious abilities. By age 2, he had learned to read. At 9, he attended college math classes. At 20, he finished his Ph.D.
Now 31, he has grown from prodigy to one of the world's top mathematicians, tackling an unusually broad range of problems, including ones involving prime numbers and the compression of images. Last summer, he won a Fields Medal, often considered the Nobel Prize of mathematics, and a MacArthur Fellowship, the "genius" award that comes with a half-million dollars and no strings.
"He's wonderful," said Charles Fefferman of Princeton University, himself a former child prodigy and a Fields Medalist. "He's as good as they come. There are a few in a generation, and he's one of the few."
Colleagues have teasingly called Dr. Tao a rock star and the Mozart of Math. Two museums in Australia have requested his photograph for their permanent exhibits. And he was a finalist for the 2007 Australian of the Year award.
"You start getting famous for being famous," Dr. Tao said. "The Paris Hilton effect."
Not that any of that has noticeably affected him. His campus office is adorned with a poster of "Ranma ½," a Japanese comic book. As he walks the halls of the math building, he might be wearing an Adidas sweatshirt, blue jeans and scruffy sneakers, looking much like one of his graduate students. He said he did not know how he would spend the MacArthur money, though he mentioned the mortgage on the house that he and his wife, Laura, an engineer at the NASA Jet Propulsion Laboratory, bought last year.
After a childhood in Adelaide, Australia, and graduate school at Princeton, Dr. Tao has settled into sunny Southern California.
"I love it a lot," he said. But not necessarily for what the area offers.
"It's sort of the absence of things I like," he said. No snow to shovel, for instance.
A deluge of media attention following his Fields Medal last summer has slowed to a trickle, and Dr. Tao said he was happy that his fame might be fleeting so that he could again concentrate on math.
One area of his research — compressed sensing — could have real-world use. Digital cameras use millions of sensors to record an image, and then a computer chip in the camera compresses the data.
"Compressed sensing is a different strategy," Dr. Tao said. "You also compress the data, but you try to do it in a very dumb way, one that doesn't require much computer power at the sensor end."
With Emmanuel Candès, a professor of applied and computational mathematics at the California Institute of Technology, Dr. Tao showed that even if most of the information were immediately discarded, the use of powerful algorithms could still reconstruct the original image.
By useful coincidence, Dr. Tao's son, William, and Dr. Candès's son attended the same preschool, so dropping off their children turned into useful work time. "We'd meet each other every morning at preschool," Dr. Tao said, "and we'd catch up on what we had done."
The military is interested in using the work for reconnaissance: blanket a battlefield with simple, cheap cameras that might each record a single pixel of data. Each camera would transmit the data to a central computer that, using the mathematical technique developed by Dr. Tao and Dr. Candès, would construct a comprehensive view. Engineers at Rice University have made a prototype of just such a camera.
Dr. Tao's best-known mathematical work involves prime numbers — positive whole numbers that can be divided evenly only by themselves and 1. The first few prime numbers are 2, 3, 5, 7, 11 and 13 (1 is excluded).
As numbers get larger, prime numbers become sparser, but the Greek mathematician Euclid proved sometime around 300 B.C. that there is nonetheless an infinite number of primes.
Many questions about prime numbers continue to elude answers. Euclid also believed that there was an infinite number of "twin primes" — pairs of prime numbers separated by 2, like 3 and 5 or 11 and 13 — but he was unable to prove his conjecture. Nor has anyone else in the succeeding 2,300 years.
A larger unknown question is whether hidden patterns exist in the sequence of prime numbers or whether they appear randomly.
In 2004, Dr. Tao, along with Ben Green, a mathematician now at the University of Cambridge in England, solved a problem related to the Twin Prime Conjecture by looking at prime number progressions — series of numbers equally spaced. (For example, 3, 7 and 11 constitute a progression of prime numbers with a spacing of 4; the next number in the sequence, 15, is not prime.) Dr. Tao and Dr. Green proved that it is always possible to find, somewhere in the infinity of integers, a progression of prime numbers of any length.
"Terry has a style that very few have," Dr. Fefferman said. "When he solves the problem, you think to yourself, 'This is so obvious and why didn't I see it? Why didn't the 100 distinguished people who thought about this before not think of it?' "
Dr. Tao's proficiency with numbers appeared at a very young age. "I always liked numbers," he said.
A 2-year-old Terry Tao used toy blocks to show older children how to count. He was quick with language and used the blocks to spell words like "dog" and "cat." "He probably was quietly learning these things from watching 'Sesame Street,' " said his father, Dr. Billy Tao, a pediatrician who immigrated to Australia from Hong Kong in 1972. "We basically used 'Sesame Street' as a babysitter."
The blocks had been bought as toys, not learning tools. "You expect them to throw them around," said the elder Dr. Tao, whose accent swings between Australian and Chinese.
Terry's parents placed him in a private school when he was 3 ½. They pulled him out six weeks later because he was not ready to spend that much time in a classroom, and the teacher was not ready to teach someone like him.
At age 5, he was enrolled in a public school, and his parents, administrators and teachers set up an individualized program for him. He proceeded through each subject at his own pace, quickly accelerating through several grades in math and science while remaining closer to his age group in other subjects. In English classes, for instance, he became flustered when he had to write essays.
"I never really got the hang of that," he said. "These very vague, undefined questions. I always liked situations where there were very clear rules of what to do." Assigned to write a story about what was going on at home, Terry went from room to room and made detailed lists of the contents.
When he was 7 ½, he began attending math classes at the local high school.
Billy Tao knew the trajectories of child prodigies like Jay Luo, who graduated with a mathematics degree from Boise State University in 1982 at the age of 12, but who has since vanished from the world of mathematics.
"I initially thought Terry would be just like one of them, to graduate as early as possible," he said. But after talking to experts on education for gifted children, he changed his mind.
"To get a degree at a young age, to be a record-breaker, means nothing," he said. "I had a pyramid model of knowledge, that is, a very broad base and then the pyramid can go higher. If you just very quickly move up like a column, then you're more likely to wobble at the top and then collapse."
Billy Tao also arranged for math professors to mentor Terry.
A couple of years later, Terry was taking university-level math and physics classes. He excelled in international math competitions. His parents decided not to push him into college full time, so he split his time between high school and Flinders University, the local university in Adelaide. He finally enrolled as a full-time college student at Flinders when he was 14, two years after he would have graduated had his parents pushed him only according to his academic abilities.
The Taos had different challenges in raising their other two sons, although all three excelled in math. Trevor, two years younger than Terry, is autistic with top-level chess skills and the musical savant gift to play back on the piano a musical piece — even one played by an entire orchestra — after hearing it just once. He completed a Ph.D. in mathematics and now works for the Defense Science and Technology Organization in Australia.
The youngest, Nigel, told his father that he was "not another Terry," and his parents let him learn at a less accelerated pace. Nigel, with degrees in economics, math and computer science, now works as a computer engineer for Google Australia.
"All along, we tend to emphasize the joy of learning," Billy Tao said. "The fun is doing something, not winning something."
Terry completed his undergraduate degree in two years, earned a master's degree a year after that, then moved to Princeton for his doctoral studies. While he said he never felt out of place in a class of much older students, Princeton was where he finally felt he fit among a group of peers. He was still younger, but was not necessarily the brightest student all the time.
His attitude toward math also matured. Until then, math had been competitions, problem sets, exams. "That's more like a sprint," he said.
Dr. Tao recalled that as a child, "I remember having this vague idea that what mathematicians did was that, some authority, someone gave them problems to solve and they just sort of solved them."
In the real academic world, "Math research is more like a marathon," he said.
As a parent and a professor, Dr. Tao now has to think about how to teach math in addition to learning it.
An evening snack provided him an opportunity to question his son, who is 4. If there are 10 cookies, how many does each of the five people in the living room get? William asked his father to tell him. "I don't know how many," Dr. Tao replied. "You tell me."
With a little more prodding, William divided the cookies into five stacks of two each.
Dr. Tao said a future project would be to try to teach more non-mathematicians how to think mathematically — a skill that would be useful in everyday tasks like comparing mortgages.
"I believe you can teach this to almost anybody," he said.
But for now, his research is where his focus is.
"In many ways, my work is my hobby," he said. "I always wanted to learn another language, but that's not going to happen for a while. Those things can wait."

