Tra Hilbert e Poincaré. Matematica: intuizione o rigore?

Telloni, Agnese Ilaria ; Toffalori, Carlo

Matematica, cultura e società, Série 1, Tome 4 (2019) no. 2, pp. 159-178

Résumé

We report and comment on the controversy of the early twentieth century between Hilbert and Poincaré on the importance of logic and set theory in the development of mathematics. We take it as a starting pointfor discussing the longstanding dichotomy between intuition and rigor in the progress of mathematics, but also for emphasizing, through the quotation of various passages and famous aphorisms of the two scientists and of some other authoritative colleagues of them, such as Weyl, Weil, Brouwer, Klein, Kovalevskaya, Severi, Enriques, the surprising verve that various great mathematicians show as writers – not only of theorems, but also of themselves and their ideas.