From Kant to Hilbert. A source book in the foundations of mathematics. Two volume set. (English) Zbl 0859.01002

Oxford: Clarendon Press. xviii, 1340 p. (1996).
These two volumes contain 89 selections taken from 28 authors: from G. Berkeley, C. MacLaurin, Jean Le Rond d’Alembert, I. Kant via Gauss, Riemann, Helmholtz, Cantor, Poincaré up to Brouwer, Zermelo, Bourbaki. There are 56 (English) translations. 36 appear for the first time being elaborated by the editor. He added longer, useful introductions to every of the 28 authors and introductory notes to different selections of one and the same author. He himself admits that his collections cannot pretend to offer a complete picture of the nineteenth-century foundations of mathematics. But it is certainly well prepared and paves the way to a profound study of the concerned subject. The selections give indeed (p. 6) an adequate representation to foundational work in each of the main branches of mathematics and show the interconnections between algebra and geometry, number theory and analogies, and of all of these subjects to logic and set theory. The editor should be praised for saying that such a compilation can serve as a general introduction to the subject, but that it cannot substitute for a thorough knowledge of the original documents.


01A05 General histories, source books

Biographic References:

Kant, I.; Hilbert, D.