Correction: March 13, 2007
A profile of Terence Tao, a world-renowned mathematician, in Science Times yesterday referred incorrectly to work he did with another mathematician on prime numbers. They proved that it is always possible to find, somewhere in the infinity of integers, a progression of any length of equally spaced prime numbers — not a progression of prime numbers of any spacing and any length.

Journeys to the Distant Fields of Prime

March 13, 2007

Functional Family: Mock theta mystery solved

www.sciencenews.org
Erica Klarreich
A pair of mathematicians has solved a problem that had tantalized number-theory researchers for more than 8 decades. It is the so-called final problem of the legendary Indian mathematical genius Srinivasa Ramanujan.
In the years before his death in 1920, Ramanujan studied theta functions, which are numerical relationships that show special symmetries. On his deathbed, Ramanujan wrote a letter to his British collaborator G. H. Hardy, in which he listed 17 complicated formulas for new functions. He called them mock theta functions because they had some properties similar to those of theta functions.
The first few pages of Ramanujan's letter were lost, and the surviving portion gives little indication of why Ramanujan grouped these functions. Since that time, the mock theta functions have cropped up in a surprising array of fields, including number theory, probability theory, and statistical mechanics. Yet mathematicians have puzzled over just what the 17 mock theta functions have in common.
"The mock theta functions are like beautiful butterflies that Ramanujan happened to find," says Freeman Dyson, an emeritus professor at the Institute for Advanced Study in Princeton, N.J. "But if you're a scientist, you want more—you want a theory of evolution, a framework of ideas to fit the butterflies in."
Now, Ken Ono and Kathrin Bringmann, mathematicians at the University of Wisconsin–Madison, have supplied that theory. They figured out a definition of mock theta functions that covers all of Ramanujan's examples and shows how to build infinitely more such functions.
"I didn't really hope to see someone actually do this," says George Andrews of Pennsylvania State University in University Park, who had called the description of the mock theta functions one of the hardest math problems for the new millennium. Ono and Bringmann's accomplishment is "absolutely stunning," he concludes.
The reason that mathematicians have had trouble figuring out what the mock theta functions are, Ono says, is that in a certain sense, the functions are missing a piece. Building on 2002 work by Dutch mathematician Sander Zwegers, then at Utrecht University, Ono and Bringmann have shown that when certain functions are added to each of the mock theta functions, the results are highly symmetric expressions known as harmonic Maass forms.
The researchers report their findings in the March 6 Proceedings of the National Academy of Sciences. In two additional papers, they use their theory to prove longstanding conjectures about properties of the mock theta functions.
The new theory is likely to be valuable in many fields, Andrews says. "Whenever a mathematical subject is developed deeply, applications seem to crawl out of the woodwork," he notes.
The new work relies on contemporary mathematics that could not have been known to Ramanujan, says Bruce Berndt of the University of Illinois at Urbana-Champaign. "The task still remains to figure out what Ramanujan's ideas were," he says. "He had a viewpoint which we are still missing."
Functional Family: Mock theta mystery solved
March 13, 2007

