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General description of the edition.

This six volume collection makes available for the first time the German text of the most important of David Hilbert's unpublished lectures on the foundations of mathematics and physics, together with a scholarly commentary. Hilbert's lectures and his personal interactions with the 'Hilbert circle' exercised a profound influence on the development of twentieth century mathematics and physics. The lecture notes presented, spanning virtually the whole of Hilbert's teaching career, document his intense engagement with the ideas of some of the central figures of modern science (among them Bernays, Boltzmann, Born, Brouwer, Cantor, Courant, Dedekind, Einstein, Frege, Heisenberg, Klein, Lie, Minkowski, Poincar沤, Russell, von Neumann, Weyl, and Zermelo), and make possible a detailed understanding of the development of his foundational work in geometry, arithmetic, logic, and proof theory, as well as in the theory of relativity, quantum mechanics and statistical physics. The lectures contain many more philosophical, foundational and methodological remarks than does Hilbert's published work. Some of the individual volumes also reprint key published works of Hilbert when these are centrally relevant to the unpublished work presented. (For example, Volume 1 reprints the first edition of Hilbert's celebrated听Grundlagen der Geometrie,听Volume 3 reprints Bernays's听Habilitationschrift听and Hilbert and Ackermann's听Grundz鸥ge der theoretischen Logik,听Volume 4 reprints Hilbert's fundamental papers on General Relativity Theory.)

Volume 1: David Hilbert's Lectures on the Foundations of Geometry, 1891-1902

Edited by Michael Hallett and Ulrich Majer.

Volume 1 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听Grundlagen der Geometrie听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.

Volume 2: David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1894-1917

Edited by William Ewald, Michael Hallett, Wilfried Sieg and Ulrich Majer

Volume 2 focuses on notes for lectures on the foundations of the mathematical sciences held by Hilbert in the period 1894-1917. They document Hilbert's first engagement with 'impossibility' proofs; his early attempts to formulate and address the problem of consistency, first dealt with in his work on geometry in the 1890s; his engagement with foundational problems raised by the work of Cantor and Dedekind; his early investigations into the relationship between arithmetic, set theory, and logic; his advocation of the use of the axiomatic method generally; his first engagement with the logical and semantical paradoxes; and the first formal attempts to develop a logical calculus. The Volume also contains Hilbert's address from 1895 which formed the preliminary version of his famous 'Zahlbericht' (1897).

Volume 3: David Hilbert's Lectures on the Foundations of Arithmetic and Logic, 1917-1933

Edited by William Ewald, Wilfried Sieg and Ulrich Majer

The bulk of Volume 3 consists of six sets of notes for lectures Hilbert gave (often in collaboration with Bernays) on the foundations of mathematics between 1917 and the early 1930s. The notes detail the increasing dominance of the metamathematical perspective in Hilbert's treatment, i.e., the development of modern mathematical logic, the evolution of proof theory, and the parallel emergence of Hilbert's finitist standpoint. The notes are mostly very polished expositions; e.g., the 1917-18 lectures are in effect a first draft of Hilbert and Ackermann's听Grundz鸥ge der theoretischen Logik听(1928), reprinted in this Volume. They are thus essential for understanding the development of modern mathematical logic leading up to Hilbert and Bernays's听Grundlagen der Mathematik听(1934, 1938). Also included is a complete version of Bernay's听Habilitationschrift听of 1918, only partially published in 1926.

Volume 4: David Hilbert's Lectures on the Foundations of Physics, 1898-1914: Classical, Relativistic and Statistical Mechanics

Edited by Ulrich Majer, Tilman Sauer and Klaus B艩rwinkel

The first part of Volume 4 documents Hilbert's efforts in the period 1898-1910 to base all known physics (including thermody颅namics, hydrodyna颅mics and electrodynamics) on classical mechanics. This period closes with a lecture course 'Mechanik der Kontinua' (1911), in which Hilbert considers the consequences of the new principle of special relativity for our understanding of physics. The second part starts with the lecture course 'Kinetische Gastheorie' (1911/12), which introduces a new approach to problems of statistical physics. The lecture course 'Molekular颅theorie der Materie' (1913) deals with a topic that was of great importance to Hilbert, returning to it repeatedly. The last lecture course contained in this volume, 'Statistische Mechanik' (1922) presents a very perceptive comparison of the dif颅ferent approaches of Max颅well, Boltzmann, Gibbs etc. to the foundational problems of statistical physics. It is a paradigm of logical analysis and conceptual clarity.

Volume 5: David Hilbert's Lectures on the Foundations of Physics, 1915-1927: Relativity, Quantum Theory and Epistemology

Edited by Ulrich Majer, Tilman Sauer and Heinz-J鸥rgen Schmidt

This Volume has three sections, General Relativity, Epistemological Issues, and Quantum Mechanics. The core of the first section is Hilbert's two semester lecture course on 'The Foundations of Physics' (1916/17). This is framed by Hilbert's published 'First and Second Communications' on the 'Grundlagen der Physik' (1915, 1917). The section closes with a lecture on the new concepts of space and time held in Bucharest in 1918. The epistemological issues concern the principle of causality in physics (1916), the intricate re颅lation between nature and mathematical knowledge (1921), and the subtle question whether what Hilbert calls the 'world equations'' are physically complete (1923). The last section deals with quantum theory in its early, advanced and mature stages. Hilbert held lecture courses on the mathematical foundations of quantum theory twice, before and after the breakthrough in 1926. These documents bear witness to one of the most dramatic changes in the foundations of science.

Volume 6: David Hilbert's Notebooks and General Foundational Lectures

Edited by William Ewald, Michael Hallett, Wilfried Sieg and Ulrich Majer

This Volume contains a selection of material exhibiting many of Hilbert's philosophical and foundational views on particular theories and the exact sciences in general, drawn from his private notebooks and from lectures for more general audiences held in the 1920s.