Clara Silvia Roero

The Formulario between Mathematics and History

For almost twenty years, from 1888 to 1908, Peano devoted all his energies to formulating and realising a project, which throughout his life he was to acknowledge as one of the most important results of his mathematical research1. This was the Formulaire de Mathematiques, a huge collection of mathematical propositions expressed in symbols, especially written with his own logic, capable of concentrating in a single volume the knowledge of mathematics of his time. To this end, Peano founded a journal and invited to collaborate on it scholars, assistants, colleagues at the University and at the military Academy, teachers and other mathematicians in Italy and abroad. His total commitment to this enterprise was also accompanied by his voluntary decision to leave his post as Professor of infinitesimal Calculus at the military Academy2, keeping only his University position, and by the purchase of a printing press so that he could set up the text himself, in view of the difficulties that the mathematical symbols created for the publishing houses3.

Gottfried Wilhelm Leibniz, first three papers on the calculus (1684, 1686, 1693)

Publisher Summary The invention of the differential and integral calculus is one of the most important and revolutionary developments in mathematics. Leibniz and Newton share out the glory of the invention of the infinitesimal calculus that they found independently. The priority of publication is because of Leibniz, who had the fortune to be followed by mathematicians of first rank who collaborated on the diffusion of his methods. The first public presentation of differential calculus appeared in October 1684 in the journal Acta Eruditorum, established in Leipzig, in only six and an half pages, written in a disorganized manner with numerous typographical errors. The first papers on integral calculus was the book by John Craig on quadratures, Methodus figurarum lineis rectis et curvis comprehensarum quadraturas determinandi, published in London in 1685, that stimulated Leibniz to draft his first exposition of the integral calculus. Craig attributed to him the paper on figures, published in the Acta Eruditorum. Leibnizs followers, especially Johann Bernoulli, reacted strongly against this slander, with the result that the mathematical community became polarized.

Corrado Segre and His Disciples: the Construction of an International Identity for the Italian School of Algebraic Geometry

It is well known that the construction of an identity for the Italian School of Algebraic Geometry directed by C. Segre was the result of a complex dynamic of scientific exchanges with the international mathematical community. In particular, Felix Klein was a reference interlocutor for Segre, Fano, Enriques and Castelnuovo, and he exerted a notable influence on mathematical studies, on the teaching of mathematics, on publishing activity, and on the organization of cultural and academic life. In this paper, in light of the correspondence that Segre carried on with Italian and foreign colleagues, we will illustrate the international relationships of the Italian School of Algebraic Geometry in the period of formation (1883–1891). Further, through the reconstruction of Segre’s partnerships with American scholars, we will show how he took on the role of a ‘Maestro a distanza’ or ‘distance Maestro’, for foreign geometers up to the first years of 20th century. From these letters and other archival sources there will emerge the cosmopolite features of the research activities pursued by the Segre’s team, the diffusion of Italian geometric methods and results abroad, as well as some aspects of the biography of Segre, related to his institutional, political and editorial committment.

Corrado Segre's Archives at the University of Turin

Corrado is born in Saluzzo to a well-to-do Jewish family. In 1870 the family moves to Turin. His father, Abramo Segre, was an industrialist in silk production, and his mother, Estella De Benedetti, came from a cultivated family of the upper-middle class. Corrado had two brothers, Mario e Arturo.

Relationships Between History of Mathematics and History of Art

During the course of centuries mathematics has interacted in many ways with culture and human activities, and among these a place of privilege has been reserved for art and architecture. In this paper I will show several examples of the existence of three levels of interaction between mathematics and art: the presence of a mathematical substrate in various archaeological and artistic relics from antiquity; the conscious or unconscious application by artists of mathematics principles whose theories had not yet been fully developed; and finally, the relationship established by some mathematicians with artists and art theorists that permitted an awareness and acquisition of mathematical knowledge and rules that were then applied to artistic creations.

Tullio Viola and his Maestri in Bologna: Giuseppe Vitali, Leonida Tonelli and Beppo Levi

The aim of this contribution is to illustrate the relationships between Tullio Viola (1904–1985) and his professors Beppo Levi (1875–1961), Giuseppe Vitali (1875–1932) and Leonida Tonelli (1885–1946) during his years as a student and just after graduation at the University of Bologna, in order to shed light on how they influenced his early research in analysis and his commitment to teaching. A transcription of Viola’s manuscript concerning his studies of eight articles by Vitali is provided in the appendix.