Hepburn Fellow Karen Stephenson Brings "Mathematical Magic" to Education Reform

www.brynmawr.edu
Karen Stephenson
Karen Stephenson

Thanks to the Katharine Houghton Hepburn Center, a pair of Bryn Mawr seniors are learning from a master how mathematics can illuminate the complex human interactions that make or break a school system. Huong Huynh '07 and Priscilla Won '07 are acting as interns to Hepburn Fellow Karen Stephenson in a project that applies Stephenson's innovative, math-based technique called Social Network Analysis (SNA) to two Philadelphia-area school districts.
The study is partially underwritten by the Math and Science Partnership of Greater Philadelphia (MSPGP), a National Science Foundation-funded education-reform project of which Bryn Mawr Professor of Mathematics Victor Donnay is a principal investigator. Donnay and Stephenson hope eventually to expand the study to include many of the 46 school districts and 13 colleges and universities that belong to MSPGP, in a project Stephenson likens to clinical trials of the effectiveness of SNA in an educational setting.
Stephenson, the founder and CEO of the management-consulting firm Netform, Inc., is a corporate anthropologist who exemplifies the Hepburn Center's characterization of Hepburn Fellows as "individuals who bridge academics and practice in nontraditional or unconventional ways." As an undergraduate, she majored in chemistry and art. After a brief career as a professional artist, she entered a graduate program in quantum chemistry at the University of Utah.
"I spent three years there doing heavy-duty math, and I also managed a laboratory to support myself," she says. "One day, as I stood on the mezzanine level of the lab, I saw repeating patterns of interaction among the lab personnel that were not unlike the patterns of interaction among particles that we described in quantum chemistry." Stephenson began looking for ways to apply the sort of computational modeling she had employed in chemistry to the phenomena of human interaction and communication — and, she says, transferred from the chemistry program "on a hunch" to study anthropology.
After earning a master's degree in anthropology, she found herself in Cambridge, Mass., where her then-husband had an appointment at Harvard, and she enrolled in a graduate anthropology course. Her paper for the course outlined an algorithm for mathematically inferring ancient trade routes, and it so impressed the professor that she was invited to join Harvard's Ph.D. program in anthropology. According to Stephenson, the department was reluctant to authorize her dissertation proposal, which involved investigating a corporate culture.
"It just wasn't done," she says. "They had to be convinced that a corporation had a culture worth studying. But all organizations have cultures," she says, "and they all have associated strengths and pathologies."
In the end, Stephenson prevailed. The innovative high-tech company she chose as a research subject had been rejecting requests to conduct a case study from Harvard's business school for years, she says. But a co-founder of the company who had been a friend of Margaret Mead was more sympathetic to an appeal from an anthropologist, and her department relented when offered a plum long denied to the business school. Stephenson deadpans: "It's always heartwarming when one vice trumps another."
The story is an apt illustration of the power of the structures Stephenson analyzes — social networks that are invisible on organizational charts and transcend divisions like disciplinary boundaries. The fact that critical lines of communication rarely conform to formal hierarchies is hardly unique to Stephenson, of course, but the mathematical rigor with which she studies informal social networks may be.
The algorithm that Stephenson began to develop for her dissertation has been improved, Stephenson says, by years of research on hundreds of organizations. "A physician knows what normal, healthy blood looks like because they've done a whole lot of blood tests. I know what a healthy corporate culture looks like because I am sitting on the world's largest social-network database. I have more than 400 case studies. Certain patterns always emerge from the data. Some of them are impossible to see just by looking at a map of connections — you have to do the math to find them."
Stephenson has taught at the UCLA Anderson Graduate School of Management and the Harvard University School of Design; she now lectures at the Rotterdam School of Management at Erasmus University. Her company, Netform Inc., lists Merrill Lynch, Saatchi and Saatchi, International Paper, the National Institutes of Health and the Defense Advanced Research Projects Agency among its clients. She has recently done work for the National Education Association and is interested in applying her techniques to education. That, says Bryn Mawr's Donnay, made her a perfect fit for MSPGP.
"We've long had what we call an 'infection theory' of educational reform — that people become excited about reform and adopt new practices when they are introduced to them by someone they trust," he says. "So we've been trying to identify 'connectors.' I had heard about Karen's work with the Philadelphia Connectors project, and I was very excited when I learned that she would be a Hepburn Fellow. When we discovered this common interest, we invited school-district administrators to a presentation and solicited participants for a pilot project."
Stephenson, accompanied by Donnay and his students, has visited the school districts to deliver presentations about the nature of the project and to collect survey data.
"The survey asks people a series of questions about their interactions with other people," Huynh explains. "For instance, 'If you have a great idea, whom do you tell? Who gives you advice about career strategies? Who talks to you every day?'" Stephenson, she says, has created computer programs that "do all the mathematical magic" and identify key actors in several different kinds of information networks.
Huynh and Won are assisting Stephenson with the analysis of the school districts' administration as part of independent research projects supervised by Donnay. In addition to observing her methods and doing prep work and data entry for Stephenson, they are doing directed readings in network theory and learning about measures of centrality within various kinds of networks. Huynh is writing a senior thesis about how the path of an epidemic can be predicted using such measures; Won is developing computer algorithms to analyze data about social networks.
"Karen is incredibly generous in discussing concepts and explaining the practical aspects of the study with the students," Donnay says. "She's a master, but she's so warm and welcoming that you forget that she's one of the world's top management gurus. While we're getting ready to go interview school administrators, she may be on the phone talking to the government about doing a study of an organization of 10,000 people."
"I've learned so much from this experience," says Huynh, "about how math can be used to identify key actors in a social network — not only for the purposes of analysis, but to help bring about change."
Hepburn Fellow Karen Stephenson Brings "Mathematical Magic" to Education Reform
March 13, 2007

RENOWNED MATHEMATICIAN TO SPEAK AT COLORADO STATE UNIVERSITY FOR 2007 ARNE MAGNUS LECTURES

newsinfo.colostate.edu
FORT COLLINS - Efim Zelmanov, a recipient of the Fields Medal in mathematics and the Rita L. Atkinson professor of mathematics at the University of California at San Diego, will deliver Colorado State University's 2007 Arne Magnus Lectures.
Zelmanov will give his general lecture, "Algebra in the 20th Century," at 7 p.m. March 26 in Room 104 of Albert C. Yates Hall. The event will be followed by a colloquium at 4:10 p.m. March 27 in Room 120 of the Engineering Building and a seminar at 4:10 p.m. March 28 in Room 120 of the Engineering Building. All presentations are free and open to the public.
Zelmanov received the Fields Medal in 1994 for solving the Restricted Burnside Problem, a fundamental conjecture in algebra that mathematicians specializing in group theory had worked on throughout the 20th century.
The Fields Medal, considered the equivalent of the Nobel Prize for mathematics, is awarded every four years at the International Congress of Mathematicians to up to four mathematicians for groundbreaking work in the field. Aside from his work on the Restricted Burnside Problem, Zelmanov is well known for his doctoral dissertation that completely changed the sub-discipline of mathematics known as Jordan algebras.
Born in the former Soviet Union, Zelmanov received his doctorate from the Academy of Sciences in Novosibirsk in 1980. He came to the United States in 1990 and held faculty appointments at the University of Wisconsin-Madison, the University of Chicago and Yale University before assuming his current position at UCSD in 2002.
Zelmanov was elected to the National Academy of Sciences and is its youngest member in the mathematics division. He has also served on the editorial board of more then 10 mathematics journals, including "The Annals of Mathematics," "The Journal of Algebra" and "The Journal of the American Mathematical Society." In addition to the Fields Medal, Zelmanov has received the Collge de France Medal and the Andr Aizenstadt Prize.
The Magnus Lectures are delivered annually at Colorado State in honor of former Colorado State mathematics professor Arne Magnus. Each spring since 1993, Colorado State's mathematics department has welcomed an outstanding researcher to campus to deliver a series of lectures for the general public and for professionals within mathematics and related fields.
For more information on the Magnus Lecture and Zelmanov's presentations, visit online at www.math.colostate.edu/events/magnus or call the mathematics department at (970) 419-1303.
RENOWNED MATHEMATICIAN TO SPEAK AT COLORADO STATE UNIVERSITY FOR 2007 ARNE MAGNUS LECTURES
March 13, 2007

