From Kant to Hilbert

This two-volume set contains extracts from principal texts on the foundations of mathematics, written from the late 18th to the early 20th centuries. Much of the work has been translated into English for the first time.

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This collection represents a comprehensive selection of the most important works on the foundations of mathematics in the period from Kant to Hilbert. Kant's Critique of Pure Reason is taken as the starting point of the modern period of mathematics while Hilbert was the last great mainstream mathematician to pursue important nineteenth century ideas. The selections are representative samples of foundational work in each of the main branches of mathematics: algebra and geometry; number theory and analysis; logic and set theory, with narratives to show how they are linked. Classic works by Bolzano, Riemann, Hamilton, Dedekind, and Poincare are reproduced in reliable translations and many selections from writers such as Gauss, Cantor, Kronecker, and Zermelo are here translated for the first time. The contents of these two volumes includes the following: George Berkeley (1685 - 1753), Immanuel Kant (1724 - 1804), Augustus De Morgan ( 1806 - 1871), Georg Cantor (1845 - 1918), David Hilbert (1862 - 1943), and Godfrey Harold Hardy (1877 - 1947). This book is intended for undergraduate and graduate students in the philosophy of mathematics or history of mathematics.