David Hilbert and the Axiomatization of Physics (1898 1918)

David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions.

Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert's intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert's overall scientific world-view.

This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.

Presents a totally fresh and comprehensive picture of Hilbert's intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon

Contenu
1: Late Nineteenth Century Background.- 2: Axiomatization in Hilbert's Early Career.- 3: The Axiomatic Method in Action: 1900-1905.- 4: Minkowski and Relativity: 19071909.- 5: From Mechanical to Electromagnetic Reductionism: 19101914.- 6: Einstein and Mie: Two Pillars of Hilbert's Unified Theory.- 7: Foundations of Physics: 19151916.- 8: Hilbert and GTR: 19161918.- 9: Epilogue.- Appendix 1: General Chronology of Events Mentioned in the Text.- Appendix 2: Hilbert's Göttingen Courses on Physics.- Appendix 3: Seminars, Miscellaneous Lectures.- 3.A. Advanced Seminars Taught by Hilbert.- 3.B. Public Lectures by Hilbert.- 3.C. Physical lectures at the GMG and GWG by Hilbert.- 3.D. Lectures on Physical Issues at the GMG by Others.- Appendix 4: Hilbert's Physics Assistants and Doctoral Students.- 4.A. Assistants for Physics.- 4.B. Doctoral Students on Physical Topics.- Apendix 5: Letters Quoted in the Book.- Appendix 6: Items from the Hilbert Nachlass referred to in the Book.- Appendix 7: Hilbert's Axioms for Radiation Theory.- References.- Commonly Used Abbreviations.- Published and Unpublished Sources.