Long Legs Are More Efficient, According To New Math Model

www.sciencedaily.com
Science Daily — Scientists have known for years that the energy cost of walking and running is related primarily to the work done by muscles to lift and move the limbs.
But how much energy does it actually take to get around? Does having longer legs really make a difference?
Herman Pontzer, Ph.D., assistant professor of physical anthropology in Arts & Sciences, has developed a mathematical model for calculating energy costs for two and four-legged animals. His research was published in a recent issue of The Journal of Experimental Biology.
"All things being equal, leg length is one of the major determinants of cost," says Pontzer, "If two animals are identical except for leg length, the animal with longer legs is more efficient."
The fossil record shows that two million years ago, there was a big increase in leg length in early humans. Pontzer suggests that one reason for this increase could have been the energy saved by having longer legs. "If you greatly increase the distance that you travel each day, then you'd expect evolution to act on walking efficiency," he says. "That way, the energy you save on travel can be spent instead on survival and reproduction."
Pontzer's LiMB model is an equation that predicts walking and running. Importantly, the model predicts that the rate of force generation — and therefore the rate of energy use — is related to limb length. Longer legs mean less force production and lower energy cost.
To test his equation, Pontzer put people, goats and dogs on a treadmill in his lab, and measured how much oxygen each used during walking and running at various speeds.
He found that the LiMB model explained more of a variation in locomotor cost than other predictors, including contact time and body mass, showing that it worked for animals with four legs as well as two.
Note: This story has been adapted from a news release issued by Washington University in St. Louis.
Long Legs Are More Efficient, According To New Math Model
March 06, 2007

Professor goes to war with Web's hackers

media.www.dailylobo.com
Issue date: 3/2/07 Section: News
by Caleb Fort
Daily Lobo
Jared Saia
Media Credit: Harrison Brooks
Computer science professor Jared Saia
talks about the development of his algorithm program
Thursday in the Ferris Engineering Center.

Hackers often use networks of hijacked computers called botnets to send spam and attack Web sites.
But defending against hackers is usually left up to single computers.
"If you have one person trying to prevent action from hundreds of thousands of computers working together, the chances aren't very good," said Jared Saia, a UNM professor of computer science. "It's a one-against-many battle."
Saia is trying to change that with an algorithm that allows a group of computers to work together, even if some members of the network are trying to disrupt it.
The algorithm is based on the Byzantine agreement problem.
In the hypothetical situation, several Byzantine generals have surrounded a city and are preparing to attack it. In order for the attack to be successful, the generals have to agree on one plan of attack.
However, a secret group of evil generals is trying to thwart the attack by disrupting the communication between the good generals.
Saia said his algorithm would allow the good generals to collaborate despite the efforts of the evil ones.
The problem is an analogy to the Internet, where hackers try to disrupt the activities of computer users.
Other people have created solutions to the problem, but they cannot be used for Internet-sized groups of computers, he said.
"With the Byzantine agreement, people have either gotten security or scalability," he said. "Getting one of those two things isn't hard, but it's difficult to get both of them."
Saia was awarded a $400,000 National Science Foundation grant to continue work on the algorithm over the next five years.
He has been working on the algorithm and proofs of its correctness for about three years.
He has co-authored more than five papers about it with researchers from Microsoft, Yahoo! and Tel Aviv University.
Once the algorithm is turned into code, it could be used for spam filters and virus protection, Saia said.
Most security relies on encrypting information, but new computers - called quantum computers ­- might be able to break the encryption. "That suggests that we need new techniques," Saia said. "People who attack systems are very clever, and they increasingly have financial incentives for what they do."
People who take over large groups of computers rent them to spammers. They also hold Web sites hostage by threatening to attack them if they don't pay up.
"That used to frequently be on Web sites that are sort of quasi-legal, like offshore gambling, but it's starting to happen to more mainstream Web sites," Saia said. "It's a bad situation right now. The
criminals are using the power of collaborative computing. In order for us to fight them, we should also be taking advantage of that. We're simply not doing that right now."
It's easier for criminals to attack than for other people to defend, Saia said.
"Not only are they evil, they're omniscient," he said. "The problem is that hackers can hide, but it's fairly easy for them to figure out what techniques we're using. The hackers have this element of surprise that we don't."
Besides making the Internet safer, Saia said he hopes his work will inspire more students to study computer science.
"I feel that there are many students who feel like computer science is just making Web sites and things like that," he said. "In fact, there are these very challenging and interesting mathematical problems that need to be solved."
Professor goes to war with Web's hackers
March 06, 2007

Bowdoin Brief: Mathematician to deliver lecture on uncertainty, unexpected

orient.bowdoin.edu
By Anna Karass
Orient Staff
Acclaimed author of "The Black Swan: The Impact of the Highly Improbable" Nassim Nicolas Taleb will deliver a lecture titled "On the Impact of the Highly Improbable."
According to his book "Fooled By Randomness: The Hidden Role of Chance in Life and in the Markets," Taleb, formerly a quantitative trader, is interested in "multidisciplinary problems of uncertainy." Taleb developed the Black Swan Theory, which asserts that there is tendency to exclude unexpected or random events that cannot be explained in data models. It these unexpected events, Taleb argues, "end up controlling our lives, the world, the economy, history, everything."
Taleb, a native of Amioun, Lebanon, holds multiple degrees, including a Ph.D from the University of Paris and an MBA from the Wharton School at the University of Pennsylvania. According to his home page, Taleb is finishing a break as a Dean's Professor in the Sciences of Uncertainty, University of Massachusetts at Amherst. He is also a fellow in mathematics in finance, an Adjunct Professor of Mathematics at the Courant Institute of Mathematical Sciences of New York University, and a research fellow at Wharton School Financial Institutions Center.
Taleb admits to finding amusement in mocking those who take themselves to seriously and overrate the quality of their data.
"My major hobby is teasing people who take themselves and the quality of their knowledge too seriously, and those who don't have the guts to sometimes say: I don't know," Taleb writes on his home page.

