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APPENDIX 1 GENERAL CHRONOLOGY OF EVENTS MENTIONED IN THE TEXT The following seven appendixes summarize some of the relevant information appearing in the foregoing chapters. The information contained here has been gathered from various sources, which are mostly documented in the main text itself. The most important sources for unpublished material include the manuscripts of Hilbert’s lecture notes at the Lesezimmer of the mathematical institute in Göttingen as well as other documents in Hilbert’s Nachlass; miscellaneous announcements in the JDMV and in the Physikalische Zeitschrift, and source books such as Biermann 1988 or Lorey 1916. I have made the necessary efforts to ensure that the information appearing here be as comprehensive as possible in the various categories considered, but it is indeed conceivable that additional sources may add further items to those appearing here. 1844: 1854: 1859: 1860: 1861: 1862: 1867: 1870: 1871: 1872: 1876: 1877: 1881: 1882: 1883: 1885: 1886: Grasmann’s Ausdehnungslehre. Riemann’s “On the Hypotheses which Lie at the Foundations of Geometry”. Kirchhoff’s law of emission and absorption. Maxwell’s first paper on kinetic theory. Clebsch and Carl Neumann create the Mathematische Annalen. January 23 – Hilbert is born in Königsberg. Boltzmann’s first article on kinetic theory. Carl Neumann’s inaugural lecture in Leipzig, on the basic principles of physical theories. Klein, Privatdozent in Göttingen, publishes his first paper on non-Euclidean geometry. Klein’s Erlanger Programm. Dedekind’s Stetigkeit und irrationale Zahlen. Boltzmann formulates the Boltzmann Equation. Lodschmidt publishes his objections on kinetic theory and its reliance on the atomistic hypothesis. Boltzmann publishes his statistical interpretation of entropy. Riecke succeeds Weber in Göttingen. Pasch’s Vorlesungen über neuere Geometrie. Voigt arrives in Göttingen as professor for theoretical physics. Hilbert completes his dissertation under Lindemann. Trip to Paris and Leipzig. Minkowski moves to Bonn (until 1894). Felix Klein arrives back in Göttingen. 445 446 1888: 1890: 1891: 1892: 1893: 1894: 1895: 1896: 1897: 1898: 1899: 1900: APPENDIX 1 Hilbert proves the finite basis theorem for the general case. Dedekind’s Was sind und was sollen die Zahlen? Poincaré’s Sorbonne lectures on electricity and optics (also in 1890-91). DMV created by initiative of Cantor. Hertz’s formulation of Maxwell’s electrodynamics. Hilbert’s first course on geometry in Königsberg. DMV meeting in Halle. Wiener lectures on the Foundations of Geometry. Veronese’s work on non-Archimedean geometries. Peano’s axioms of arithmetic. Klein’s failed attempt to bring Hilbert to Göttingen. Weber came instead. October 12 - Hilbert marries Käthe Jarosch. Hilbert’s summary article on algebraic invariants. Mach’s Science of Mechanics. Early discussions on the EMW project - Meyer, Weber, Klein. Minkowski returns to Königsberg. Nernst appointed ordinary professor at Göttingen. He heads the newly created Institute for Physical Chemistry. Hertz’s Principles of Mechanics. March - Hilbert arrives in Göttingen. Cantor’s Beiträge zur Begründung der tranfiniten Mengenlehre, that summarized and helped spreading his theory. Dyck and Burkhardt join the editorial committee of the EMW. Lorentz’s article on the electrodynamics of moving bodies. Zermelo’s debate with Boltzmann on kinetic theory. Minkowski moves to Zurich. Wien’s law of radiation. Hilbert’s Zahlbericht. Boltzmann’s Lectures on the Principles of Mechanics. Wiechert and Zermelo join the Göttingen faculty. Hilbert’s first course on mechanics in Göttingen. Schur’s results on projective geometry. First articles of the EMW published: Schubert on the foundations of arithmetic, Netto on combinatorics and Pringsheim on irrational numbers and convergence. Hilbert elected head of the DMV. Hilbert’s first course on geometry in Göttingen. Weber-Gauss monument unveiled. Grundlagen der Geometrie is published. Riecke establishes the Physikalische Zeitschrift and acts as its first editor. September - joint meeting of the DMV-GDNA in Munich. Boltzmann’s popular lecture on recent developments in physics. Hilbert is present in the audience. December – Frege and Hilbert start their correspondence on the meaning of axiomatization. Hilbert’s Über den Zahlbegriff. August – ICM in Paris. Hilbert presents his list of twenty-three problems. Volkmann’s textbook on theoretical physics. GENERAL CHRONOLOGY 1901: 1902: 1903: 1904: 1905: 1906: 1907: 1908: 1909: 1910: 1911: 1912: 447 Planck’s law of radiation. September 18 - 150th anniversary of the GWG. In the keynote address, Hilbert analyzes the conditions of validity of the Dirichlet Principle. November 18 – Hilbert presents his solution of the fifth problem for the plane. Schwarzschild appointed professor of astronomy and director of the observatory in Göttingen. Voss’s EMW article on the principles of mechanics. Husserl comes to Göttingen. Hilbert refuses an offering to take Fuchs’ chair in Berlin. Minkowski comes to Göttingen. Hilbert starts working on linear integral equations. Moore teaches GdG in Chicago opening the way to postulational analysis in USA. Rusell’s paradox published. ICM in Heidelberg. Hilbert’s “On the Foundations of Logic and Arithmetic”. Runge, Prandtl and Herglotz arrive in Göttingen. Lorentz’s EMW article on electron theory. Hilbert’s lectures on axiomatization, including physics. Hilbert and Minkowski’s seminar on electron theory. Einstein’s annus mirabilis. January - Poincaré’s article on the dynamics of the electron, including a section on gravitation. New building of the physics institute inaugurated in Göttingen. Planck’s textbook on radiation. Boltzmann and Nabl’s EMW article on kinetic theory. Einstein adopts the “equivalence principle” as fundamental for any relativistic treatment of gravitation. November - Minkowski’s first talk on electrodynamics at the GMG. December 21 - Minkowski’s second talk on electrodynamics at the GMG. Sketch of a relativistic theory of gravitation. Zermelo’s proof of the well-ordering theorem. ICM in Rome: Hilbert calls for a “methodologically unified reorganization of algebra and analysis”, using his theory of integral equations. Lorentz lectures on black body radiation. September 21 - GDNA meeting in Köln. Minkowski’s “Space and Time”. January 12 – Minkowski’s death. Hilbert’s proof of Waring’s conjecture. Landau appointed successor of Minkowski. Hilbert is awarded the second Bolyai Prize. Born’s articles on rigidity in STR (partly based on Minkowski’s ideas). Sommerfeld’s two-part article on Minkowski’s four-vectors and relativity. Hilbert’s first course on kinetic theory. First Solvay Conference in Brussels. January 9 - Mie’s theory of matter, first installment. 448 1913: 1914: 1915: APPENDIX 1 June 7 - Mie’s theory of matter, second installment. Hilbert publishes his article on kinetic theory. Paul and Tatyana Ehrenfest’s EMW article on statistical mechanics. Ewald appointed as Hilbert’s first assistant for physics. August: Einstein takes his position at the ETH Zurich. Reencounters with Grossman and starts working seriously on general relativity. Hilbert’s first course on radiation theory. September – GDNA meeting in Münster. Hilbert lectures on radiation theory November 2 – Mie’s theory of matter, third installment. December – Born and Carathéodory discuss with Pringsheim the contents and implications of Hilbert’s work on radiation theory. Hilbert publishes several versions of his approach to radiation theory. Pringsheim publishes two critical articles. April – Hilbert corresponds with Planck on radiation theory. May-June – Einstein and Grossmann publish their Entwurf theory. September – 85th GDNA meeting in Vienna. Einstein discusses several existing theories of gravitation. December 16 – Born’s version of Mie´s theory. Hilbert’s publishes the final version of his radiation theory. April – Einstein moves to Berlin. April – Kinetic theory week in Göttingen. Lectures by Planck, Debye, Nernst, Von Smoluchowski, Sommerfeld. August – The Great War breaks out. October – Aufruf an die Kulturwelt - Neither Einstein nor Hilbert among the signees. November – Einstein’s “On the Formal Foundations of the General Theory of Relativity”. An elaborate, comprehensive version of the Entwurf theory. Spring – Emmy Noether arrives in Göttingen. June 29 to July 7 – Einstein’s Wolfskehl lectures. Summer – Einstein corresponds with Paul Hertz on the ‘hole argument’. July-November – No known contact between Hilbert and Einstein. The two may have coincided for a short time at Rügen. Over the month of October, Einstein became increasingly dissatisfied with his theory, and increasingly convinced of the need to return to generally covariant field equations. November – In four successive sessions of the Berlin academy Einstein reads four papers on gravitation and relativity. November 7 – Beginning of the Hilbert-Einstein correspondence. November 18 – Einstein’s third Academy talk, with an explanation of Mercury’s perihelion deviation. November 20 – Hilbert’s lecture at the GWG on the “Foundations of Physics”. November 25 – Einstein present the final version of his gravitational field equations. GENERAL CHRONOLOGY 1916: 1917: 1918: 1921: 1922: 1923: 1924: 1925: 1926: 1927: 1930: 1943: 449 December 6 – Hilbert receive the galley proofs of his article on the proceedings of the GWG. December 20 – After a brief tension against the background of a possible priority issue over the formulation of the equation, Einstein writes a conciliatory letter to Hilbert. January – First solution of the gravitational field equations of GTR, formulated by Schwarschild’s for a special case, is communicated by Einstein at the Berlin Academy. March – First published version of Hilbert’s communication. April – Hilbert start corresponding with Russell on foundations of arithmetic. May – Einstein’s first systematic presentation of GTR published in Annalen der Physik. Hilbert teaches GTR at Göttingen. October – Einstein publishes his variational derivation of the gravitational field equations. December 23 – Hilbert’s second communication at the GWG. Spring – Einstein publishes the first semi-popular presentation of GTR Einstein’s first cosmological paper. Mathematische Zeitschrift created through the efforts of Courant and Ferdinand Springer. January – Klein lectures on the status of energy conservation in Hilbert’s theory and GTR. This is followed by a series of related lectures by Hilbert, Noether and others. Easter – Weyl’s Raum-Zeit-Materie. Bernays arrives in Göttingen to work with Hilbert on the foundations of arithmetic December – Discharged soldiers start returning from the front. Pauli completes his EMW article on GTR and moves to Göttingen to work with Born. June – Bohr’s Wolfskehl lectures on atomic structure. Hilbert’s “New Foundations of Mathematics”. Hilbert teaches a course on the mathematical foundations of quantum theory. Heisenberg completes his dissertation under Born in Göttingen. Hilbert’s GTR papers republished in the Mathematische Annalen. Hilbert and Courant’s Methoden der mathematischen Physik. Hilbert contracts pernicious anemia. Von Neumann arrives in Göttingen. December – Jordan’s article on the axiomatization of quantum mechanics. Construction of the new building for the mathematical institute begins. Hilbert, von Neumann and Nordheim’s paper on the foundations of quantum mechanics. Hilbert’s official retirement. Autumn - Hilbert nominated honorary citizen of Königsberg. Lectures on Naturerkennen und Logik. February 14 – Hilbert dies in Göttingen. APPENDIX 2 HILBERT’S GÖTTINGEN COURSES ON PHYSICS (and related fields): 1895-1927 In compiling the following list I have relied on several documents, mainly the Nachlassverzeichnisse at the mathematical institute (HLN) and at the Handschriftenabteilung, SUB Göttingen (DHN). These documents, however, omit several items registered in the printed version of the Göttingen Vorlesungsverzeichnisse (GVV) for the years in question. In addition, DHN 520 contains another list of Hilbert’s courses over 46 years, between 1886 and 1932. This list is complied in Hilbert’s own handwriting until WS 1917-18. It indicates, in particular, that while at Königsberg, Hilbert taught one course on Hydrodynamics in SS 1887 (notes preserved in DHN 522). Needless to say, there are also many additional lectures throughout the years on more purely mathematical topics not included here, and ranging from geometry, to integral and differential calculus, to invariants, number theory, set theory and logic. I have added in parentheses a reference to the existing notes for the lecture notes of most courses and their locations. WS 1895/96 SS 1896 SS 1898 SS 1899 WS 1900/01 SS 1901 WS 1901/02 SS 1902 WS 1902/03 SS 1903 WS 1903/04 WS 1904/05 SS 1905 SS 1905 WS 1905/06 WS 1905/06 SS 1906 Partial Differential Equations (Notes by Nosse - HLN) Ordinary Differential Equations (GVV) Mechanics (DHN) Variational Calculus (DHN) Partial Differential Equations (DHN) Linear Partial Differential Equations (Notes by A. Andrae - HLN) Potential Theory (Notes by A. Andrae - HLN) Selected Topics in Potential Theory (Notes by A. Andrae - HLN) Continuum Mechanics - Part I (Notes by Berkowski - HLN) Continuum Mechanics - Part II (Notes by Berkowski - HLN) Partial Differential Equations (Notes by Prinz & TieffenbachHLN) Variational Calculus (Notes by E. Hellinger - HLN) Logical Principles of Mathematical Thinking (and of Physics) (Notes by E. Hellinger – HLN; Notes by Born - DHN) Integral Equations (Notes by E. Hellinger - HLN) Partial Differential Equations (Notes by E. Hellinger - HLN) Mechanics (Notes by E. Hellinger - HLN) Integral Equations (Notes by E. Hellinger - HLN) 450 COURSES ON PHYSICS WS 1906/07 SS 1907 WS 1909/10 SS 1910 WS 1910/11 SS 1911 WS 1911/12 SS 1912 SS 1912 SS 1912 WS 1912/13 WS 1912/13 WS 1912/13 SS 1913 WS 1913/14 SS 1914 WS 1914/15 SS 1915 WS 1915/16 SS 1916 WS 1916/17 SS 1917 SS 1918 WS 1918/19 HS 1919 WS 1920 SS 1920 WS 1920-21 SS 1921 SS 1921 SS 1922 451 Continuum Mechanics (Notes by E. Hellinger - HLN) Differential Equations (Notes by E. Hellinger - HLN) Partial Differential Equations (Notes by R. Courant - HLN) Selected Chapters in the Theory of Partial Differential Equations (Notes by R. Courant - HLN) Mechanics (Notes by F. Frankfurther, W. Behrens - HLN) Continuum Mechanics (Notes by E. Hecke - HLN) Statistical Mechanics (Notes by E. Hecke - HLN) Radiation Theory (HLN) Ordinary Differential Equations (HLN) Mathematical Foundations of Physics (GVV) Molecular Theory of Matter (HLN) Partial Differential Equations (Notes by B. Baule - HLN) Mathematical Foundations of Physics (GVV) Foundations of Mathematics (and the axiomatization of Physics) (GVV) Electron Theory (HLN) Electromagnetic Oscillations (HLN) Analytical Mechanics (GVV) Exercises in Mechanics (together with H. Weyl) (GVV) Statistical Mechanics (Notes by L.Lange - HLN) Differential Equations (GVV) Lectures on the Structure of Matter (GVV) Structure of Matter (Born’s Theory of Crystals) (HLN) Differential Equations (HLN) Partial Differential Equations (HLN) Foundations of Physics I (General Relativity) (HLN) Foundations of Physics II (General Relativity) (Notes by R. Bär – HLN; Hückel - EHN) Electron Theory (Notes by H. Humm - HLN) Ordinary Differential Equations (GVV) Space and Time (Notes by P. Bernays – HLN; E. Hückel - EHN) Partial Differential and Integral Equations (GVV) Nature and Mathematical Knowledge (Notes by P. Bernays – HLN. Special Autumn Semester) Mechanics (GVV) Higher Mechanics and the New Theory of Gravitation (Notes by A. Kratzer – HLN; E. Hückel - EHN) Mechanics and the New Theory of Gravitation (Notes by A. Kratzer – HLN; E. Hückel - EHN) Einstein’s Gravitation Theory (GVV) Basic Principles of the Theory of Relativity (Notes by P. Bernays HLN) – for students of all faculties On Geometry and Physics (Partial Notes by E. Hückel – EHN) Statistical Mechanics (Notes by L. Nordheim - HLN) 452 WS 1922/23 SS 1923 WS 1923/24 SS 1924 WS 1926/27 SS 1930 WS 1930/31 WS 1931/32 APPENDIX 2 Mathematical Foundations of Quantum Theory (Notes by L. Nordheim, G. Heckhausen - HLN) Knowledge and Mathematical Thought (Notes by W. Ackermann HLN) – for students of all faculties Our Conception of Gravitation and Electricity (generally understood) (GVV) On the Unity of Science (HLN) Mechanics and Relativity Theory (Notes by L. Nordheim - HLN) Mathematical Methods of Quantum Theory (Notes by L. Nordheim - HLN) Mathematical Methods of Modern Physics Nature and Thought Philosophical Foundations of Modern Natural Science APPENDIX 3 SEMINARS, MISCELLANEOUS LECTURES The main sources of information for lists 3.C and 3.D are the periodical announcements of mathematical courses and activities at the various German universities reported in the relevant sections of the JDMV. Additional information concerning these, as well as the other two sections, appears in various documents in DHN, some journals quoted in the text, and in the Vorlesungsverzeichnisse of the University of Göttingen. 3.A. ADVANCED SEMINARS TAUGHT BY HILBERT: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Mechanics (with Klein) 1896 (?) Stability Theory (with Minkowski) SS 1903 Exercises in Mechanics (with Minkowski) SS 1904 Mechanics WS 1904-05 Electron Theory (with Minkowski et al) SS 1905 The Equations of Electrodynamics (with Minkowski) SS 1907 Hydrodynamics ??? Electrodynamics ??? Kinetic Theory of Gases 1912 Structure of Matter (with Debye) WS 1914-15 to SS 1920 Structure of Matter WS 1920-21 Structure of Matter (with Born) SS 1921 to SS 1928 Theoretical and Math. Physics (with Born and Herglotz) WS 1927/28 3.B. PUBLIC LECTURES BY HILBERT: 1. 2. 3. 4. 5. 6. 7. 8. Stability Theory Maxwell’s Theory of Gases Statistical Mechanics On Nernst’s Law of Heat Space and Time On the Laws of Chance Nature and Mathematical Knowledge The Knowledge of Nature and Logic 453 (Kassel) 1903 1912 1912 1913 (Bucharest) 1918 1920 (Copenhagen) 1921 (Königsberg) 1930 454 APPENDIX 3 3.C. PHYSICAL LECTURES AT THE GMG AND GWG BY HILBERT: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. Continuum Mechanics Feb. 24, 1903 Continuum Mechanics Aug. 4, 1903 The relations between variational principles and the theory of partial differential equations, with applications to the integral principles of mechanics. Jan. 18, 1910 Kinetic theory of gases Dec 19, 1911 Axiomatic Foundations of Physics (Ferienkurs for high-school teachers) April 15-27, 1912 Theory of Radiation July 30, 1912 Theory of Radiation Jan. 21, 1913 Theory of Radiation July 28, 1914 The Fundamental Equations of Physics (General Relativity) Nov. 16, 1915 Foundations of Physics – First Part November 20, 1916 Foundations of Physics December 4, 1915 Theory of Invariants and the Energy Principle Jan. 25, 1916 The Causality Principle in Physics Nov. 21 & 28, 1916 Foundations of Physics – Second Part Dec. 23, 1916 Non-Euclidean Geometry and the new Gravitation Theory Jan. 23, 1917 Laue’s Theorem June 12, 1917 Reply to Klein’s “On Hilbert’s first note on the Foundations of Physics” Jan. 29, 1918 The Energy Principle for the Motion of Planets in the New Theory of Gravitation June 4, 1918 On Weyl’s Communication (May 2, 1918) to the Berlin Academy “The Energy Principle in the General Theory of Relativity” July 15, 1918 3.D. LECTURES ON PHYSICAL ISSUES AT THE GMG BY OTHERS: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. On the Axioms of Vector Addition (R. Schimmack) Molecular Theory of Heat Conduction (G. Prasad) Capillarity (H. Minkowski) Linear Heat Conduction in Surfaces (G. Prasad) Maxwell’s Work on Stress Systems (Klein) Euler’s Equations of Hydrodynamics (Minkowski) Electromagnetic Quantity of Motion (Abraham) Gibb’s Thermodynamical Surfaces (H. Happel) Variational Principles in Electrodynamics (Schwarzschild) Can the Electron Reach the Speed of Light (P. Hertz) On a Seminar on Hydrodynamics and Hydraulics (Klein) Motion of a Material Particle on a Uniformly Moving Plane (P. Ceresole) June 9, 1903 June 9, 1903 June 23, 1903 June 23, 1903 June 23, 1903 June 28, 1903 July 14, 1903 Dec. 8, 1903 Jan. 26, 1904 Jan. 26, 1904 Feb. 9, 1904 May 17, 1904 SEMINARS ON PHYSICS 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 455 On the Elasticity of the Earth (G. Herglotz) June 28, 1904 On Sommerfeld’s Works on Electron Theory (G. Herglotz) Dec. 6, 1904 Motion of a Fluid with Little Friction (L. Prandtl) Dec. 13, 1904 On a Talk by Poincaré on n the Future of Mathematical Physics (C.H. Müller) Jan. 24, 1905 On Gases ans Vapors (L. Prandtl) May 23, 1905 On Poincaré’s Published Lectures on Mathematical Physics (M. Abraham) Feb. 6, 1906 Poincaré’s Research on Rotating Fluid Masses (H. Müller) Feb. 13, 1906 On Gibb’s Book on Statistical Mechanics (Zermelo) Feb. 20, 1906 Graphical Methods in Mechanics and Physics (C. Runge) Feb. 27, 1906 On Painlevé’s Work on the Foundations of Mechanics (Carathéodory) May 28, 1906 On W. Nernst’s “On Chemical Equilibrium” (Minkowski) June 26, 1906 Problems of Aeronavigation (Prandtl & Wiechert) Oct. 