Peano, Giuseppe
Peano, Giuseppe
1858-1932, Italian mathematician. Professor of mathematics at the University of Turin, 1890-1932. His work in mathematical logic marks a transition stage between the old algebra of logic and the newer methods. It is inferior to Frege’s by present standards of rigor, but nevertheless contains important advances, among which may be mentioned the distinction between class inclusion (?) and class membership (?) — which had previously been confused — and the introduction of a notation for formation of a class by abstraction (q. v.). His logical notations are more convenient than Frege’s, and many of them are still in common use.
Peano’s first publication on mathematicil logic was the introduction to his Calcolo Geometrico, 1888. His postulates for arithmetic (see arithmetic, foundations of) appeared in his Arithmetices Principia (1889) and in revised form in Sul concetto di numero (Rivista di Matematica, vol. 1 (1891)), and were repeated in successive volumes (more properly, editions) of his Formulaire de Mathematiques (1894-1908). The last-named work, written with the aid of collaborators, was intended to provide a reduction of all mathematics to symbolic notation, and often the encyclopedic aspect was stressed as much as, or more than, that of logical analysis.
Peano is known also for other contributions to mathematics, including the discoverv of the area filling curve which bears his name, and for his advocacy of Latino sine flexione as an international language. — A.C.
P. E. B. Jourdain,
Giuseppe Peano, The Quarterly Journal of Pure and Applied Mathematics, vol. 43 (1912), pp. 270-314.
Giuseppe Peano, supplement to Schola et Vita, Milan, 1928.
U. Cassina,
Vita et opera de Giuseppe Peano, Schola et Vita, vol. 7 (1932), pp. 117- 148.
E. Stamm,
Jozef Peano, Wiadomosci Matematyczne, vol. 36 (1933). pp. 1-56.
U. Cassina,
L’opera scientifica di Giuseppe Peano, Rendiconti del Seminario Matematico e Fisico di Milano, vol. 7 (1933), pp. 323-389.
U. Cassina,
L’oeuvre philosophique de G. Peano, Revue de Metaphysique et de Morale, vol. 40 (1933), pp. 481-491.