His lecture will take occur on March 26 at 7:00 p.m. in Kresge Auditorium.
Bowdoin Brief: Mathematician to deliver lecture on uncertainty, unexpected

March 06, 2007

Two seniors earn Schafer math honors

www.dailyprincetonian.com
By Tatiana Lau
Princetonian Senior Writer
A Princeton senior received the national Alice T. Schafer award for excellence in mathematics in January. Ana Caraiani was named the winner of the prestigious prize at the Joint Mathematics Conference in New Orleans. Tamara Broderick '07 was a runner-up.
The award is given annually to a woman based on research accomplishment, demonstration of an interest in mathematics, academic course work and achievements in mathematical competitions such as the William Lowell Putnam competition — a prominent math contest for college math majors in the United States and Canada.
When Caraiani went down to New Orleans to accept the award, she said, "It was really impressive because they presented a lot of awards to [prominent mathematicians], and I got to sit on the same stage with them."
Former roommates Alexandra Ovetsky '06 and Allison Bishop '06 were named the winner and the runner-up for the Schafer award last year.
Caraiani said she was flattered by the award. "I knew I was getting nominated, but I didn't think I'd win," she said. "I know some of the former winners, and they are amazing."
Broderick also emphasized her excitement over being recognized as one of the two runners-up for the prize.
Caraiani, an international student from Romania, is the only woman to have won the Putnam competition twice. In the history of the competition, only three women have won.
She was nominated for the Schafer Prize by Professor Joseph Gallian at the University of Minnesota Duluth, with whom she did an undergraduate research program for two summers.
"She ranks up there with the best I've had," Gallian said in a phone interview. "She's quiet and unassuming, but when she talks about math there is a noticeable change. She speaks with confidence and authority."
"[Ana] was a perfect candidate," Gallian said in an email. "It was an honor for me to make the nomination."
Professor Andrew Wiles, Caraiani's thesis advisor, said in an email that Caraiani's "quickness, her ability to see the main point, her ability to focus and her ability to work out the background to very sophisticated mathematics are all part of a remarkable talent, ideally suited to research."
Broderick was nominated by her secondary thesis advisor, Robert Schapire, a professor in the computer science department.
"I've always liked math," Broderick said. She recalled participating in a math contest in fourth grade which covered material that she had not been taught in class. "I just had so much fun with it."
Broderick is currently writing her thesis on finding parameters of the Gibbs distribution when given a large state space.
After graduation, she plans to spend two years in England on a Marshall scholarship.
Caraiani's thesis deals with algebraic number theory. She has applied to graduate schools in the United States and will be soon deciding where to spend her next few years.
Caraiani's professors have high expectations for her future in the field of mathematics. "She has already shown great aptitude for [research]," Wiles said. "I expect to see her become a leader in whatever branch of mathematics she chooses."
Two seniors earn Schafer math honors
March 06, 2007

Ancient masters of maths

WORLD OF SCIENCE - BOB BROCKIE
For the last three years I have been struggling with a big book about higher mathematics and physics. I had hoped to report to you from the frontiers of these disciplines but, regrettably, I must now admit to almost total defeat and incomprehension.

I'm talking about that 2004 scientific tour de force – The Road to Reality: A Complete Guide to the Laws of the Universe by Sir Roger Penrose, Professor of Maths at Oxford University.
Penrose is no slouch, leading the mathematical fields of twistor theory, supersymmetry, string theory, inflationary cosmology, loop gravity, manifolds in Euclidean space, the cosmic censorship hypothesis, quantum theory and the workings of consciousness etc. He has a special interest in the origin of the universe and black holes.
You get the picture. The book so bristles with mathematical hieroglyphics that I could only thumb through its 1100 pages again and again in awe and disbelief. Luckily, the first and last chapters are written in English so I can report on one or two of his take-home messages.
After reviewing 2000 years of scientific achievements, Penrose concludes that the 21st century will uncover new things about maths and the workings of the universe that will leave our present understandings for dead. He is convinced that we are on the verge of developing a theory of quantum gravity which might explain how consciousness evolved and how our minds work.
Penrose has had an abiding interest in geometry, especially the geometry of tiling patterns. That's right. There's a whole world of complex mathematical theory behind the designing of tiled patterns.
Armed with pencil and paper, Penrose spent 20 years calculating a new sort of seemingly impossible, extraordinary pattern using only two differently-shaped tiles, the like of which had never been seen before in human history. At first glance the pattern seems to repeat regularly, but on closer examination you find its a set of interlocking units whose 5-fold symmetrical pattern never repeats itself from here to infinity. In 1976 the pattern, which he patented, became known as Penrose tiling. Now tiling theory might appear to be an exercise in arcane geometry but, only 10 years later, atoms were found that arranged themselves as Penrose tiling patterns in many crystals, such as aluminium and zinc alloys. Penrose's discovery rewrote large areas of the science of crystallography.
One day the knighted professor's wife brought home rolls of quilted toilet paper embossed with her husband's famous tiling pattern. The offended professor sued the American Kleenex company in 1997 for unlawfully appropriating his patterns.
Last week Sir Roger must have been surprised again to read that American physicists, Peter Lu and Paul Steinhardt, had discovered Penrose tiling on an Islamic shrine built nearly 500 years ago in Iran.
A controversy now rages about those medieval Muslims. Did they master the supersophisticated maths behind the patterns 500 years ahead of their time? Or did some tiling craftsman genius strike it lucky – dreaming up the patterns by sheer aesthetic inspiration?
Ancient masters of maths

