A Museum for Mathematics
| The Garden of Archimedes
A Museum for Mathematics |
The University of Berlin, during the mid Nineteenth century, became, of all the European schools, one of the most important centres for the study of calculus, and a privileged centre of research towards a more rigorous definition of its foundations. The trend of liberating analysis from notions of geometry, of motion or intuition, found a fundamental contribution in Karl Weierstrass (1815-1897). His formulation of the concept of continuity of functions in terms of inequalities of the type "epsilon-delta", had already been approached by Riemann and was inspired by the lectures of Dirichlet.
Weierstrass started lecturing in 1659, but only much later was the relevant material collected. In 1894 it began to be published. It was essentially through his courses, which were followed by students coming from all over Germany and abroad, that the process developed and spread. Such process was striving for a new formulation of analysis according to the application of arithmetics, that Klein called "arithmetisation".
An evidence of the diffusion of the conceptions of Weierstrass in Europe is represented by the Foundations of the theory of functions of a real variable published by Ulisse Dini (1845-1918) in 1878. In the introduction, Dini thanks Schwarz, a student of Weierstrass with whom he corresponded, for the news of the new methods followed by the German mathematicians with the intention of giving the proper attention to detail to the terms and demonstration of the analysis. On this new basis, Dini set out his Foundations which were followed in 1880 by the volume Fourier's series and other analytical representations. His lectures at the University of Pisa were later revised in the treatise Lectures of infinitesimal analysis, which was released in various editions - first lithographed and then finally printed in 1907-1915. The Foundations were read by Cantor who, with Dedekind, planned a German translation that was only completed in 1892.
In 1884, the treatise of Differential calculus and principles of integral calculus was published, where Giuseppe Peano (1858-1932) compiled the lectures given by Angelo Genocchi that he followed in Torino. Genocchi was a friend and correspondent of the major mathematicians of the time: from Hermite to Schwarz, Kronecker and Weierstrass. There, Peano included important "supplements" of theorems on the existence and the differentiability of implicit functions, on the uniform continuity of functions in more variables, on integral calculus with explanations and counter examples.