30, 1906 The Mathematical Theory of Elasticity (C.H. Müller) Nov. 6, 1906 On Botzmann’s H-Theorem (P. Ehrenfest) Nov. 13, 1906 The Evolution of the Theory of Radiation through the Works of Lorentz, Rayleigh, W. Wien and Planck (Minkowski) Dec 1, 1906 On H. Witte’s “On the Possibility of a Mechanical Explanation of Electromagnetic Phenomena” (Abraham) Dec. 18, 1906 On the Application of Probability Calculus to Astronomy (Schwarzschild) Jan. 8, 1907 Theories of the Effects of Air Resistance (L. Prandtl) Jan. 22, 1907 Seismic Waves (E. Wiechert) Jan. 29, 1907 Statistical Stellar Astronomy (Schwarzschild) Feb. 19, 1907 Seismic Rays (G. Herglotz) May 14, 1907 Solutions of Differential Equations for Gas Spheres (Gaskügeln) (K. Schwarzschild) July 30, 1907 On the Equations of Electrodynamics (Minkowski) Nov. 5, 1907 Graphical Methods in Fluid Mechanics (C. Runge) Nov. 26, 1907 Applications of Quaternions to Electron Theory (Klein) Dec. 10, 1907 A New, Simple General Proof of the Second Law of Thermodynamics (Carathéodory) Dec. 17, 1907 An Overview of Man’s Attempts to Fly (C. Runge) March 3, 1908 Report on a Joint Seminar on Hydrodynamics (F. Klein, L. Prandtl, C. Runge, E. Wiechert) May 5, 1908 An Experiment on Stabilization of Air Balloons (L. Prandtl) May 12, 1908 On Lanchester’s Book “Aerodynamics” (C. Runge) May 12, 1908 On the Equations of Electrodynamics (Minkowski) July 28, 1908 On Recent French Research on Aviation (C. Runge) Nov. 3, 1908 Recent Works on Earth Pressure (Th. Van Kármán) Nov. 24, 1908 Theory of Earth Pressure (A. Haar & Th. Van Kármán) Dec. 8, 1908 The New Mechanics (Poincaré, Wolfskehl Lectures) April 22-28, 1909 Position Determination from and Air Balloon (Runge) May 11 & 18, 1909 456 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. APPENDIX 3 Defintion of a Rigid Body on the “Einstein-Minkowski” System of Electrodynamics (M. Born) June 8 & 15, 1909 Average Motion in the Theory of Perturbations and Applications of Probability to Astronomy (F. Bernstein) June 22, 1909 On Minkowski’s Nachlass (Electrodynamics) (M. Born) Feb. 8, 1910 On the Definition of a Rigid Body (M. Born) Juni 21, 1910 Old and New Problems in Physics (Lorentz, Wolfskehl Lectures) Summer 1910 Stable Orderings of Electrons in the Atom (L. Föppl - PhD Dissertation supervised by Hilbert) Nov. 21, 1911 On Herglotz Work on Deformable Bodies in the Theory of Relativity (M. Born) Dec. 12, 1911 The Behavior of Solid Bodies and Hooke’s Law (L. Prandtl) Jan. 16, 1912 A Newly Discovered Relation Between Elasticity of Crystals and Optical Oscillations (M. Born & Th. van Kármán) Feb. 13, 1912 Molecular Oscillations and Specific Heat (Born & van Kármán) May 14, 1912 Theory of Dispersion in Crystals (P.P. Ewald - PhD Diss.) June 4, 1912 New Works of Poincaré and Ehrenfest on the Axiomatic Foundation of Quantum Theory (Th. van Kármán) Juli 16, 1912 Statistical Mechanics (P. Hertz) Nov. 26, 1912 On Sommerfeld’s Article on the Theory of Oscillating Equations (H. Weyl) Dec. 10, 1912 Mie’s Theory of Matter (M. Born) Dec. 17, 1912 Motion of Fluids (L. Prandtl) Feb. 4, 1913 Reports on the Solvay Conference, Brussels 1911 (Born & van Kármán) Feb. 25 & March 4, 1913 Kinetic Theory Week (Debye, Nernst, Von Smoluchowski, Lorentz, Sommerfeld, Planck - Wolfskehl Lectures) May 1913 An Application of Diophantine Approximations to a Question in Statistical Mechanics (E. Hecke) May 20, 1913 On the Structure of Crystals (M. Born) June 7, 1913 Recent Work of J.J. Thomson on Canal Waves (Kanalstrahlen) (C. Runge) Juni 24, 1913 An Application of Quantum Theory to Capillarity (M. Born & R. Courant) July 1, 1913 On a Recent Work of E. Noether on Turbulences in a Fluid (Th. van Kármán) July 30, 1913 On Poincaré’s Book on Cosmogonic Hypotheses (L. Föppl) July 30, 1913 Propagation of Light in Transparent Media (W. Behrens) Nov. 4, 1913 On Mie’s theory of Matter (M. Born) Nov. 25, 1913 The Solution of an Equation of Spectroscopy (C. Runge) Dec. 2, 1913 Recent Work of Einstein and Grossmann on Gravitation (F. Böhm) Dec. 9, 1913 On Mie’s Theory of Matter (M. Born) Dec. 16, 1913 SEMINARS ON PHYSICS 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 457 Theoretical Treatment of Phenomena in Diluted Gases (B. Baule - PhD Dissertation Supervised by Hilbert) Feb 24, 1914 Review of Recently Published Works by von Smoluchowski (Brownian Movement), and Einstein (On Light Deflection; On the Determination of Molecular Dimensions) (P. Hertz) Feb. 24, 1914 Lattice Theory of Diamonds (M. Born) March 3, 1914 Intensity Distribution in Spectral Lines (P. Debye) Dec. 18, 1914 Foundation and Problems of Quantum Theory (P. Debye) Feb. 23, 1915 Dynamics of Crystal Lattices (M. Born) Feb. 25, 1915 Structure of Crystals (F. Klein, with Hilbert and Mügge) May 18, 1915 On Herglotz’s Research on Potentials in the Interior of Attracting Masses (Wiarda) June 1, 1915 On Modern Physics (A. Sommerfeld) June 15, 1915 On Gravitation (A. Einstein, Wolfskehl Lectures) June 29 – July 7, 1915 Theory of Distant Forces (Uhlich-Pirna) July 20, 1915 History of Mechanics up until Galileo (C. Müller, Wolfskehl Lectures) March 2-4, 1916 Diffusion, Brownian Movement, Colloidal Particles (Von Smoluchowski, Wolfskehl Lectures) June 20-22, 1916 Four-dimensional Vectorial Analysis (C. Runge) Dec. 5, 1916 Foundations of a Theory of Matter (G. Mie, Wolfskhel Lectures) June 5-8, 1917 On the Riemannian Curvature (Klein) Oct. 30, 1917 On the Riemannian Curvature (Klein) Nov. 6, 1917 On G. Herglotz’s Paper on Curvature and Gravitation (Klein) Dec. 4, 1917 On Liquid Crystals (M. Born) Dec. 11, 1917 On Invariants of Arbitrary Differential Expressions (E. Noether) Jan. 15, 1918 On Hilbert’s First Note on the Foundations of Physics (Klein) Jan. 22, 1918 On Einstein’s Cosmological Ideas of 1917 (F. Klein) May 7, 1918 On Quantum Theory (M. Planck, Wolfskehl Lectures) May 13-17, 1918 On Einstein’s “On Gravitational Waves” (C. Runge) Jun. 31, 1918 On Einstein’s Cosmological Ideas of 1917 (Klein) June 11, 1918 On the Three-body Problem (C. Carathéodory) June 24, 1918 Einstein’s “Energy Principle in General Relatitvity” (Klein) July 4, 1918 Hilbert’s Energy Vector (Klein) July 22, 1918 Invariant Variational Problems (E. Noether) July 23, 1918 Organic Causality (Hans Driesch, Wolfskhel Lectures) Dec. 16-19, 1918 On the Structure of the Atom (N. Bohr, Wolfskehl Lectures) June 1922 APPENDIX 4 HILBERT’S PHYSICS ASSISTANTS AND DOCTORAL STUDENTS 4.A. ASSISTANTS FOR PHYSICS: Some of the persons listed below worked with Hilbert officially under this denomination (e.g., Ewald and Landé). Others (e.g., Bernays) may be classified as such simply for having actually fulfilled this role (e.g., by maintaining Hilbert updated on recent developments on physics, by preparing the notes for his physical courses, etc.) in the period mentioned. 1. 2. 3. 4. 5. 6. 7. 8. 9. 1912-13: Paul P. Ewald 1913-14: Alfred Landé 1914-16: Louise Lange 1916-17: Richard Bär 1918-19: Paul Bernays 1920-21: Adolf Kratzer 1921-22: Erich Hückel 1922-27: Lothar Nordheim 1927-28: Eugene Wigner 4.B. DOCTORAL STUDENTS ON PHYSICAL TOPICS: 1. 2. 3. 4. 5. As listed in HGA Vol. 3, 430-432. Ludwig Föppl: “Stabile Anordnungen von Elektronen im Atom” (March 1, 1912) Hans Bolza: “Anwendungen der Theorie der Integralrechnungen auf die Elektronentheorie und die Theorie der verdünnten Gasen.” (July 2, 1913) Bernhard Baule: “Theoretische Behandlung der Erscheinungen in verdünnten Gasen.” (Feb. 18, 1914) Kurt Schelenberg: “Anwendungen der Integralgleichung auf die Theories der Elektrolysie.” (June 24, 1914) Hellmuth Kneser: “Untersuchungen zur Quantentheorie.” (July 22, 1921) 458 APPENDIX 5 LETTERS QUOTED IN THE BOOK Numbers for each entry indicate the chapter and footnote where a letter is quoted in the book, and where its exact reference can be found. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. Abraham to Stark Apelt to Grassmann Birkhoff to van der Waerden Born to Hilbert Born to Hilbert Born to Hilbert Born to Hilbert Born to Hilbert Born to Hilbert Cantor to Hilbert Carathéodory to Hilbert Carathéodory to Hilbert Dedekind to du Bois-Reymond Dingler to Hilbert Einstein to Besso Einstein to Besso Einstein to Besso Einstein to Ehrenfest Einstein to Ehrenfest Einstein to Ehrensfest Einstein to Freundlich Einstein to Freundlich Einstein to Habitch Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Hilbert Einstein to Klein Oct. 10, 1914 Sept. 3, 1845 Nov. 1, 1973 April 4, 1916 Aug. 24, 1916 Nov. 23, 1915 Aug. 3, 1909 Jan. 7, 1913 Oct. 28, 1915 Jan. 1, 1900 Dec. 12, 1912 April 4, 1913 March, 1888 Jan. 2, 1915 Dec. 10, 1915 Jan. 1, 1916 Jan. 3, 1916 Undated, 1914 April 1, 1914 Dec. 26, 1915 Aug. 1, 1913 Jan. 1, 1914 Dec. 24, 1907 Nov. 7, 1915 Nov. 12, 1915 Nov. 14, 1915 March 16, 1916 May 30, 1916 May 30, 1916 June 2, 1916 June 2, 1916 May 19, 1917 Nov. 15, 1915 Nov. 18, 1915 Dec. 15, 1917 459 (Ch. 6, # 62) (Ch. 1, # 85) (Ch. 9, # 41) (Ch. 8, # 23) (Ch. 8, # 26) (Ch. 7, # 116) (Ch. 4, # 67) (Ch. 5, # 94) (Ch. 7, # 100) (Ch. 2, # 60) (Ch. 5, # 91) (Ch. 5, # 106) (Ch. 2, # 10) (Ch. 8, # 40) (Ch. 7, # 50, 94) (Ch. 4, # 85) (Ch. 7, # 95) (Ch. 6, # 20) (Ch. 6, # 26) (Ch. 7, # 95) (Ch. 6, # 58) (Ch. 6, # 54) (Ch. 6, # 10) (Ch. 7, # 98) (Ch. 7, # 101, 104) (Ch. 7, # 56) (Ch. 7, # 108) (Ch. 8, # 30) (Ch. 8, # 76) (Ch. 8, # 30) (Ch. 8, # 93) (Ch. 8, # 55) (Ch. 7, # 108) (Ch. 7, # 111) (Ch. 9, # 97) 460 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. APPENDIX 5 Einstein to Klein Einstein to Kleiner Einstein to Lorentz Einstein to Lorentz Einstein to Lorentz Einstein to Mie Einstein to Mie Einstein to Sommerfeld Einstein to Sommerfeld Einstein to Sommerfeld Einstein to Sommerfeld Einstein to Stark Einstein to Weyl Einstein to Wien Einstein to Zangger Einstein to Zannger Einstein to Zannger Ewald to Hilbert Frege to Hilbert Hecke to Hilbert Hilbert to Einstein Hilbert to Einstein Hilbert to Einstein Hilbert to Einstein Hilbert to Einstein Hilbert to Einstein Hilbert to Frege Hilbert to Frege Hilbert to Frege Hilbert to Hurwitz Hilbert to Klein Hilbert to Klein Hilbert to Klein Hilbert to Poincaré Hilbert to Poincaré Hilbert to Poincaré Hilbert to Poincaré Hilbert to Russell Hilbert to Schwarzschild Hilbert to Schwarzschild Hilbert to Sommerfeld Hilbert to Weyl Klein to Pauli Klein to Pauli Klein to Pauli Mie to Hilbert April 12, 1917 (Ch. 8, # 61) April 3, 1912 (Ch. 4, # 86) Aug. 16, 1913 (Ch. 6, # 18) Oct. 12, 1915 (Ch. 7, # 92) Jan. 17, 1916 (Ch. 8, # 2) May 1, 1917 (Ch. 6, # 58) June 1, 1917 (Ch. 6, # 58) July 15, 1915 (Ch. 7, # 17, 89) Nov. 28, 1915 (Ch. 7, # 