An arithmetician against arithmetization: the principles of Charles Hermite (Q2849097)

The author is a capacity on the history of number theory, in particular Fermat, Gauss, Dirichlet and Hermite. This paper does not go much into Hermite's mathematics but into his philosophical, for the most part anti-modernistic, positions with respect to the foundations of mathematics. In extensive quotes (mostly from his published correspondence with the Italian A. Genocchi and with Dutch T. J. Stieltjes), Hermite's doubts about the accomplishments and the pedagogical merits of non-Euclidean geometry, set theory, and real function theory are documented. Particular emphasis is given to the viewpoint -- rarely found before in the literature -- that Hermite considered mathematics to be an observational (natural) science. The author makes sensitive allusions to the political and religious background of some of Hermite's remarks. She does not hide the fact that several of his positions with respect to the ongoing process of arithmetization and the loss of intuitiveness in mathematics are contradictory or still in need of full clarification and investigation.NEWLINENEWLINEFor the entire collection see [Zbl 1236.03004].