Giuseppe Peano and formalism

The term formalism is often used ambiguously in the study of the sciences. It can refer to three broad senses: logical, mathematical, or philosophical. Giuseppe Peano (1858-1932) contributed to all three facets of formalism, although his influence was stronger in logic and mathematics than in the philosophy of mathematics.

A mathematician attuned to social causes -----------------------------------------------------

Giuseppe Peano (1858-1932) was born in Spinetta, a small village in Piedmont, in northern Italy. In 1880, he defended a thesis in geometry and became assistant to Angelo Genocchi in his course on infinitesimal analysis before being appointed professor of infinitesimal calculus at the University of Turin. Outside his scientific work, Peano was attuned to social causes, particularly those of women students and female factory workers. For example, when the strike by the female workers of the Bass cotton mill spread to Turin, Peano supported the strikers' cause and, as a sign of sympathy, welcomed them, through the Chamber of Labour, to his villa in Cavoretto on 6 May 1906. He also led educational initiatives for secondary school teachers and for children, for whom he wrote a book of fun and practical arithmetic games (see the end of this article.

Giuseppe Peano around 1910.

Giuseppe Peano's most notable mathematical results include his research on the concepts of geometric curve and surface, and his contributions to the foundations of differential and integral calculus. Two constructions, however, remain particularly well known to the general public today: first, the Peano curve, an example of a space-filling curve. He set out its principle in a short four-page article written in French in the Mathematische Annalen under the title Sur une courbe, qui remplit toute une aire plane (On a curve that fills an entire plane area), published in 1890. He summarized the article as follows: "two functions x and y are determined, single-valued and continuous, of a (real) variable t, which, as t varies over the interval (0, 1), take on every pair of values such that 0 ≤ x ≤ 1, 0 ≤ y ≤ 1. If, as is customary, continuous curve is used to denote the locus of points whose coordinates are continuous functions of a variable, one thus obtains an arc of a curve that passes through every point of a square." David Hilbert in 1896, then Henri Lebesgue in 1904, drew on this to create other models of space-filling curves (see the curves below).

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Giuseppe Peano and formalism | Tangente

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