93, 118) Dec. 9, 1915 (Ch. 7, # 119) Summer 1910 (Ch. 4, # 85) Nov. 1, 1907 (Ch. 4, # 58) Nov. 23, 1916 (Ch. 8, # 53) Oct. 10, 1915 (Ch. 8, # 42) April, 1915 (Ch. 6, # 1, 30) July 7, 1915 (Ch. 7, # 36) Aug. 7, 1915 (Ch. 7, # 40) April 11, 1912 (Ch. 5, # 80) Jan. 6, 1900 (Ch. 2, # 95) March 7, 1916 (Ch. 2, # 86) Nov. 19, 1915 (Ch. 7, # 114) May 27, 1916 (Ch. 8, # 40) Nov. 13, 1915 (Ch. 7, # 106) May 25, 1916 (Ch. 8, # 93) March 30, 1912 (Ch. 5, # 77) Oct. 3, 1912 (Ch. 5, # 145) Jan. 15, 1900 (Ch. 2, # 96) Nov. 7, 1903 (Ch. 3, # 5) Dec. 29, 1899 (Ch.2, 93,94,98, 99) June 6, 1894 (Ch. 2, # 25) May 23, 1893 (Ch. 2, # 12) Nov. 15, 1893 (Ch. 2, # 13) Sept. 14, 1892 (Ch. 1, # 38) Nov. 6, 1908 (Ch. 5, # 13) Nov. 19, 1908 (Ch. 5, # 13) Nov. 25, 1908 (Ch. 5, # 13) May 6, 1912 (Ch. 5, # 62) April 12, 1916 (Ch. 8, # 40) July 17, 1915 (Ch. 7, # 37) Oct. 23, 1915 (Ch. 7, # 46) April 5, 1912 (Ch. 5, # 63) April 22, 1918 (Ch. 9, # 78) May 8, 1921 (Ch. 7, # 84, 87) May 8, 1921 (Ch. 8, # 129) May 8, 1921 (Ch. 8, # 49) Feb. 13, 1916 (Ch. 6, # 66; Ch. 8, # 43) LETTERS QUOTED 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. Mie to Hilbert Mie to Hilbert Mie to Hilbert Mie to Hilbert Mie to Hilbert Mie to Hilbert Mie to Stark Mie to Wien Mie to Wien Minkowski to Einstein Minkowski to Hilbert Minkowski to Hilbert Planck to Hilbert Planck to Hilbert Planck to Hilbert Planck to Hilbert Planck to Hilbert Planck to Hilbert Runge to Hilbert Sommerfeld to Hilbert Voigt to Lorentz Volkmann to Hilbert Voss to Hilbert Weber to Dedekind Feb. 29, 1916 May 8, 1917 May 16, 1917 June 10, 1917 July 2, 1917 Dec. 26, 1917 Dec. 10, 1913 Oct, 10, 1915 Feb. 6, 1916 Oct. 9, 1907 March 31, 1896 Dec. 20, 1890 Jan. 12, 1917 Feb. 8, 1917 Jan. 20, 1918 Jan. 27, 1918 April 4, 1913 April 15, 1913 May 8, 1918 May 4, 1916 May 19, 1911 Jan. 1, 1900 July 19, 1899 End of 1879 461 (Ch. 8, # 46) (Ch. 8, # 48) (Ch. 8, # 48) (Ch. 8, # 50) (Ch. 8, # 51, 52) (Ch. 8, # 50) (Ch. 6, # 62) (Ch. 8, # 42) (Ch. 8, # 42) (Ch. 4, # 5) (Ch. 1, # 46) (Ch. 1, # 18) (Ch. 8, # 33) (Ch. 8, # 31, 33) (Ch. 8, # 31) (Ch. 8, # 31) (Ch. 5, # 108) (Ch. 5, # 109) (Ch. 8, # 102) (Ch. 8, # 24) (Ch. 5, # 17) (Ch. 1, # 158) (Ch. 1, # 176) (Ch. 1, # 14) APPENDIX 6 ITEMS FROM THE HILBERT NACHLASS REFERRED TO IN THE BOOK Numbers for each entry indicate the chapter and footnote where an item is referred to in the book. DHN 40A, 1. 19091918. Correspondence Born-Hilbert Passim. DHN 55, 4-5. Dec. 12, 1912, Apr. 4, 1913. Letters Carathéodory to Hilbert Ch. 5, # 91, #106. DHN 98, 1. April 11, 1912. Letter Ewald to Hilbert Ch. 5, # 80. DHN 141, 7. March 7, 1916. Letter Hecke to HIlbert Ch. 7, #86. DHN 254. 1913-1917. Correspondence Mie-Hilbert Passim. DHN 308A, 4. 19121917. Correspondence Planck-Hilbert Ch. 5, # 108, 109; Ch. 8, # 31, 33. DHN 379A. May 14, 1916. Letter Sommerfeld to Hilbert Ch. 8, # 24. DHN 416. 1886-1913. Correspondence Hilbert-Volkmann Ch. 1, #158, #163. DHN 418, 1. July 19, 1899. Letter Voss to Hilbert Ch. 1, #176. 462 ITEMS FROM HILBERT’S NACHLASS 463 DHN 457, 17. April 22, 1918. Letter Hilbert to Weyl Ch. 9, # 78. DHN 504. SS 1882. Lecture notes of a course on number theory taught by Weber (Annotated by Hilbert) Ch 1, #4. DHN 505-519. Undated, probably around 1880. Hilbert’s student notebooks Ch. 1, # 6-7; 11. DHN 520. Undated. A list of Hilbert’s courses over 46 years, between 1886 and 1932. This list is complied in Hilbert’s own handwriting until WS 1917-18 Ch.1, # 38, Ch. 2, # 30, Ch. 5 # 158. DHN 522. SS 1887. Hydrodynamics – Lecture Notes Ch. 1, # 20, Ch. 2, # 30. DHN 535. SS 1891. Projective Geometry – Lecture Notes Ch. 2, # 3. DHN 553. WS 189899. Mechanics – Lecture Notes Ch. 9, # 44-47. DHN 558a. SS 1905. Logical Principles of Mathematical Thought – Lecture Notes (Annotated by Max Born) Ch. 3. DHN 570, 9. 1905. Notes from a seminar on electron theory taught by Hilbert, Minkowski, Wiechert, and Herglotz Ch. 3, # 43. DHN 570, 1. Undated. Random collection of handwritten notes related to many different courses and seminars of Hilbert Ch. 3, # 36. 464 APPENDIX 6 DHN 570, 5. 1907. Notes by Hermann Mierendorff from a seminar on electrodynamics taught by Hilbert and Minkowski, Ch. 4, #15. DHN 586. August 1912. Notes of a talk on radiation theory Ch. 5, # 73, 82. DHN 590. January 1913. Notes of a lecture on Nernst’s law of heat Ch. 5, #144. DHN 593. Undated. Probably 1903. Notes of a talk on stability theory Ch. 2, #78; Ch. 3, # 37. DHN 596. July 26, 27, 28, 1923. Notes on three talks about “Foundations of Physics” Ch. 8, #121. DHN 600. Undated. Probably before 1900. Tagebuch Ch. 3, #1. DHN 634, 15-22. Undated. Around 1916. Manuscripts with notes related to Hilbert 1917 Ch. 8, # 21, # 22. DHN 634. Before or on Dec 6, 1915. Galley proofs of Hilbert 1916 Ch. 7, # 63. DHN 642. Undated. Around late 19151916. Talk on the causality principle Ch. 7, # 65. DHN 696. Undated. Random collection of handwritten notes related to many different courses and seminars of Hilbert Ch. 3, # 36. DHN 707. SS 1907. Radiation Heath – Minkowski’s Lecture Notes Ch. 4, #3. DHN 742. June 1915. Lecture of Einstein on GTR Ch. 7, # 33. APPENDIX 7 HILBERT’S AXIOMS FOR RADIATION THEORY The precise context of Hilbert’s various systems of axioms for radiation theory is discussed in § 5.3. 1. FIRST VERSION (HILBERT 1913): Axiom I: In a state of thermal equilibrium of radiation no interchange of energy among colors takes place for a given portion of matter. Moreover, the radiation of each color is itself in a state of equilibrium. Axiom II: The values of the three characteristic magnitudes of any wavelength at a given temperature (the emission coefficient K, the absorption coefficient D, and the speed of light q) are uniquely determined by the physical properties of matter at the given position in space where that matter is currently found. Axiom III: There exist substances whose absorptions coefficient D and refraction capacity are such that the quotient D/q2 falls short of the wavelength O by a function which is arbitrarily prescribed in advance. 2. SECOND VERSION (HILBERT 1913A): Axiom 1 (Axiom of the compensation of the total energy): In a state of thermal equilibrium of radiation the total amount of energy emitted by any given volume element for all colors equals the amount energy absorbed by it. Axiom 2 (Axiom of the compensation of energy for each individual color): In a state of thermal equilibrium of radiation there is no exchange of radiant energy across different colors at any given region of matter. Moreover, the radiation corresponding to each color is itself in a state of independent equilibrium. Axiom 3 (Axiom of the physical nature of the coefficients q, K, D): The characteristic magnitudes of radiation for any given wavelength (speed of light q, emission coefficient K, absorption coefficient D) are uniquely determined by the physical conditions of matter in the region where the matter is found, and by them alone. Axiom 4 (Axiom of the physical nature of the radiation density): In a state of thermal equilibrium of radiation, the density of the radiant energy for each wavelength for which matter is not diathermic, is uniquely determined by the physical conditions of matter in the region where the matter is found, and by them alone. 465 466 AXIOMS OF RADIATION THEORY Axiom 5 (Axiom of the existence of certain diversities in matter): There exist substances whose absorptions coefficient D and refraction capacity are such that the quotient D/q2 falls short of the wavelength O by a function which is arbitrarily prescribed in advance. 3. THIRD VERSION (HILBERT 1914): Axiom A (Axiom of the compensation of the total energy): Every optical system admits a state of radiation equilibrium. In this state, the total amount of energy emitted by all colors from any given volume element equals its total absorbed energy. Axiom B (Axiom of the compensation of energy for each individual color): Every optical system admits a state of radiation equilibrium. In this state, there is no exchange of radiant energy corresponding to different colors at any given region of matter. Moreover, the radiation corresponding to each color is itself in a state of independent equilibrium. Axiom C (Axiom of the physical nature of the radiation density): In the —always possible— state of equilibrium, the density of the radiation energy of every wavelength is uniquely determined by the physical conditions of matter in the region where the matter is found, and by them alone. Axiom D (Axiom of the existence of certain differences among substances): There are substances for which the values of D (absorption coefficient) and q (velocity of propagation of light) are such that the quotient D/q2 equals the value of any arbitrarily function of O prescribed in advance. REFERENCES COMMONLY USED ABBREVIATIONS AHES AIHS AJP AM AMP AMS AP ASN BSL BSPS CPAE CRN DHN DMV DSB EHN EMV ES GdG GDNA GMG GN GTR Archive for History of Exact Sciences Archives int. d’histoire des sciences American Journal of Physics Annals of Mathematics Archiv für Mathematik und Physik American Mathematical Society Annalen der Physik Nachlass Arnold Sommerfeld, Deutsches Museum, Munich. The Bulletin of Symbolic Logic Boston Studies in the Philosophy of Science The Collected Papers of Albert Einstein (Princeton, Princeton University Press). Nachlass Runge – Du Bois Reymond, Staatsbibliothek Berlin, Preußischer Kulturbesitz Nachlass David Hilbert – Niedersächsische Staats- und Universitätsbibliothek Göttingen, Abteilung Handschriften und Seltene Drucke, Nachlass Hilbert (Cod. Ms. D. Hilbert). Deutschen Mathematiker-Vereiningung Dictionary of Scientific Biography Nachlass Erich Hückel, Staatsbibliothek Berlin, Preußischer Kulturbesitz Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen Einstein Studies Grundlagen der Geometrie Gesellschaft Deutscher Naturforscher und Ärzte Göttingen Mathematische Gesellschaft Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematische-Physikalische Klasse General Theory of Relavitity 467 468 GWG HGA HLN HM HPL HSPS ICM JDMV JRAM JRE JSHS JSL JSN LCP MA MBN MPIWG MZ PAWS PB PiP PZ SHPMP SHPS SiC SN STR SUB Göttingen Trans. AMS VDPG VGDNA ZMP ZP REFERENCES Königlichen Gesellschaft der Wissenschaften zu Göttingen David Hilbert – Gesammelte Abhandlungen Manuscript/Typescript of Hilbert Lecture Notes. Bibliothek des Mathematisches Insititut, Universität Göttingen Historia Mathematica History and Philosophy of Logic Historical Studies in the Physical Sciences International Congress of Mathematicians Jahresbericht der Deutschen Mathematiker-Vereiningung Journal für die reine und angewandte Mathematik Jahrbuch der Radioaktivität und Elektronik Japanese Studies in the History of Science Journal of Symbolic Logic Nachlass Johannes Stark – Staatsbibliothek Berlin, Preußischer Kulturbesitz. Collected Papers of Hendrik Anton Lorentz Mathematische Annalen Nachlass Max Born, Staatsbibliothek Berlin, Preußischer Kulturbesitz Max Planck Institut für Wissenschaftgeschichte, Berlin Mathematische Zeitschrift Königlich Preussische Akademie der Wissenchaften (Berlin) Sitzungsberichte Physikalische Blätter Physics in Perspective Physikalische Zeitschrift Studies in History and Philosophy of Modern Physics Studies in History and Philosophy of Science Science in Context Science Networks Special Theory of Relativity Niedersächsische Staats- und Universitätsbibliothek, Göttingen. 