David Hilbert’s Lectures on the Foundations of Geometry 1891–1902

This volume contains six sets of notes for lectures on the foundations of geometry held by Hilbert in the period 1891-1902. It also reprints the first edition of Hilbert’s celebrated Grundlagen der Geometrie of 1899, together with the important additions which appeared first in the French translation of 1900. The lectures document the emergence of a new approach to foundational study (the ‘axiomatic method’), which concentrates on assessing the logical weight of central propositions by exploiting to the full the method of independence proofs by modelling. This culminates in the lectures of 1898/1899 (the immediate precursor of the 1899 monograph) and 1902. The lectures contain many reflections and investigations which never found their way into print.

• 01A55, 01A60, 01A75, 03-03, 51-03, 03A05, 00A30
• Hilbert
• analysis
• foundations
• geometry
• philosophy of mathematics

From the reviews:

"This book represents … Hilbert’s work on the foundations of mathematics, understood in a broad sense as an enterprise impinging on all exact knowledge. … The editors have clearly taken great care in their handling of this source material, making this important collection of texts finally accessible to the wider community of historians of mathematics." (David E. Rowe, Historia Mathematica, Vol. 34, 2007)

• McGill University Dept. Philosophy, Montreal, Canada

  Michael Hallett

• Universität Göttingen Philosophisches Seminar, Göttingen, Germany

  Ulrich Majer