March 03, 2007

Staying Alive

focus.aps.org
Mathematical models often predict that predators will hunt their prey to extinction or that predators will starve to extinction when the prey population drops. Real species are far more stable, in part because the animals live in many spatially separated areas that can replenish one another through migration. But this result has been difficult to recreate in mathematical models, and researchers haven't understood exactly which conditions prevent extinction. In the 2 March Physical Review Letters, a team describes a stable model that includes migration and determines the precise mechanism that prevents extinction. The study could be helpful for designing conservation strategies and in medicine, the researchers say.
When the number of prey grows, its predators flourish too. But eventually there are too many predators and the prey population drops. Deprived of food, the predator population drops a bit later. In the 1920s and 30s, mathematicians came up with differential equations to model these oscillations. But as their creators recognized, the solutions aren't stable. Adding some random fluctuations to represent external effects--such as disease, competition with other species, or changes in the weather--can make the model populations swing more and more to extremes, until one species goes extinct.
More recently researchers have also used the alternative approach of computer simulations, where they start with rules for behaviors of individual animals and then "watch" the virtual populations change over time. These computational "experiments" have suggested that populations stabilize if the animals inhabit several regions, with some migration between them. That way, the regional populations can oscillate and sometimes go extinct, but the overall populations of both predator and prey can persist. Lab experiments, with bacteria as prey and viruses as predators, for example, have also found that multiple regions help stabilize the populations. But the precise relationships that prevent extinctions haven't been clear.
Now a rigorous mathematical solution to this problem comes from a team led by Nadav Shnerb of Bar-Ilan University in Israel. Starting from the classic differential equations for predator-prey systems, they modeled a pair of regions, each with a predator and prey species, and allowed some migration between them.
The model was designed to tease out the precise relationships that lead to stable populations. Shnerb and colleagues found that the key property is to have the frequency of the oscillations dependent on their amplitude. This has a straightforward interpretation in real life, backed up by observations: when populations are small, they tend to grow or shrink slowly, whereas when they're large, the population size can change much more quickly. With this key property, adding in some random population fluctuations--the "noise" of the real world--kept the regions' population oscillations out of sync, so that the overall population of both species never died out. The study affirms an old solution ecologists had intuited--that desynchronization between regions, coupled with migration between them, could create stability overall. But the new results put that idea on firm mathematical footing.
Shnerb says that the results could be useful for improving models of threatened species living in fragmented habitats. They could also find use in medicine, aiding new antibacterial therapies that use bacteria-killing viruses. In this case, scientists could calculate the conditions that would make the system unstable, ensuring that the bacteria would all die off.
In many cases, "natural populations are more stable than [earlier] models would suggest," says Vincent Jansen, a mathematical biologist at the Royal Holloway University of London, in Surrey, England. "What this paper shows is that if you look at it in an appropriate way, you can see that spatial interactions would stabilize things." He adds, "I think it goes a long way to explain the behavior of populations in nature."

--Mason Inman
Mason Inman is a freelance journalist in Cambridge, Massachusetts.
Staying Alive

March 06, 2007

Littérature et mathématiques : rencontres dans la fiction

www.humanite.presse.fr
Les mathématiques comme instrument d'intimidation pour la troupe innombrable des profanes. Les mathématiques comme précieuse source d'approvisionnement artistique et intellectuel, par exemple dans la philosophie, dans la peinture ou dans la musique. Les mathématiques, disons-le avec Musil, comme l'une « des aventures les plus fascinantes de l'existence humaine » et non comme un désert de calculs abstraits, arides et inaccessibles. Les mathématiques qui ne cessent jamais de fournir des réponses à des problèmes jusque-là insolubles, mais qui en même temps placent l'homme face à des défis toujours nouveaux et toujours plus captivants. Quand David Hilbert, en 1900, dresse la liste des vingt-trois problèmes ouverts qui doivent inspirer et orienter la recherche mathématique dans le siècle qui va commencer, il souligne implicitement sa grande vitalité et le long chemin qu'elle doit encore accomplir. Un chemin qui a ponctuellement conduit à de nouvelles découvertes, à des paradoxes encore à ce jour irrésolus, à des antinomies imprévisibles, à d'intrépides attentats de toutes sortes au sens commun et aux certitudes accumulées jusqu'alors : une constante impulsion problématique qui se ramifie dans différentes directions, parfois même diamétralement opposées.
Les mathématiques sont la plus grande manifestation de la liberté individuelle, la seule discipline qui ne peut connaître aucune forme de censure ni de conditionnement idéologique. Même le nazisme ou le stalinisme n'ont pas été capables de les réduire à devenir un outil de propagande, ni de les bannir en tant qu'expression d'une culture « dégénérée » ou « bourgeoise ». Et malgré cela les mathématiques restent principalement une activité de fiction, un territoire dans lequel l'imagination peut se donner libre cours et les idées se combiner à loisir. Les mathématiques créent des mondes, des espaces, des univers, des relations entre les objets, qui peuvent d'autant plus fasciner qu'on en déchiffre mieux la signification ; elles opposent, comme disait Calvino, « la légèreté des idées à la pesanteur du monde » et apparaissent comme le produit le plus authentique du vagabondage intellectuel de l'homme.
Or en tant qu'activité de fiction, les mathématiques pouvaient-elles ne pas rencontrer cette autre activité de fiction qu'est par excellence la littérature, et pas seulement en la croisant par hasard de temps en temps ? Littérature et mathématiques, de fait, se reflètent réciproquement, donnant vie à des images, des échos, des suggestions, des contaminations, des consonances et des dissonances. Bien sûr, les résultats des mathématiques sont souvent utiles à d'autres disciplines, par exemple à la physique, et en facilitent le développement, avec toutes les implications pratiques qui en découlent. Mais cela vaut également pour la littérature qui souvent, non seulement interprète la réalité existante, mais est aussi capable d'anticiper, voire d'être le vecteur premier de changements de cap socioculturels qui marqueront une époque. Peut-être que ni la littérature ni les mathématiques n'aspirent à la vérité, mais qu'elles sont mues l'une et l'autre, comme l'avait bien compris Platon, par des idéaux esthétiques, en particulier par la beauté et la rigueur de la syntaxe. Il est même possible que la valeur linguistique d'un théorème mathématique soit supérieure, en ce qu'il vise à la réduction de son propre objet aux seuls termes essentiels, termes exempts de toute redondance émotive, comme le remarquait Wislawa Szymorska, alors que cette redondance est la marque même de la littérature.
La complémentarité de la littérature et des mathématiques, parfois sous une forme dissimulée, varie d'un écrivain à l'autre, d'une époque à l'autre. Elle a été particulièrement profonde dans le romantisme (que l'on songe à Novalis) et au siècle dernier, durant lequel les consonances mathématiques sont immédiatement repérables chez des écrivains comme Musil, Broch, Borges, Gadda, Frisch, Calvino, Queneau et les membres de l'Oulipo, jusqu'à des auteurs plus proches de nous comme Hans Magnus Enzensberger, Don DeLillo ou Daniele Del Giudice. La littérature qui subit la fascination des mathématiques et se laisse volontairement influencer par elles possède trois caractéristiques saillantes. En premier lieu, elle ne se propose pas une assimilation exhaustive, correcte et didactique de la matière, se limitant au contraire à des renvois imparfaits, à de vagues analogies, à d'obscurs reflets, dont on peut cependant dire avec André Weil que « rien n'est plus fécond ». En second lieu, la tension intellectuelle et imaginative qui sous-tend la rationalité mathématique en lui imprimant souvent une charge de passion lucide et fébrile (qui fait de beaucoup de grands mathématiciens des figures excentriques et humainement très attirantes) peut constituer en soi une inquiétante et stimulante séduction poétique. Enfin, derrière une complexité parfois trompeuse, cette littérature-là offre une capacité d'affabulation non moins accessible que d'autres genres littéraires plus usités et plus traditionnels, en vertu de sa structure architecturale qui se conforme de façon rigoureuse aux schèmes de la logique et de la cohérence narrative. Il existe cependant un autre genre littéraire qui reproduit les stylèmes de la raison et la cohérence du processus logico-déductif typiques des mathématiques : il s'agit du roman policier. L'enquête policière procède en effet en parfaite analogie avec la méthodologie utilisée pour la démonstration d'un théorème mathématique, dans laquelle l'établissement du résultat final advient par phases progressives et lemmes intermédiaires. Mais il s'est évidemment trouvé des gens pour exprimer leur scepticisme à l'égard des consonances mathématiques du polar, comme par exemple Dürrenmatt qui, dans La Promesse, a démontré l'incapacité de la logique investigatrice d'entrer en résonance avec l'irruption - par définition imprévisible - de l'événement.
Les mathématiques ne sont donc pas un « savoir autre », mystérieux ou ésotérique, et de ce fait inhibiteur pour le lecteur ordinaire, mais un instrument privilégié et quotidien d'enquête, y compris littéraire : toutes les passions ont leur géométrie, comme le savaient bien les grands moralistes français, tels que Laclos, Chamfort ou La Rochefoucauld.