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INDEX Anschauung, 36, 62, 69, 83-84, 117, 118, 124, 399, 423-425 anthropomorphism, 9, 379, 393, 399, 423 Apelt, Ernst Friedrich (1812-1859), 36 Appell, Paul (1855-1930), 92 applied mathematics, 47, 69, 73-78, 321 Arabatzis, Theodor, 131 Archimedean axiom, 41, 86, 97, 123, 141 Archiv der Mathematik und Physik, 74 arithmetic, 7, 22-27, 35-43, 51-52, 66, 94106, 113-115, 121-125, 183, 229, 255, 281, 370, 396-397, 424-428, 446 consistency, 97, 101-104, 121-122, 426 foundations, 36, 75, 102, 104, 120123, 296, 318, 369, 396, 409, 413, 427, 434, 438, 446, 449 Aronhold, Siegfried (1819-1884), 17 Ascoli, Giulio (1843-1896), 228 astronomy, 81, 123, 130, 149-151, 166168, 175, 186, 447 atomic theory, 50, 65, 246, 412-415 atomistic conceptions/atomistic hypothesis, 46-49, 55, 62-63, 69, 80, 92, 106, 148, 151, 169, 198, 219, 231, 234, 267-268, 282, 284, 377, 445 Aufruf an die Kulturwelt, 325, 448 Ausdehnungslehre, 36 axiom of completeness (Vollständigkeitsaxiom), 97, 100, 121 A Aachen, 136 Abraham, Max (1875-1922), 8, 49, 133136, 174, 215-219, 273, 297, 299, 305, 306-308, 328, 419, 454-455, 459 Abrams, Len, 381 absolute differential calculus, 292, 295 absorption capacity (coefficient), 239, 242, 247-250, 255, 259-261, 417, 445, 465-466 Ackermann, Wilhelm (186-1962), 438 action and reaction principle, 305 action at a distance, 69, 150, 296, 377, 387 adiabatic process, 156, 161 aerodynamics, 73 Alexandrov, Pavel (1896-1982), 109 algebraic invariants, 3, 17, 19, 25, 89, 112, 359, 437, 446 algebraic number fields, 3, 20-21, 85, 89, 96, 227, 438 Althoff, Friedrich (1839-1922), 72 Ambronn, Leopold Friedrich Anton (1854-1930), 81 Ampère, André Marie (1775-1836), 70 Annalen der Physik, 229, 304, 310, 363, 374, 449 497 498 INDEX axiom of parallels, 29 axiom systems completeness, 95-100, 111, 114, 164, 165, 181, 274, 426, 438 consistency, 56, 96-100, 104, 111-114, 122-124, 165-166, 176, 181, 183, 397, 415 ordinal independence, 44 relative consistency, 111 simplicity, 57, 59, 66, 95, 98, 114, 164 independence, 43-44, 56-58, 87, 95-104, 111-115, 121-126, 140, 164-165, 176, 181, 183, 216-217, 260, 264, 267, 276, 325, 376, 384, 397, 402, 413, 416, 424-425, 430, 436, axiomatic approach, 3, 6, 20, 24-25, 38, 50, 59, 65, 83-85, 88, 93-98, 101, 104, 119, 142, 151, 157, 174-176, 179, 221, 262, 289, 372, 374, 396, 426, 431 axiomatic method, 3, 7, 11, 20, 54, 88, 90, 110, 118, 121-126, 157, 162, 177178, 198, 230, 239, 262, 266-278, 334, 344, 350-351, 357, 373-374, 397, 403, 418, 442 B Baade, Walter (1893-1960), 322, 353 Babbage, Charles (1791-1871), 35 Baird, D., 55 Baltic Sea, 326 Bandomir, C.A., 178 Bär, Richard (1892-1940), 369, 440, 451, 458 Barbour, Julian, 51, 53, 145, 290 Bargmann, Valentin (1908-1989), 224 Barkan, Diana, 81, 244 Basel, 51, 472, 478, 480--484, 489-494 Baule, Bernhard (1891-1976), 265, 274, 317, 451, 457-458 Bauschinger, Julius (1860-1934), 168 Becquerel rays, 133 Becquerel, Jean (1878-1953), 133, 437 Behmann, Heinrich (1891-1970), 319, 369, 370, 427, 438 Behrens, Wilhelm, 263, 451, 456 Belna, J.P., 111 Bergia, Silvio, 364 Berlin, v, vi, viii, 2, 8, 13-15, 30, 34, 47, 72-73, 76, 81, 102, 119, 133, 168, 215, 289, 296-297, 320, 326-330, 345-346, 348, 351-353, 364-369, 413, 414, 428, 447-449, 454 Berlin Academy, 8, 15, 289, 296, 330, 345, 351, 364, 428, 449, 454 Bernays, Paul (1888-1977), 295, 296, 370, 427, 436, 449, 451, 458 Bernstein, Felix (1878-1956), 121, 319, 321, 326, 369, 456 Bertrand’s principle, 146-147 Besso, Michele (1873-1955), 225, 295, 328, 347, 363, 364, 459 Bianchi identities, 341 Bibliotheca Mathematica, 73 Bierhalter, G., 154 binary quadratic forms, 17 Birkhoff, Garrett (1911-1996), 420 black-body radiation, 242-246 Blackmore, J.T., 50, 55 Blaschke, Wilhelm (1885-1962), 385 Blasius, Paul Heinrich (1883-1970), 130 Blum, P., 109, 149 Blumenthal, Otto (1876-1944), 3, 18, 20, 21-24, 85, 89, 345 body alpha, 52 Bohlmann, Georg (1869-1928), 107, 164166, 171, 176 Böhm, Friedrich (1885-1965), 323, 456 Bohr Festspiele, 412 Bohr, Harald (1887-1951), 409 Bohr, Nilels (1885-1962), 412-413, 442 Boi, L., 45 Boltzmann distribution, 48, 238 Boltzmann equation, 2, 171, 229, 237, 238, 441 Boltzmann, Ludwig (1844-1906), 2, 4650, 60-65, 76, 77, 80, 92, 106-107, 129, 140, 141, 148-153, 168-171, 179180, 229, 235-251, 276-277, 441-447 Bolyai, Janos (1802-1860), 26-30, 227, 447 Bolza, Hans, 265, 458 Bonn, 14, 15, 30, 86, 129, 160, 445 Boole, George (1815-1864), 17 Boolean algebra, 116 Boos, W., 112 Borga, M., 44 Boring, E.G., 175 INDEX Born, Max (1882-1970), viii, 4, 130, 134, 161-163, 183-189, 214-219, 225, 227, 238, 241, 246-248, 253, 263-271, 282, 287, 291, 309-326, 333, 335, 341-354, 366-368, 376, 377, 411-421, 440, 447463 Born-Wiener operator method, 415 Bortkiewicz, Ladislaus von (1868-1931), 164 Bosworth, Anne Lucy (1868-?), 120 Bougoslawski, S., 263 Brendel, Martin (1862-1939), 81 Breslau, 214, 215, 241, 252, 434 Brest-Litovsk, 322 Brigaglia, Aldo, 36, 122 Brill, Alexander von (1842-1935), 21, 30, 150, 278 Broggi, Ugo (1880-1965), 166 Brotherus, Hjalmar V. (1885-1962), 248 Brouwer, Luitzen E.J. (1881-1960), 396, 434 Browder, Felix E., 109 Brownian motion, 241 Brush, Stephen G., 2, 46, 47, 237, 265 Brussels, 161, 244, 447, 456 Bucherer, Alfred H. (1863-1927), 153 Budde, Emil (1842-1921), 92, 129 Burali-Forti, Cesare, 45 Burkhardt, Heinrich (1861-1914), 74 C Cambridge, 75, 130, 161, 214 Caneva, Keneth, 36, 45 Cantor, Georg (1845-1918), 18, 23, 35, 37, 42, 68, 100, 101, 104, 166, 446, 459 Cantor’s continuum hypothesis, 104 capillarity theory, 12, 129, 186, 454 Carathéodory, Constantin (1873-1950), 160-163, 183, 252-257, 262, 321, 440, 448, 455-459, 462 Cario, Günther (1897-1984), 411 Carnot processes, 163 Castelnuovo, Guido (1865-1952), 75 Cattani, Carlo, 8, 297, 307 Cauchy problem, 338, 340, 362, 385 causality principle, 68, 294-296, 304, 331, 338, 340, 346, 360, 362, 377, 378, 385-386, 400-403, 435-436, 464 Cayley, Arthur (1821-1895), 17, 20, 32 499 Celestial Mechanics (Laplace), 173 Cercignani , Carlo, 2, 46 Chapman, Sidney (1888-1970), 265 Chasles, Michel (1793-1880), 30 Chicago, 19, 20, 115, 323, 447 Christiansen, M., 91 Christoffel symbol, 340 Christoffel, Elwin Bruno (1829-1900), 29, 292 civilian war prisoner, 322, 409 Clausius, Rudolf (1822-1888), 154, 161 Clifford, William Kingdon (1845-1879), 28, 29, 33 Cohn, Emil (1854-1944), 197 Compton, Karl Taylor (1887-1954), 411 Condon, Edward U. (1902-1974), 411 conductivity, 79, 196, 272 conservation laws, 204, 355, 391 conservation of mass principle, 199 continuity equation, 152, 239 contraction hypothesis, 132, 194, 211 Contro, Walter, 40, 41, 45 coordinate conditions, 295, 337, 339, 348, 352-361, 386, 405, 436 coordinate systems, 202, 273, 294, 346, 346, 385-386 coordinate transformations, 292, 309, 380-381 rotating, 294, 345 Corry, Leo, 6, 12, 21, 25, 30, 36, 37, 95, 116, 117, 118, 142, 189, 307, 322, 330, 352, 409, 420, 442 cosmology, 29, 322, 364, 388, 449 Coulomb’s law, 62, 300 Courant, Richard (1888-1972), 409, 411, 413, 414, 420, 440 covariance/invariance Galilean, 132, 173, 174 general, 2, 7, 214, 225, 292-294, 296, 309, 316, 328, 329, 332-361, 381386, 391-394, 401, 403, 423, 433, 436, 448 limited, 307, 345, 357 Lorentz, 132, 191, 194, 196, 198, 200, 204, 205, 217, 218, 220, 222-223, 226, 235, 271, 289-292, 300-303, 333, 377, 433 Cremona, Luigi (1830-1903), 30 Crilly, Anthony, 17 cross-ratio, 32, 33, 41 Crowe, Michael, 138, 153 500 INDEX crystal physics, 232, 234, 322 Cyclotomic fields, 19 Czuber, Emanuel (1851-1925), 21, 164167, 171 D d’Alembert principle, 93, 146 Darboux, Gaston (1842-1917), 30, 91, 138, 140 Darrigol, Olivier, vi, 49, 71, 134, 136, 197 De Finetti, Bruno (1906-1985), 166 De Sitter, Willem (1872-1934), 364 Debye, Peter (1884-1966), 271, 317, 318, 321, 366, 411, 448, 453, 456-457 Dedekind, Richard (1831-1916), 12, 13, 21-23, 36-43, 85, 99, 100, 101, 166, 379, 380, 421, 445-446, 459-461 Dedekind's theory of cuts, 39, 99 Dehn, Max (1878-1952), 41, 120 density charge, 189, 300 current, 189 electricity, 196, 216 energy, 302 mass, 152, 199, 290 optical, 147 radiation, 258, 261, 465, 466 Desargues, Girard (1591-1661), 30 Desargues’s theorem, 30, 32, 42, 89, 96, 97, 98 Despeyrous, Th., 91 Deutschen Mathematiker-Vereiningung, 21-22, 42, 64, 66, 72, 74, 85, 86, 99, 112, 132, 167, 189, 446 Dickson, Leonard Eugene (1847-1952), 116 dielectric constant, 196 Dieudonné, Jean (1906-1992), 6, 17, 77, 118, 228 differentiability conditions, 28, 105 differential equations, 12, 15, 19, 35, 59, 109, 151-152, 162-163, 169-170, 185186, 189, 199, 228-229, 235-236, 280, 336-338, 375, 385, 410, 427, 434, 454 Encyklopädie article, 76 dilute gases, 241, 317, 319 Dirac, Paul A.M. (1902-1984), 412- 415 Dirichlet principle, 22, 109, 127, 445 Dirichlet, Gustav Lejeune (1805-1859), 22, 37, 109, 127, 447 DiSalle, Robert, 51, 53 divergence, 211, 338-339, 355, 360, 390 covariant, 355 Dolezalek, Friedrich (1873-1920), 81 Doppler effect, 79-80 Dorier, J.L., 141 Droste, Johannes (1886-1963), 364 Du Bois-Reymond, Emil (1818-1896), 102 Dugac, Paul, 85 Duhamel, Jean-Marie C. (1797-1872), 129 Duhem, Pierre (1861-1916), 47 Dühring , Eugene (1833–1921), 92 E Earman, John, 189, 290, 295, 330, 430 Eckert, Michael, 232 Eddington, Arthur S. (1882-1944), 394, 437 Edwards, Harold, 21 Edwards, M.R., 284 Ehrenfest, Paul (1880-1993), 47, 76, 77, 150, 179, 183, 220, 243, 246, 265, 291-295, 348, 364, 440, 448, 455- 459 Ehrenfest-Afanaseva, Tatyana (18761964), 47, 76, 77, 150, 179, 265, 440, 448 Einstein, Albert (1879-1956), v, vii, 2, 7, 8, 81, 132, 136, 149, 168, 182, 186195, 205-206, 211-226, 235-236, 243, 249, 271, 284-297, 300, 302-317, 320462 Einstein's 1915 Prussian Academy communications, 375 first, 348, 351, 353 fourth, 