Collana Cd-Rom del Dipartimento di Matematica Università di Torino

 The Mathematical Works of Francesco Faà di Bruno in Cd-Rom
edited by Livia Giacardi


«Ce n'est en effet que lorsqu'une vérité est devenue accessible
au plus grand nombre de personnes
qu'on peut vraiment affirmer que
la science humaine a fait un progrès» 
(F. Faà di Bruno, Théorie des formes binaires, 1876, p. V)

  Francesco Faà di Bruno (1825-1888) is undoubtedly a pre-eminent figure in the scientific world of the nineteenth century, owing not only to his extraordinary involvement in charitable work for the community but also to his stature as an internationally renowned mathematician, and as a professor at the University of Turin. Among the students attending his course of Higher Analysis we find Giuseppe Peano and Corrado Segre, whose schools of mathematical logic and algebraic geometry put Turin centre stage on the international mathematics scene.

    Like other famed mathematicians in the period of the Italian Risorgimento, as, for example, Luigi Cremona, Enrico Betti and Francesco Brioschi, throughout his life Faà di Bruno adhered to a very precise agenda in his scientific studies and teaching practice: on the one hand, his aim was to revitalise university teaching by introducing new areas of study (Elimination Theory, Invariant Theory, Elliptic Functions etc.), on the other, to make the results of the most advanced international research, which appeared in specialist scientific journals, known to young people, thus stimulating research in Italy.

    A distinguishing feature of his research work was his skill in writing treatises, where he was much admired for his painstaking work of organising, simplifying and clarifying theories which till then had lacked a definitive form, and which he accompanied with his own original contributions.

    The most famous of his results is the formula giving an explicit expression for the nth derivative of a function of a function, known today as the Faà di Bruno formula. There was, however, another important aspect of Faà di Bruno the scientist: his international standing. He had studied in Paris under some of the greatest mathematicians of that time (A. Cauchy, C. Hermite, J. Liouville) and it was there that he completed his degree in Mathematical Sciences. In addition, most of his scientific works were written in French, and he corresponded with the most eminent researchers in Europe.

    Outside Italy his treatises were very highly regarded, since they were considered to be comprehensive and clearly explained, and also to contain some original results. In particular, his most important work, Théorie des formes binaires (1876), was so well received by the international scientific community that M. Nöther, together with Th. Walter, supervised the German edition, and D. Hilbert set it as a text book for his course at the University of Göttingen, one of the most advanced in Europe for mathematical research. Faà's scientific works, considered in the context of the history of Invariant Theory and of Algebraic Combinatorics, constituted a major contribution to the defining and perfecting of these theories. 

    However, Faà di Bruno's scientific and didactic activities formed part of a wider plan which involved the other of the two points of reference, science and religious commitment to the community, around which his life's work revolved. Thus, on his return from Paris, in the space of a very few years, while teaching at the university and carrying out research work, he set up in Turin a impressive number of charitable initiatives aimed at raising the social status of women, as well as improving the welfare of the poorer classes and the education system.

    The link between the two different areas of interest, scientific research and charitable work in the community, can be seen in Faà's deep commitment to popularising science. He was intensely active in this regard, not only in the academic sphere, but also in his work with the poor, as he regarded science as a means of educating the general public. In actual fact, he considered the progress of the human race to be closely connected to the progress of the sciences which he saw, on one hand, as indispensable for the material and intellectual improvement of mankind, while, on the other, as "having a value of a higher order, in that they proclaim and foster the principles of unity, justice and faith." 

    His work in popularising science grew from a unique fusion between positivist principles, religious faith and commitment to the welfare of the community, and it found many different avenues of expression. He organised the publication of an almanac explaining simple principles of popular science (the metric system of measurement, meteorology, astronomy); he set up courses in physics for ladies; he established a lending library with books on religious and scientific subjects, at a time when there was no library for public use in Turin; he invented aids for the teaching of physics and chemistry which were awarded prizes in several national and international expositions; he wrote text books for teaching the sciences, addressed specifically to women; he organised scientific experiments in the church of Our Lady of Suffrage to raise money for charity. His interest in the mass media led him to write articles to popularize science and to set up a printing press to print low cost educational books and pamphlets.

  The publication of The Mathematical Works in Cd-Rom forms part of a project - aimed at exploiting the resource materials in history, science and bibliography - which the Department of Mathematics of the University of Turin has been developing for several years through its collection of cd-roms (http://www.dm.unito.it/collanacdrom/index.html). The Mathematical Works supplements Livia Giacardi's book Francesco Faà di Bruno. Ricerca scientifica, insegnamento e divulgazione, Studi e Fonti XII, Deputazione subalpina di Storia patria, Torino, 2004, published by the Centro di Studi per la Storia dell'Università di Torino with the collaboration of the Centro Studi Francesco Faà di Bruno. 
   The aim of this Cd-rom is to bring together all of Francesco Faà di Bruno's mathematical works, published and unpublished. In particular, the recent rediscovery of a copy of the lost treatise on elliptic functions allows the reader to construct a complete and more detailed picture of his research activities. The Cd-Rom, with texts in English and Italian, offers a useful information bank with all the multimedia aids needed to consult the texts easily and quickly.
   The material is divided into the following sections and sub sections:

Introduction

  • Introduction to Faà di Bruno; Structure and aims of this Cd-Rom 
  • Chronology: Events in the Life of Faà di Bruno
  • Image Gallery: family; engineering and architectural works; inventions and scientific instruments from the collection of the Museo   Faà di Bruno (Turin) 
  • Authors, contributors and funding Bodies
Sources
  • Bibliographical sources: general bibliography; occasional or minor contributions; reviews of Faà di Bruno's articles and works (with links to the  most important reviews);degree theses on his work. 
  • Archive sources on his scientific and teaching work
  • Catalogue of Faà di Bruno's scientific correspondence
Math Works, digitalised texts of:
  •  Articles
  •  Books
  •  Unpublished writings
        The complete list of all publications and the detailed indexes (by chapter and paragraph) of the writings allow rapid and easy consultation of  the entire body of work. 

Other publications, full list of non-scientific publications:
        - Musical compositions and texts about music
        - Religious texts; military writings