Francesco Magris
Littérature et mathématiques : rencontres dans la fiction

March 06, 2007

Dieu joue-t-il aux dés ?

www.opusdei.fr
La physique quantique est un bon point de départ pour parler de la liberté, du destin et de Dieu. C'est ce que pensent les universitaires de 9 pays différents qui se sont retrouvés à Londres pour débattre autour du sujet « L'évolution, le hasard et l'intelligence dans la nature »
28/02/2007
Rencontre universitaire interdisciplinaire, à Londres, avec des intervenants de 9 pays différents

La science facilite énormément la vie et elle peut aussi aider l'homme à se comprendre lui-même. Pour ce faire, il faut que les avancées scientifiques soient étayées par une réflexion humaniste et anthropologique.
Afin d'arriver à cette vision globale, depuis 1992, différentes associations d'étudiants et d'enseignants se retrouvent tous les ans et débattent sur les progrès faits dans chaque secteur de la science pour partager leur savoir et leurs opinions.
L'édition 2007 de « L'international Interdisciplinary Seminars » a rassemblé récemment à Londres des ingénieurs, des biologistes, des physiciens, des mathématiciens, des philosophes et des juristes autour du sujet : « Does God play dice ? Evolution, Randomness and Intelligence in Nature. »
Nous avons recueilli les propos d'Antoine Suarez et de Lorenzo de Vittori, participants à ce forum qui a eu lieu à Netherhall House, résidence d'étudiants et œuvre collective de l'Opus Dei.
À quoi bon se demander si Dieu joue ou non aux dés ?
Cet intitulé fait allusion à la polémique d'Einstein contre la physique quantique. Cette branche du savoir prétend que les phénomènes physiques ne peuvent pas exclusivement être expliqués de façon déterministe, par des causes matérielles et observables.
Einstein, partisan du déterminisme, répondait : « Dieu ne joue pas aux dés ». Or, si le monde ne fonctionnait que de façon déterministe, il n'y aurait aucune place pour la liberté. Cette polémique est toujours d'actualité.
Mathématiciens, ingénieurs, philosophes, physiciens… quel est votre intérêt commun ?
La liberté. Dès leur démarrage en 1992, c'est le fil conducteur qui donne une unité à des séminaires interdisciplinaires pour universitaires. Avec ces débats, nous voulons promouvoir une réflexion scientifico-philosophique à partir des résultats des sciences expérimentales et des mathématiques, afin de décrire un monde où la liberté est possible.
Quel est le profil des participants ?
Des étudiants et des enseignants intéressés par la liberté, l'évolution et Dieu, questions débattues par scientifiques et philosophes.
Le forum a réuni des chercheurs, des professeurs et 60 étudiants provenant de 9 pays : Grande Bretagne, Irlande, Hollande, Italie, Suisse, Croatie, France, Canada et Taiwan. Le nombre était limité par notre capacité d'hébergement. La moyenne d'âge était de 25 ans.
Cette activité cherche à encourager la communication interdisciplinaire. Je pense que le but est réussi puisqu'il y a eu des représentants de pratiquement toutes les disciplines scientifiques : physiciens, mathématiciens, ingénieurs, biologistes, médecins, statisticiens, informaticiens ainsi que des philosophes, des juristes, des étudiants de sciences politiques, voire aussi des artistes.
Quels ont été les principaux débats ?
Ils ont tous tourné autour des conséquences philosophiques de la physique quantique et des mathématiques ; la tension entre évolution et création ; l'importance du hasard quantique pour la liberté ; le rapport entre l'âme spirituelle et le cerveau et la définition de la mort.
Quelles ont été les propositions les plus originales ?
Le premier résultat original est l'idée qu'il est possible de concilier la perspective philosophique de Thomas d'Aquin et les expériences récentes de la physique quantique. Comme l'ont exposé les groupes de Zurich (Lorenzo de Vittori, Andreas Schwaab) et de Zagreb (Vuko Brigljevic et Roco Plestina), Ces expériences révèlent l'existence de phénomènes dont l'origine ou la cause est hors de l'espace et du temps parce qu'elle est immatérielle. Elles permettent aussi d'actualiser la vision thomiste de l'âme en tant que forme du corps : dans les mouvements spontanés de notre corps, l'énergie nécessaire joue le rôle de cause matérielle ; l'âme, en revanche, intervient comme cause formelle au niveau des choix posés (par exemple : tourner à gauche au lieu d'à droite). Juléon Schins (de Delft, Pays-Bas) a proposé son expression « hylémorphisme quantique ». Nous avons essayé d'appliquer cette explication à la définition de la mort et cela semble marcher correctement.
Cesare Stefanini et Federico Favali (Pise, Italie) nous ont proposé des réflexions encourageantes lorsqu'ils ont comparé la créativité humaine aux capacités des robots autonomes. Il y a encore beaucoup à travailler sur la relation âme-cerveau.
Un autre résultat intéressant : la vision « positive » du hasard proposée par les groupes d'Utrech (Alfred Driessen, Daan Van Schalkwijk) et de Zurich. Le hasard n'aurait rien d'aveugle, comme on le pense, mais viendrait d'une cause intelligente et libre, il serait comme le jeu que Dieu permet dans le « mécanisme » du monde afin que celui-ci ne soit pas totalement rigide et permette des mouvements des corps libres, comme les mouvements de mes doigts sur le clavier de l'ordinateur lorsque j'écris les réponses à vos questions.