328, 354, 356, 358, 363 fourth, 360 second, 349, 355 third, 352, 363, 375 Einstein 1915 visit to Göttingen, 320, 333, 405 Eisenstaedt, Jean, 364, 381 elasticity, 93, 214, 234, 287, 301, 311, 390 electric current, 196 INDEX electricity, 12, 45, 56, 64, 88, 114, 125, 133, 134, 135, 189, 191, 194, 198, 208, 216, 217, 219, 246, 272, 301, 388, 446 electrodynamic potentials, 387 electrodynamics, 7, 15, 49, 54-55, 79-81, 107, 128-136, 149, 152-153, 172, 178200, 205, 210-225, 239, 246-248, 272281, 300, 304-305, 311-316, 324, 333337, 342-345, 350, 356-357, 362, 367, 375-376, 387, 390-391, 397, 401, 432434, 440, 444-447, 464 of moving bodies, 136, 149, 186-190, 194-198, 210, 213, 446 electrolysis, 317 electromagnetic field, 136, 216, 283, 310, 337 electromagnetic mass, 310 electromagnetic oscillations, 228, 280, 316, 317 electromagnetic potentials, 335, 341, 374, 377 electromagnetic reductionism, 231 electromagnetic view of nature, 49, 132134, 182, 191, 195, 206, 213, 219, 299, 311-315, 377 electromagnetism, 153, 198, 236, 242, 267, 278, 299, 337, 351, 378, 391, 430 electron deformable, 132 high-speed, 133 rigid, 133, 216, 218 electron theory, 49, 79-81, 130-137, 149, 174, 187, 193, 198, 213, 216, 219, 228, 241, 244, 271-272, 277, 281, 300, 309, 312, 314, 317, 368, 377, 447, 463 conduction electrons, 216, 283 magnetization electrons, 216, 283 polarization electrons, 216, 283 electro-technology, 130 Ellison, W. and F., 22 emission capacity (coefficient), 239, 242, 247, 248, 255, 445, 465 Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, 54, 66, 67, 74-77, 92, 107, 129, 135, 144, 153, 164, 168, 174, 179, 183, 197, 249, 252, 326, 436, 446-449 French version, 76 enduring core, 400, 402 501 energy, 302, 465-466 absorbed and emmited, 242 conservation principle, 46 current vector, 302 density, 282, 304 elements, 243 equal energy elements, 243 equilibrium, 253 kinetic, 146, 147, 172, 276, 277 magnetic, 133 momentum, 315 potential, 46, 149, 151, 173, 234 quanta, 244 radiant, 261, 294 self-energy, 217, 218, 300, 310 total energy density, 250 energy conservation principle, 45, 62, 93, 145-147, 156, 194, 199, 200, 214, 220, 264, 276, 293, 294, 301-302, 305-306, 311-315, 338-340, 356, 359-360, 369, 377, 384-388, 407, 435, 449 Enriques, Federigo (1871-1946), 34, 42, 75, 122 Enskog, David (1884-1947), 265, 436 entropy, 46-48, 154-161, 163, 168-169, 178, 239, 242-243, 257, 268, 270, 397, 445 Entwurf Theory (Einstein-Grossmann), 289-297, 306-307, 311, 323-333, 337, 346-349, 354, 371, 448 equation of state, 268, 270, 271 equilibrium, 48, 142, 144, 146, 155, 161, 216, 251, 253, 255, 257, 259, 262, 264, 269, 313, 465-466 chemical, 241 thermal, 154-155, 242-243, 250, 254257, 465 equivalence principle, 205, 289, 290, 291, 294, 307, 323, 373, 447 ergodic hypothesis, 241 Erlangen, 66, 222, 321, 436 Erlanger Programm, 33-35, 44, 75, 445 ether, 45, 56, 70, 130- 136, 189-191, 195, 198, 208, 216-217, 233, 273, 299-304, 311, 371 Euclid’s Elements, 37, 39 Euler equations, 129, 152, 153, 454 evangelist church, 299 Ewald, Paul P. (1888-1985), 232, 241, 249, 253, 317, 321, 440, 448, 456, 458, 460, 462 502 INDEX Ewald, William, 26, 28, 39, 40, 398 F Fachwerk von Begriffen, 123, 124, 393, 396, 425 Fano, Gino (1871-1952), 34, 44, 75, 77, 86 faster-than-light motion, 136 Fechner, Gustav (1801-1887), 175 Fermat’s theorem, 102, 231 Fisch, Menachem, 35 Fokker, Adriaan (1887-1968), 364 Fölsing, Albrecht, vi, 54, 55, 325, 328 Föppl, A., 129, 454, 456 Fortschritte der Physik, 252 Fowler, Ralph H. (1889-1944), 163 Franck, James (1882-1964), 411 Franco-Prussian war, 31 Frankfurt, 215, 485 Frederiks, Vsevolodk F. (1885-1943), 322, 408, 440 Fredholm, Ivar (1866-1927), 228 Frege, Gottlob (1846-1925), 86, 107, 111-114, 121, 143, 165, 446, 460 Frei, Gunther, 11, 18, 20, 72, 85, 86 Frenkel, V., 322 Fresnel, Augustine J. (1788-1827), 52, 265 Freudenthal, Hans (1905-1990), 30, 98 Freundlich, Erwin Finlay (1885-1964), 306, 307, 346, 354, 459 Friedmann, Alexander (1888-1925), 322 Friedmann, Michael, 430 Frobenius, Georg Ferdinand (1849-1917), 76, 297 Fuchs, Lazarus (1833-1902), 76, 447 G Gabriel, G., 112-114, 121, 143, 165 Galison, Peter L., 187, 189, 191 Galois theory, 15 Gans, Richard (1880-1954), 153 Gauss, Carl Friederich (1777-1855), 11, 17, 21-27, 68, 81, 87, 88, 107, 126, 134, 145-148, 167-168, 279, 292, 324, 378-379, 387, 427, 446 Disquisitiones Arithmeticae, 23 error theorem, 167 square law, 168 three mountain peaks experiment, 87, 126, 279, 378-379, 387, 427 Gaussian coordinates, 386, 403 Gaussian integers, 21 Gauss-Weber Festschrift, 81, 107, 134 genetic approach, 99-100, 123-124, 424, 425 geodesics, 292, 384 geometry analysis situs, 83, 116 analytic, 32, 39, 42, 48, 83-86, 98, 109, 182, 265 consistency, 96, 104 continuity assumptions, 32, 38-43, 8589, 94-101, 105, 426 differential, 29, 292, 324, 378, 380, 385 Euclidean, 26-43, 58, 86-98, 104, 113, 125, 139, 148, 209, 278-279, 290291, 296, 306, 378-388, 396, 423427, 454 foundations, 1, 3, 6, 7, 11, 19- 25, 2829, 36-44, 50, 58, 65, 84, 85-86, 90, 93, 105-106, 115, 120-123, 277, 292, 413, 417, 423, 428, 437-438 hyperbolic, 28, 33, 202 metrization, 42, 87, 98 non-Archimedean, 44, 87, 99,125, 446 non-Euclidean, 23-33, 40, 85-86, 96, 125, 190, 195, 387, 391, 445, 495 parallel postulate, 32, 87, 88, 96, 112, 427 projective, 25, 29-36, 40-44, 58, 83, 84-89, 95, 97, 111, 116, 446 pseudo-geometry, 387 Riemannian, 30, 404 spherical, 12, 28, 33, 299, 381 unification, 30-31 variable curvature spaces, 28, 33 geophysics, 81 Gesellschaft Deutscher Naturforscher und Ärzte, 64, 128, 132, 189, 206, 249, 271, 306, 310, 446-448 Giannetto, E., 187 Gibbs, Josiah Willard (1839-1903), 138, 153, 161, 168 Gispert, Helène, vi, 76, 78 Gleason, Andrew, 106 Glymour, Clark, 189, 290, 330, 432 Gnedenko, J., 1 INDEX Goenner, Hubert, 364 Goethe, Johann Wolfgang von (17491832), 176, 409 Goldberg, Stanley, 133 Goodstein, Judith, 297 Gordan, Paul (1837-1912), 17-20, 30, 227, 326 Gordan’s basis theorem, 17 Göttingen Mathematische Gesellschaft (GMG), 20, 73, 120, 128-130, 179, 186, 187, 189, 193, 214-217, 222, 237, 271, 310- 311, 316, 319, 323, 324, 330-331, 352, 356, 369, 388-390, 447, 454 Göttingen Nachrichten, 366, 390, 400, 434, 467 Göttinger Vereinigung zur Förderung der Angewandten Physik, 74 Grand Prix des Sciences Mathématiques, 13 Grassmann, Hermann Gunther (18091877), 35-36, 42-44, 86, 177, 459 Grattan-Guinness, Ivor, 101, 109, 111 gravitation, 63, 84, 132-133, 153, 172, 187-205, 220, 225, 235, 273, 283-289, 289, 293, 302-404, 434, 437, 442, 447, 448 Euler-Lagrange equations, 340 Euler-Lagrange equations, 375 geometrical interpretation, 292 Mie’s theory, 300-306 Minkowski’s theory, 200-204, 212 Newtonian, 149, 200, 289, 293 Newtonian limit, 355 Nordström’s theory, 307 gravitational field, 152, 289, 290, 292, 293, 294, 304, 307, 342, 346, 356, 357, 362, 364, 375, 381, 382, 384, 430, 433, 435, 437, 441, 442, 448, 449 non-static, 407 static, 293 gravitational field equations, 8, 168, 289302, 320-329, 333, 337, 340, 342, 345, 346-362, 373-380, 383, 387, 402-404, 421, 427, 435, 436, 442, 448 first exact solution, 363 Schwarzschild solution, 380- 385, 435 trace term, 355, 358-359, 406 gravitational light rays bending, 290, 306, 307 gravitational mass, 289, 305-306, 383 503 gravitational potentials, 225, 290, 292, 305, 306-307, 335-342, 351, 357, 380, 386 gravitational red shift, 290, 306, 384, 394 Gray, Jeremy, vi, 45, 102-106 Greffe, J.L., 71 Greifswald, 299, 371 Grelling , Kurt (1886-1942), 121, 319, 326 Grommer, Jakob (1879-1933), 322, 364, 408, 436 Grossmann, Marcel (1878-1936), 289295, 311, 323-324, 348, 352, 359, 374, 448, 456 Grotrian, Walter (1890-1954), 411 group theory, 25, 29-34, 41, 73, 94, 95, 96, 98, 115-116, 126, 164, 206-210, 222, 223, 319, 391, 392 groups continuous geometrical, 77 invariance, 291, 293, 333 transformations, 29, 32, 33, 348 Grundlagen der Geometrie (Hilbert), 11, 23, 25, 29, 32, 35, 63, 66, 69, 81-107, 114-120, 124-127, 164-166, 179-183, 257, 421, 423, 424-426, 447 Guth, E., 329, 432 GWG, see König. Ges. Wiss. Gött. H Halle, 42, 51, 85, 299, 370, 446 Hamel, Georg (1877-1954), 120, 138, 140, 142, 178, 183, 440 Hamilton principle, 57, 68, 93, 147, 173, 199, 218, 244, 312, 335, 373, 387, 427, 434, 436 Hamiltonian function, 147, 173, 218-219, 295, 297, 302, 312, 334-340, 346, 371374, 383, 387, 391, 403, 427, 434-435 Hardy, Godfrey H. (1877-1947), 227, 409 Harman, P.M., 45 Harvard, 420 Hashagen, Ulf, vi, 74-76 Hasse, Helmut (1898-1979), 22-23 Hausdorff, Felix (1868-1942), 117 Hawkins, Tom, vi, 29-35, 77 Heaviside, Oliver (1850-1925), 138 504 Hecke, Erich (1887-1947), 241, 265, 344, 440, 451, 456, 460, 462 Heidelberg, 12, 121, 122, 153, 299, 318, 447 Heilbron, John, 45, 47, 195, 393 Heisenberg, Werner (1901-1976), 411, 413-417, 440, 449 Hellinger, Ernst (1883-1950), 77, 215, 228, 326, 450-451 Helm, Georg Ferdinand (1881-1923), 49 Helmholtz, Hermann von (1821-1894), 15, 25-29, 42, 53, 105, 128, 129, 154, 176, 270 Helmholtz-Lie space problem, 29, 105 Hentschel, Klaus, 212, 309, 323 Herglotz, Gustav (1881-1953), 130, 136, 215, 311, 411, 447, 453-457, 463 Hermite, Charles (1822-1901), 12 Hershel, John (1792-1871), 35 Hertz, Heinrich (1857-1894), 54- 71, 8696, 106-107, 113, 136, 140-144, 147150, 153-154, 179-181, 221, 235, 273, 277-278, 299, 321, 326, 424-446, 454457 Hertz, Paul (1881-1940), 136, 241, 321, 326, 345, 346, 448 Hesse, Otto (1811-1874), 17 Hessenberg, Gerhard (1874-1925), 89 Hiebert, Erwin N., vi, 47, 50, 154 Hilbert, David (1862-1943) 1900 list of problems, 1, 3, 6, 83, 91, 92, 104, 109-111, 120, 129, 421, 426 courses on mechanics, 83, 91, 93, 129, 172, 185, 228, 234-235, 367 sixth problem, 1, 3, 6, 104, 106-110, 119, 137, 164, 178, 220, 239 theory of infinite determinants, 25 unified theory, 7, 8, 284-287, 295, 307, 309, 316, 329, 330-362, 374, 382, 391, 404-407, 415, 422 1924 version, 340, 357, 359, 392, 399, 402-404, 408 Axiom of Space and Time, 339340, 360, 402 energy concept, 338, 342-344, 351, 356, 360, 389, 422 first communication, 352 first printed version, 343, 353, 355, 361, 402-405 INDEX Proofs version, 330, 334-345, 357361, 371, 383, 386, 400-404, 489 Proofs version, missing lines, 340 second communication, 8, 329, 340, 350, 356, 360, 366, 368, 376, 377, 379, 381, 383-388, 397, 423, 426, 431, 434-436, 449 Theorem I, 336-338, 350, 358, 386, 391, 392, 403, 422 Hirosige, Tetu, 133, 197 Hochkirchen, Thomas, 110, 164, 166 Höhnl. H., 299, 301 Holton, Gerald, 212 homogeneous bodies, 154, 248, 268 Hon, Giora, 133 Hopf, Ludwig (1884-1939), 284 Hopmann, J., 168 Howard, Don, 321, 324, 326 Hückel, Erich (1896-1980), viii, 413, 451, 458 Hund, Friederich (1896-1997), 411 Huntington, Edward V. (1847-1952), 95, 115, 116 Hurwitz, Adolf (1859-1919), 13, 15, 21, 88, 227, 460 Husserl, Edmund (1859-1938), 110, 121, 323, 447 hydrodynamics, 15-16, 47, 75, 79, 90, 93, 129, 153, 239, 287, 448, 451-453, 463 hydrogen atom, 354 I ideal oscillator, 242 Immanuel Kant (1724-1804), 12, 57, 6970, 94, 117, 299, 429-431 incompressible fluids, 150 inertia of a charge flow, 219 principle, 70 relativity of, 364 transverse, 133 inertia (principle of), 208, 290, 323, 430 Carl Neumann’s criticism, 51, 52, 53, 54 Hertz’s discussion, 59 Hilbert’s discussion, 143 Minkowski’s discussion, 191 inertial fields, 292 inertial mass, 218, 289, 303-306, 384 inertial motion, 143, 204 INDEX inertial properties of matter, 49, 213 infinite matrices, 414 infinitesimal element, 27, 201 Ingrao, Bruna, 75 insurance mathematics, 107, 164, 171173, 177, 323 integral equations, 2, 3, 21, 25, 77, 109, 127, 171, 228-230, 238-239, 246-261, 265, 267, 285, 317, 377, 414, 417, 438, 447 intensity magnitudes, 301-303 International Congress of Mathematicians (ICM), 1, 20, 101, 121-122, 153, 166, 228, 244, 325, 446, 447 intuitionism, 396, 434 invariant theory, 15, 17, 20, 93, 321, 339, 389 isothermal, 157-158 Israel, Giorgio, 35, 75 J Jacobi principle, 12, 91, 93 Jacobi, Carl Gustav (1804-1851), 12 Jahrbuch der Radioaktivität und Elektronik, 211, 308 Jahresbericht der Deutschen Mathematiker-Vereiningung, 20, 21, 22, 64, 75, 86, 109, 128, 129, 130, 179, 186, 193, 214, 215, 237, 253, 254, 257, 259, 261, 262, 271, 296, 310, 311, 319, 323, 324, 330, 331, 352, 356, 368, 369, 388, 390, 445, 453 Janssen, Michel, vi, 132, 287, 291, 293, 294, 295, 346 Jeans, James (1877-1946), 243-244 Johann Georg Rosenhain (1816-1887), 12 Jordan, Camille (1838-1921), 30 Jordan, Pascual (1902-1980), 411, 414418, 437, 440 Jungnickel, Christa, 13, 45, 48, 49, 51, 54, 61, 79, 92, 132, 134, 232, 234, 297, 317, 321 K Kahle, R., 104, 121 Karachalios, Andreas, 411 Kármán, Theodor von (1881-1963), 241, 265, 455, 456 505 Kassel, 129, 453 Kast, W., 299 Katzir, Shaul, vi, 187, 232 Kaufmann, Walter (1871-1947), 49, 130, 133-134, 196, 211-212, 299 Kennedy, H., 43-44 Kepler’s law, 204, 213, 382 Kerszberg, Pierre, 364 Khinchin, Aleksandr Y. (1894-1959), 227 Killing , Wilhelm (1847-1923), 29, 33, 34, 42 kinetic theory, 2, 3, 7, 12, 46-49, 64, 76, 107, 168-171, 179, 214, 226, 229-250, 265, 267-274, 284, 301, 310, 317, 320, 382, 397, 417, 445-448 equipartition theorem, 48, 252 H-curve, 48 Stossanzahlansatz, 179 Umkehreinwand, 47 Wiederkehreinwand, 47, 179 Wiederkehreinwand, 179 Kirchhoff, Gustav (1824-188), 51, 55, 64, 91, 129, 239, 242, 247-264, 445 Kirchhoff’s laws, 239-264, 445 Klein, Felix (1849-1925), 4, 11, 12-14, 18-47, 54, 58, 66, 72-97, 119, 130, 193, 214-224, 263, 266, 321-326, 338, 359, 365, 366, 369, 376, 388-392, 399, 407-409, 419, 431, 435-450 Klein, Martin, 46, 150, 152, 179, 266 Kneser, Adolf (1862-1930), 76 Kneser, Hellmuth (1898-1973), 413, 416 Koebe, Paul (1882-1945), 251 Kohl, G., 306 Kohlschütter, Arnold (1883-1969), 130 Kolmogorov, Andrei N. (1903-1987), 166 Köln, 199, 206, 223, 447 Königlichen Gesellschaft der Wissenschaften zu Göttingen (GWG), 127, 138, 193, 249, 263, 320, 329-330, 334, 354, 357, 361, 366, 384, 390, 417, 447-449, 457 Königsberg, 4, 12-20, 51, 58, 61, 73, 7883, 89, 90, 129, 166, 180, 227, 416, 429, 447-453 Köthe, G., 77 Kox, Anne J., 364 Kragh, Helge, 13, 134, 243, 414 Krakow, 271 Kratzer, Adolf (1893-1983), 451, 458 506 INDEX Kremer, R.L., 176 Kretschmann, Erich (1887-1973), 365 Kronecker, Leopold (1823-1891), 18, 2124, 72, 102-104, 123, 379, 417 Kuhn, Thomas .S., 46-48, 79, 154, 168, 242-247 Kummer, Edward E. (1810-1893), 21-24 L Lacki, J., 412, 413 Ladenburg, Rudolf (1882-1952), 248, 253, 263-264 Laemmel, Rudolf (1879-1962), 166 Lagrange, Joshep-Louis (1736-1813), 17, 70, 91, 128, 129, 277-278, 312, 315, 324, 336, 340, 375 Lagrangian equations, 109, 145-147, 277, 278, 312, 377, 390, 391 Lagrangian function, 133, 152, 174, 235, 278, 312-316, 335, 342-346, 358 Lamb, Horace (1849-1934), 75, 153 Lanczos, Cornelius, 145, 335 Landau, Edmund (1877-1938), 215, 409, 447 Landé, Alfred (1888-1975), 232, 321, 368, 440, 458 Lange, Louise, 323 Lange, Ludwig, 53, 145 Laplacian operator, 152, 290 Larmor, Joseph (1857-1942), 69, 130, 132, 143-144 Laub, Jakob (1882 – 1962), 224 Laue, Max von (1879-1960), 130, 224, 225, 243, 278, 359, 381, 440, 454 Laugwitz, Detlef, 28 Le Sage, Georges L. (1724-1803), 283 least action principle, 68, 133 least squares principle, 145, 167 Leibniz, Gottfried W. (1646-1716), 52 Leiden, 130, 271, 364 Leipzig, 12-13, 44, 51, 54, 74, 175, 411, 445 Leopold Infeld (1893-1968), 310 Lesezimmer, 4, 91, 129, 445 Levi-Civita, Tulio (1873-1941), 8, 292, 297, 320, 328, 365 Lewis, Gilbert .N., 136, 187, 276 Lewy, Hans (1904-1988), 420 Lexis, Wilhelm (1837-1914), 171 Lie , Sophus (1842-1899), 25-34, 86, 105, 106, 391, 445 light-cone, 212 Lindemann, Ferdinand (1852-1939), 13 line element, 27, 225 linear associative algebras, 116 Liouville's theorem, 48, 178-179 Lipschitz , Rudolf (1832-1903), 29, 37, 38, 292 Listing, Johann Benedikt (1808-1882), 78 Littlewood, John E. (1885-1977), 227 Lobatchevskii, Nikolai (1792-1856), 26-30 logic foundations, 37, 47, 51-52, 57, 97, 100-111, 116-122, 125, 183, 296, 318-319, 370, 398, 426, 429, 450 symbolic, 66 longitudinal mass, 133 Lord Kelvin, 150, 161 Lorentz, Hendrik Anton (1853-1928), 49, 76, 77, 79, 129-136, 153, 174, 187235, 243, 244, 271-273, 280-289, 291293, 300-306, 312, 314, 333, 345, 346, 363-364, 375-377, 432-435, 446-447, 455-456, 460-461 Lorey, Wilhelm, 91, 92, 241, 445 Loria, Gino (1862-1954), 75 Loschmidt, Josef (1821-1895)., 47 Love, Augustus E.H. (1863-1940), 75, 153 Lübeck, 86 Lützen, Jesper, vi, 58, 60, 91, 148 M Mach, Ernst (1838-1916), 47-51, 55, 57, 64, 68, 92, 106, 129, 145, 251, 290, 323, 446 Madelung, Erwin (1881-1972), 241, 284, 440 magnetic permeability, 196 Majer, Ulrich, vi, 54, 87, 111, 400, 428, 464 Maltese, Giulio, 218, 377 Mancosu, Paolo, vi, 319, 326, 370 Manegold, Karl-Heinz, 74 Marburg, 91, 409 Marxsen, Sophus, 20 Masani, P.R., 414 INDEX Mathematische Annalen, 18, 34, 54, 73, 102, 163, 215-216, 229, 331, 340, 357, 359, 399-403, 445, 449 Mathematische Zeitschrift, 410, 449 matrix calculus, 190, 414 matrix mechanics, 414-417 Maxwell equations, 191, 193, 216, 273, 282-284, 299-304, 312, 341, 351, 362, 432 Maxwell, James Clerk (1831-1879), 46, 48, 54, 55, 64, 114, 131, 134, 153, 169, 170, 191, 193, 195, 216, 237-240, 248, 264, 273, 282-284, 296-304, 310-312, 314, 341, 344, 351, 362, 394, 430, 432, 433, 445, 446, 453, 454 Maxwell’s electromagnetic theory, 54, 55, 64, 114, 134, 248, 264, 300, 310, 394, 430 Mazzoni, L., 364 McCormmach, Russell, 13, 45, 48, 49, 51, 54, 61, 79, 92, 132, 134, 232, 234, 284, 297, 317, 321 mechanical models, 49, 50, 65 mechanical world view of nature, 50 mechanics analytical, 93, 129, 311 applied, 263 axiomatic approach, 93 Boltzmann’s presentation, 63, 148 celestial, 411 classical, 92, 173, 174, 191, 198, 208, 218, 235, 278, 281, 290, 390, 391 fluid, 130 foundations, 54-58, 69-71, 86, 100, 147, 148, 277, 405, 424 Hertz’s presentation, 55-59, 64, 69, 144 Hilbert’s presentation, 147 history, 368 Lagrangian, 312 lectures, 73 Newtonian, 51, 132, 199, 204, 206, 209, 217, 272, 276, 297 non-Galilean, 144 non-Lagrangian, 276 non-Newtonian, 276 of a mass-point, 92 of continua, 127, 128, 129, 149, 150, 151, 185, 228, 234, 236 of continua (Euler’s approach), 150 507 of continua (Lagrange’s approach), 150 principles, 67-71, 142, 145, 148, 178, 199, 447 rational, 70, 75, 251 relativistic, 280, 287 statics, 142, 397 statistical, 76, 179, 183, 228, 266, 268, 270, 284, 287, 323, 417, 448 Medicus, Hermann, 329 Mehra, Jagdish, 189, 265, 399, 411, 412, 413, 415, 419, 432 Mehrtens, Herbert, 112, 118 Mercury anomalous perihelion motion, 291, 294, 346, 352-355, 384, 407, 448 Mertens, Franz (1840-1927), 17 Methoden der mathematischen Physik (Hilbert-Courant), 410-411, 440 Michelson-Morley experiment, 187, 191, 210, 212, 279, 323, 430 Mie effect, 299 Mie, Gustav (1868-1957), vi, viii, 7, 182, 234, 251, 271-273, 280-285, 287, 298319, 324, 333-382, 404-407, 421, 433436, 447-448, 456-462 Mie’s electromagnetic theory of matter, 234, 298-319, 333-382, 405, 421, 435436, 447, 448, 456 Born’s version, 311, 315, 316, 335, 341, 344, 448 Milan, 297 Miller, Arthur I., 88, 133, 189, 191, 197, 218 minimal constraint principle, 68, 93, 145, 148 Minkowski metric, 380, 427 Minkowski, Hermann (1864-1909), viii, ix, 7, 13-15, 20-23, 73, 86-87, 101, 105, 110-111, 119, 128-136, 149, 152, 175, 182-228, 231, 235-236, 239, 242, 247, 250, 265, 268, 271, 278, 289-305, 309, 313, 318, 324, 333-34, 345, 361, 367, 380, 388, 402, 405, 411, 421, 427, 433, 436, 440-447, 453-456, 461-464 Minkowskian limit, 382 Möbius, August Ferdinand (1790-1868), 30, 32, 36 Molk, Jules (1857-1914), 76 Montgomery, D., 106 508 INDEX Moore, Eliakim H. (1862-1932), 95, 115, 116, 447 Moore, G.H., 45, 47, 97, 100, 121, 141 Müller, Conrad, 215, 368 Müller, Georg Elias (1850-1934), 178 Munich, 64, 74, 99, 232, 271, 317, 323, 326, 411, 446 Münster, 249, 251, 253, 257, 261, 262, 271, 310, 448 Murray, D., 178 N Nabl, J., 77, 447 Nagel, Ernst, 40 natural numbers, 37-39, 43, 169 n-body problem, 102, 281 n-electron problem, 273, 281, 282 Nelson, Leonard (1882-1927), 121, 319, 323 Nernst, Walter (1864-1941), 81, 129, 160, 241, 249, 252, 271, 317, 446, 448, 453-456, 464 Netto, Eugene (1848-1919), 75-76, 446 Neumann, Carl G. (1832-1925), 8, 51-53, 70, 73, 84, 143, 145, 179, 445 Neumann, Franz Ernst (1798-1895), 12, 51, 79, 166 Newtonian physics, 51, 57, 62, 63, 131, 132, 145-151, 162, 176, 200, 235-236, 272, 289-290, 295, 341, 352, 382, 393, 394, 430-431, 483, 486 n-manifold, 26 Noether, Emmy (1882-1935), 21, 38, 321, 326, 337, 356, 362, 369, 376, 388, 390-392, 403-409, 420, 441, 448-449, 456, 457 Noether, Max (1844-1921), 30 Noether’s invariance theorems, 337, 362 Noll, W., 178 non-holonomic systems, 150 Nordheim, Lothar (1899-1985), 8, 413418, 440, 449-452, 458 Nordström, Gunnar (1881-1923), 289, 306, 307, 364 Norlund, Niels E. (1885-1969), 76 North, J., 284 Norton, John D., vi, 192, 206, 222, 287, 289, 290, 291, 294, 306, 321, 324, 326, 349 nostrifizierung, 8, 99, 328, 406 number theory, 12, 13, 15, 20-25, 37, 78, 84, 86, 89, 93, 101, 104, 136, 169, 170, 222, 227, 396, 409, 429, 437, 450, 463 O observational errors, 166 Olesko, Katheryn M., 13, 61, 79, 92, 166 Oppenheimer, Robert (1904-1967), 411 Oppolzer, Egon Ritter von (1869-1907), 175-176 optics, 12, 