Archimedes

Preface. Acknowledgements and Credits. Introduction. 1: Late Nineteenth Century Background. 1.1. Hilbert's Early Career. 1.1.1 Algebraic Invariants. 1.1.2 Algebraic Number Fields. 1.1.3 Deep Roots in Tradition. 1.2. Foundations of Geometry. 1.2.1 Riemann. 1.2.2 Projective Geometry. 1.2.3 Nineteenth-Century Axiomatics. 1.2.4 Pasch and the Italian School. 1.3. Foundations of Physics. 1.3.1 Kinetic Theory, Mechanistic Foundations. 1.3.2 Carl Neumann. 1.3.3 Heinrich Hertz. 1.3.4 Paul Volkmann. 1.3.5 Ludwig Boltzmann. 1.3.6 Aurel Voss. 1.4. Mathematics and Physics in Gottingen at the Turn of the Century. 1.4.1 Felix Klein. 1.4.2 The Physicists. 2: Axiomatization in Hilbert's Early Career. 2.1. Axiomatics, Geometry and Physics in Hilbert's Early Lectures. 2.1.1 Geometry in Konigsberg. 2.1.2 Geometry in Gottingen. 2.1.3 Mechanics in Gottingen. 2.2. Grundlagen der Geometrie. 2.2.1 Independence, Simplicity, Completeness. 2.2.2 Fundamental Theorems of Projective Geometry. 2.2.3 On the Concept of Number. 2.3. The 1900 List of Problems. 2.3.1 Foundational Problems. 2.3.2 A Context for the Sixth Problem. 2.4. Early Reactions to the Grundlagen. 3: The Axiomatic Method in Action: 1900-1905. 3.1. Foundational Concerns -- Empiricist Standpoint. 3.2. Hilbert and Physics in Gottingen circa 1905. 3.3. Axioms for Physical Theories: Hilbert's 1905 Lectures. 3.3.1 Mechanics. 3.3.2 Thermodynamics. 3.3.3 Probability Calculus. 3.3.4 Kinetic Theory of Gases. 3.3.5 Insurance Mathematics. 3.3.6 Electrodynamics. 3.3.7 Psychophysics. 3.3.8 A post-1909 addendum. 3.4. The Axiomatization Program by 1905 -- Partial Summary. 4: Minkowski and Relativity: 1907-1909. 4.1. The Principle of Relativity. 4.2. The Basic Equations of Electromagnetic Processes in Moving Bodies. 4.2.1 Three Meanings of "Relativity". 4.2.2 Axioms of Electrodynamics. 4.2.3 Relativity and Mechanics. 4.2.4 Relativity and Gravitation. 4.3. Space and Time. 4.3.1 Groups of Transformations. 4.3.2 Empirical Considerations. 4.3.3 Relativity and Existing Physical Theories. 4.4. Max Born, Relativity, and the Theories of the Electron. 4.4.1 Rigid Bodies. 4.5. Minkowski, Axiomatics and Relativity -- Summary. 5: Mechanical to Electromagnetic Reductionism: 1910-1914. 5.1. Lectures on Mechanics and Continuum Mechanics. 5.2. Kinetic Theory. 5.3. Radiation Theory. 5.3.1 Hilbert and Kirchhoff's Law: 1912. 5.3.2 Reactions and Sequels: Early 1913. 5.3.3 Pringsheim's Criticism: 1913. 5.3.4 Hilbert's Final Version: 1914. 5.3.5 Kinetic and Radiation Theory: General Remarks. 5.4. Structure of Matter and Relativity: 1912-1914. 5.4.1 Molecular Theory of Matter - 1912-13. 5.4.2 Electron Theory: 1913. 5.4.3 Axiomatization of Physics: 1913. 5.4.4 Electromagnetic Oscillations: 1913-14. 5.5. Broadening Physical Horizons - Concluding Remarks. 6: Einstein and Mie: Two Pillars of Hilbert's Unified Theory. 6.1. Einstein's Way to General Relativity. 6.2. Mie's Electromagnetic Theory of Matter. 6.2.1 First and Second Installment: Early 1912. 6.2.2 Third Installment: November 1912. 6.3. Contemporary Debates on Gravitation. 6.4. Born's Formulation of Mie's Theory. 6.5. The Background to Hilbert's Unified Theory -- Summary. 7: Foundations of Physics: 1915-1916. 7.1. Einstein in Gottingen -- Summer of 1915. 7.2. Hilbert's Unified Theory -- General Considerations. 7.3. Hilbert's Communication to the GWG -- November 1915. 7.3.1 Axioms and Basic Assumptions. 7.3.2 The Hamiltonian Function and the Field Equations. 7.3.3 Summary and Additional Considerations. 7.4. The Hilbert-Einstein Correspondence and Einstein's Four Communications -- November 1915. 7.5. Hilbert's Unified Theory: First Printed Version -- March 1916. 7.6. Foundations of Physics -- Summary. 8: Hilbert and GTR: 1916-1918. 8.1. Mie's Reaction. 8.2. Einstein's Reaction. 8.3. Hilbert Teaches GTR -- 1916-1917. 8.4. Hilbert's Second Communication -- December 1916. 8.5. Gottingen Debates on Energy Conservation in GTR -- 1918. 8.6. Later Talks and Writings on GTR. 8.7. Last Versions of Hilbert's Theory. 8.8. Hilbert's Way to GTR -- Summary and Concluding Remarks. 9: Epilogue. 9.1. Foundations of Quantum Theory. 9.2. The Culture of "Nostrification" in Gottingen. 9.3. General Relativity and Geometry. 9.4. Hilbert and Participant Histories of GTR. 9.5. Hilbert and Physics -- Concluding Remarks. Appendix 1: General Chronology of Events Mentioned in the Text. Appendix 2: Hilbert's Gottingen 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. Appendix 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. Index.