On peut en quelque sorte comparer le hasard à la « terre informe » ou matière première que Dieu créa au début, d'après le récit biblique. Cette perspective est un éclairage intéressant sur la théorie de l'Évolution.
L'Évolution est, en fait, un sujet d'une grande actualité scientifique, philosophique et religieuse…
Les universitaires ont fait des exposés sur des sujets de grande actualité et d'un très haut niveau scientifique. En parlant du débat actuel sur l'évolution et le dessein intelligent Mark Fox (Sheffield), Tomory Leslie (Toronto), Jimmy Bakker (Dublin) et Andrea Manazza (Turin) ont insisté sur ce qu'il n'y a pas de conflit entre la notion de Création et la théorie scientifique de l'évolution.
Par ailleurs, les économistes Ed Tredger (Londres) et Jan Everhard Renaud (Amsterdam) ont analysé l'idée de hasard et le physicien informaticien Peter Adams (Londres) a attiré l'attention sur le fait que, bien que Dieu ne se révèle pas facilement à la science, la description du monde que la science quantitative fait ne doit pas être totalisante et rester ouverte à des principes non quantifiables.
La perspective mathématique des groupes italiens (Max Berti, Rocco Tarchini) et de Zurich a été très intéressante aussi. Des théorèmes fondamentaux en mathématiques (Gödel, Turing) montrent bien, d'une part, que la pensée humaine ne peut pas être réduite à un pur processus mécanique de calcul, et que dans ce sens, elle n'est pas matérielle.
Par ailleurs, il se fait qu'aucun esprit humain ne peut contenir toute la vérité mathématique. Si, comme l'assure Kant, la mathématique est un « a priori » mental, ne découlant pas de l'expérience sensorielle, il faut conclure qu'elle a son origine dans un esprit omniscient qui dépasse la capacité humaine. Ironiquement, l'idée de mathématique qu'expose Kant dans la Critique de la raison pure semble impliquer l'existence de Dieu.
Vous avez dit que les assistants étaient des « jeunes » et des « scientifiques » : ce sont précisément les deux publics apparemment le moins intéressés par Dieu et par le spirituel.
La science s'occupe de comprendre le monde, de le décrire dans la mesure du possible et d'expliquer le rôle, toujours central, que l'homme joue dans ce contexte. Il est donc logique qu'un scientifique honnête se pose des questions à la base de la vie : Dieu, l'origine du monde, l'évolution…
Et ces scientifiques sont de plus en plus nombreux, fort heureusement. Après plusieurs siècles où les sciences se sont développées chacune de leur côté, en compartiments étanches, il semble que désormais les jeunes générations veulent trouver une unité au-delà de leurs spécialisations.
Afin de confirmer cette tendance, on n'a qu'à consulter les discussions virtuelles sur internet. La plupart concernent les blogs, très en vogue chez les jeunes scientifiques. Il suffit de taper dans google « existence de Dieu » ou « Physique quantique et liberté » pour avoir des milliers de pages sur ces questions.
Cependant, il n'y a pas que les jeunes qui sont préoccupés par ces questions métaphysiques. Des professeurs et des chercheurs sont touchés eux aussi.
Il y a un siècle, il était impensable d'oser critiquer le déterminisme (il suffit de noter la réaction d'Einstein : « Dieu ne joue pas aux dés ! »). En revanche, maintenant, cela semble une voie sérieuse pour montrer qu'il n'y a pas de contradiction entre science et religion.
Actuellement, il s'agit d'un débat ouvert, sans doute critiqué, mais en discussion continuelle et vivante. Il est plaisant de voir comment de grands spécialistes en physique quantique assurent que dans ce monde il y a un espace pour la liberté et pour Dieu.
Alors, ouvrir ces débats dans le domaine de la science, n'est-ce pas aller à contre-courant ?
En effet, cela peut choquer l'esprit de celui qui est habitué à considérer le monde sous un angle « déterministe ». Cependant, ce nouveau discours n'est plus rejeté. Au contraire, il est écouté avec intérêt.
Ce qui est positif c'est que le courant de pensée scientifique ne fonctionne plus que dans un sens. Le fleuve est désormais plein de remous et c'est l'humus le meilleur pour que la science progresse !
Si j'ai bien compris, vos débats se poursuivent sur un blog.
Oui, à l'adresse http://www.scienceandbeyond.net
Quelle a été l'ambiance de votre congrès ?
Très encourageante. Il y a une anecdote qui reflète bien cela. À la fin de notre rencontre, le modérateur a pris la parole : « Pour finir, Dieu, joue-t-il aux dés, oui ou non ? » Oui…. Répondit le public… Et il s'amuse bien! » C'est sans doute une façon d'expliquer le ludens in orbe terrarum (Pr. 8, 31). Les participants en ont également profité pour visiter Londres.
Et l'an prochain ?
Le Séminaire aura lieu encore à Londres, du 2 au 6 janvier 2008. Le sujet sera « Y-a-t-il dans la neuroscience une place pour l'âme? Nos débats tourneront autour des bases neuro-physiologiques de l'identité personnelle et du libre arbitre.
Dieu joue-t-il aux dés ?