15, 88, 135, 147, 176, 215, 232, 246, 262, 264, 265, 322, 446 Orlando, L., 218, 377 Osterbrock, Don, vi, 322 Ostrowski, Alexandre (1892-1986), 409 Ostwald, Wilhelm (1853-1932), 47, 49, 50 Oxford, England, 13, 441 Oxford, Ohio, 323 P Padoa, Alessandro (1868-1937), 111-112 Padova, 297 Pais, Abraham, 189, 224, 307, 322, 329, 432 Pappus’s theorem, 42, 89, 96-98 parallelogram law, 138, 140, 209, 396 Pareto, Vilfredo (1848-1923), 75 Paris, 1, 12, 13, 30, 35, 62, 65, 101, 105, 111, 122, 128, 149, 220, 445, 446 Paris Academy, 13 Parshall, Karen H., 17, 20, 31, 115 Pasch, Moritz (1843-1930), 25, 40-44, 57, 84, 85, 113, 115, 445 Pauli, Wolfgang (1900-1958), 77, 195, 306, 326, 375, 406, 411, 415, 416, 431, 436, 437, 449, 460 Peacock, George (1791-1858), 35 Peano ,Giuseppe (1858-1930), 36, 43, 44, 45, 86, 92, 111, 115, 446 Peckhaus, Volker, 47, 97, 104, 112, 121, 123, 319 perpetuum mobile, 145, 146, 154, 270 Perron, Oskar (1880-1975), 76 perturbation theory, 411 Petersen, Julius (1839-1910), 91, 129 Petrograd, 322 INDEX phenomenology, 49, 64, 66, 79, 80, 195, 234-239, 251, 268, 273, 285 mathematical, 65 physics continuity assumptions, 59, 68, 69, 139, 140-147, 156, 172, 177-178, 182, 214, 220, 418 foundations, 3, 6, 7, 11, 28, 49, 63, 71, 246, 267, 278, 290, 316, 331-334, 357, 366, 368, 380, 390, 396, 399, 403, 428, 432, 434, 438 Newtonian, 46, 47, 51, 131, 144-153, 173, 192, 203-205, 218, 235, 272, 276-277, 287, 290, 291, 294, 323, 380, 383, 394, 404, 405, 431 non-Archimedean, 141, 416 physics theoretical, 237, 373 Physikalische Zeitschrift, 76, 241, 249, 250, 251, 252, 262, 271, 307, 310 Physikalische Zeitung, 76 Picard, Émile (1856-1941), 12 Pieri, Mario (1860-1913), 44, 45, 111 piezoelectricity, 232, 319, 322 plagiarism, 417 Planck, Max (1858-1947), v, 46, 47, 64, 81, 129, 130, 154, 162, 168, 178, 179, 190, 191, 195, 212, 231-233, 242-257, 261-266, 271, 278, 284, 326, 369, 393, 423, 447-448, 455-457, 461-462 Planck’s law, 447 Planck’s radiation law, 232, 244, 447 Plücker , Julius (1801-1868), 30, 33 Pohl, Robert Wichard (1884-1976), 411 Poincaré, Henri (1854-1912), 12, 29, 34, 47, 71, 102, 135, 136, 149, 164, 165, 174, 186, 187, 190, 191, 194, 205, 212, 220, 223, 224, 227, 231, 244, 246, 289, 446, 447, 455, 456, 460 Poisson equation, 152, 162, 290, 293, 362 Poncelet, Jean Victor (1788-1867), 30 postulational analysis, 111-116 potential theory, 12, 15, 51, 73, 93, 127 Prandtl , Ludwig (1875-1953), 73, 119, 130, 153, 215, 411, 447, 455, 456 pre-established harmony, 103, 186, 213, 214, 252, 394, 423, 429 pressure, 58, 152, 155, 161, 169, 267, 268, 301, 397 Principia Mathematica (Russell Withehead), 319 509 mechanics, 66 Principles of Mechanics (Hertz), 221 Pringsheim, Alfred (1850-1941), 75-76 Pringsheim, Ernst (1859-1917), 75, 247266, 373, 446, 448 priority, 8, 134, 187, 280, 328, 350, 353, 362, 407, 408, 436, 449 probabilistic arguments, 170 probability calculus, 21, 47, 81, 107, 164, 166, 168, 169, 170, 171, 229, 267, 276 proper time, 199, 200, 204, 213, 385 propositional logic, 123 pseudo-geometry, 385, 387 psychophysics, 175-177, 276, 397 Purkert, Walter, vi, 117 Pycior, Elena, 35 Pyenson, Lewis, 103, 129, 130, 136, 174, 186, 187, 188, 189, 198, 324, 394, 432 Pythagoras, 393 Q q-calculus, 414 q-numbers, 415, 417 quantity magnitudes, 301-302 quantum discontinuity, 243, 244 quantum hypothesis, 231, 268-271 quantum mechanics, 8, 214, 413-419, 440, 449 quantum theory, 49, 79, 178, 179, 232, 243, 246, 284, 300, 317, 369, 377, 393, 397, 411-418, 449 quaternions, 193 R Rademacher, Hans (1892-1969), 227 radiation diffuse, 283, 284 monochromatic, 259 thermal, 231, 242 radiation theory, 7, 129, 154, 226-255, 256, 261, 264-268, 273, 276, 310, 317, 329, 358, 373, 397, 403, 408, 415, 417, 421, 438, 448, 464, 465 radioactivity, 49 Ramser, L., 61 Raum und Zeit (Minkowski), ix, 143, 205, 206, 209, 217, 222, 278, 279, 313, 345, 399, 402, 442, 451, 453, 480, 485 510 Raum-Zeit-Materie (Weyl), 364, 433-435, 449 Rausenberg, Otto, 92, 129 Rayleigh-Jeans law, 243 real numbers, 35-39, 96-104, 121, 138 continuity assumptions, 96, 101 Rechenberg, H., 410, 411, 413, 415, 419 reductionism electromagnetic, 7, 231, 285, 310, 313, 316, 333, 384 energicist, 49, 64 mechanical, 7, 46, 49, 50, 69, 221, 231, 235, 268, 285, 313 reference frame, 212, 292 accelerated, 187, 289, 293 inertial, 205, 235, 290 Reich, Karin, 29, 66, 190, 292 Reid, Constance, 3, 8, 22, 118, 185, 227, 232, 241, 325, 369, 409, 416, 420, 440, 442 Reiff, Richard (1855-1908), 149, 152 relativity of the gravitational potential principle, 305 postulate, 152, 187, 193, 198-216, 220221, 236 principle, 7, 8, 130, 185, 186, 187, 190-223, 239, 268, 274, 278, 285, 287, 290, 300-307, 321, 364 general theory, 2, 3, 7, 8, 77, 81, 106, 141, 152-153, 168, 182, 189, 206, 214, 225, 246, 284-287, 290-297, 302, 304, 309, 311, 320-333, 341, 345, 353, 356, 361-449, 464 eclipse expedition, 365-394 gravitational field-equations, 2, 225, 403, 441 Renn, Jürgen, vi, 287, 294, 330, 331, 337, 338, 340, 341, 345, 353, 380, 386, 387, 404, 405, 437 Resnik, Michael, 112, 118 reversible processes, 47, 156 Reye, Theodor (1838-1919), 83, 84 Ricci-Curbastro, Gregorio (1853-1925), 292 Richards, Joan L., 29 Riecke, Eduard (1845-1915), 72, 78, 79, 81, 232, 297, 307, 321, 411, 445, 446 Riemann curvature scalar, 341, 353 Riemann, Bernhard (1826-1866), 22-29, 33, 36, 37, 42, 44, 70, 84, 87, 105, 251, INDEX 292-293, 309, 324, 337, 341, 346, 352353, 359, 445 rigid body, 29, 133, 142, 150, 210, 217, 218, 219, 246, 272-273, 291, 312, 368, 376, 377, 447 free mobility of, 27, 28, 105 Rockefeller Foundation, 410 Rodriguez, Laura, 229 Röhle, S., 365 Rome, 166, 228, 244, 447 Röntgen, Wilhelm Conrad (1845-1932), 49 Rostock, 299 rotating disk, 291 Routh, Edward J. (1831-1907), 92, 129 Rowe, David E., v, 12, 17, 18, 22, 23, 24, 31, 32, 33, 35, 54, 72, 73, 74, 76, 85, 104, 112, 115, 296, 322, 341, 359, 364, 374, 375, 389, 390, 391, 421, 429, 434, 440, 441 Rüdenberg, L., 15, 20, 22, 105, 129 Rudolf Alfred Clebsch (1833-1872), 17, 20, 30, 54, 66, 73, 445 Rügen, 326, 448 Runge, Carl (1856-1914), 73, 119, 130, 142, 214-215, 321, 322, 391, 411, 447, 455-457, 461 Russell, Bertrand (1872-1970), 121, 319, 369, 370, 398, 427, 449, 460 S Saalschütz, Louis (1835-1913), 12 Sabidussi, G., 91 Sackur, Otto (1880-1914), 241 Sánchez-Ron, José M., 364 Sarkowski, H., 410 Sauer, Tilman, vi, 287, 294, 314, 325, 326, 329, 330, 339, 340, 345, 349, 351, 355, 356, 358, 360, 366, 369, 400 Scanlan, W., 97, 116 Schell, Wilhelm (1826-1904), 91 Schellenberg, Kurt, 265 Schemmel, Matthias, 321 Scherrer, Paul (1890-1966), 317, 321, 411 Schirrmacher, Arne, xii, 79, 129, 186, 230, 232, 234, 247, 249, 250, 251, 253, 257, 317 INDEX Schlömilch, Oscar Xavier (1823-1901), 142 Schmidt, Arnold (1902-1967), 95, 413 Schmidt, Erhard (1856-1959), 414 Schmidt, Friderich, 322 Schneider, Ivo, 166 Schoenflies. Arthur M. (1853-1928), 21, 61, 73, 89 Scholz, Erhard, vi, 28, 73, 88, 434 Schottky, Heinrich (1851-1935), 76, 297 Schrödinger equation, 415 Schrödinger, Erwin (1887-1961), 365, 414-416 Schubert, H.A. (1848-1911), 74, 75, 446 Schubring, Gert, 78 Schur, Friedrich (1856-1932), 42-43, 8790, 95, 97-99, 115, 138, 140-142, 297, 446 Schur, Issai (1875-1941), 297 Schwarz, Hermann Amandus (18431921), 47, 297 Schwarzschild, Karl (1873-1916), 72, 81, 130, 136, 174, 215, 321-326, 363, 364, 380-385, 435, 447, 454-455, 460 Schwermer, Joachim, 13-15, 61, 222 Seelig, Carl, 224 segments arithmetic (Streckenrechnung), 98 Segre, Michael, 34-36, 43, 75 set theory, 21, 45, 47, 101-102, 104, 120122, 229, 274, 321, 369, 379-398, 413, 450 axiomatization, 319 well-ordering axiom, 121, 369 Shimmack, Rudolf (1881-1912), 138 Siebert, H., 12 Sieg, Wilfried, 319, 370 Siegel, Carl Ludwig (1896-1981), 409 Siegmund-Schultze, Reinhard, 228, 410, 420 Sigurdsson, Skuli, 324, 442 Simon, Hermann Theodor (1870-1918), 130, 146, 321, 366, 372 Sinaceur, Houria, 89 Smith, Henry J.S (1826-1883), 13 sodium flames, 248 Solvay conference, 244 Sommer, Klaus, viii, 257, 326 Sommerfeld, Arnold (1868-1951), 73, 76, 129, 136, 187, 190, 205, 218, 224, 225, 232, 247, 250-251, 271, 302, 317, 320, 511 321, 324, 327, 345-349, 351, 356, 364, 368, 374, 41, 413, 416, 436, 447, 448, 455-462 Sommerfeld-Bohr atomic model, 416 space absolute, 52, 178, 187 space-time manifold, 224, 347 space-times coordinates, 339 spatial intuitions (Raumanschauungen), 36 Spehl, Helmut, vi, 299 Speiser, Andreas, (1885-1970), 20, 216 Springer, Ferdinand (1881-1965), 408 Springer’s Grundlehre Yellow Series, 410, 440 St. Petersburg, 150, 164, 266 stability theory, 128, 464 Stachel, John, vi, 212, 287, 291, 292, 294, 330, 331, 337-345, 353, 380, 386, 387, 403-405, 437 Staley, Richard, vi, 189, 195, 198, 212, 216, 225, 432 Stark, Johannes (1874-1957), viii, 211, 212, 277, 308, 459-461 Steiner, Jacob (1796-1863), 30 Stern , Otto (1888-1969), 284 Stoltz, Otto (1842-1905), 30 Stölzner, Michael, 419 straightest path principle, 93, 148 Strasbourg, 72 Strobl, W., 13 structural algebra, 25, 37, 116, 321, 409, 420 structure of matter, 7, 148, 168, 216, 231, 234, 267, 283, 284, 285, 315-319, 333, 344, 350-368, 403-405, 411 Struik, Dirk (1894-2000), 421 Strutt, John William - Lord Rayleigh (1842-1919), 243 Study, Eduard (1862-1930), 17 Swiss Mathematical Society, 396 Sylvester, James Joseph (1814-1897), 17, 20 symmetric function, 149, 228 Szanton, A., 411 T tensor contravariant, 335 gravitational, 293 512 metric, 291, 293, 294, 316, 333, 335, 344, 378, 385, 387, 407 Ricci, 293, 341, 348, 349, 355, 359, 375 Riemann, 293, 352, 359 second-rank, 407 stress-energy, 293, 294, 315, 316, 342, 344, 349, 355, 383, 390, 404, 435 stress-energy, 315 theology, 18, 299 theoretical physics, 13, 47, 49, 51, 78, 79, 81, 251, 280, 281, 299, 317, 411, 441, 445, 446 theory of bilinear forms, 66 theory of invariants, 12, 19, 20, 23, 91, 101, 228, 344, 361, 376 theory of matter, 8, 182, 191, 194, 226228, 237, 246, 249, 268, 271-272, 285, 287, 299-302, 308-309, 315- 319, 407, 435, 447, 448 thermochemistry, 241 thermodynamics, 15, 49, 79, 128, 129, 154-163, 171, 173, 181, 183, 212, 234, 241-249, 270, 271, 276, 397 continuity axiom, 159 relativistic, 191, 287 second law, 46, 47, 220, 239, 270, 271, 393 third law (Nernst law of heat), 241, 270, 317 Thiele, Rüdiger, 109 Thirring, Hans (1888-1976), 365 Thomson, Joseph James (1856-1940), 15, 91, 129, 130, 150, 284, 456 Tobies, Renate, 35, 54 Toepell, Michael Markus, 32, 44, 66, 83, 84-90, 93-99, 118, 323, 423 Toeplitz, Otto (1881-1940), 24, 77, 215, 227, 228, 436 Tollmien, Cordulla, 356 Tolman, Robert C., 276 Torretti, Roberto, 28, 29, 32, 40, 43, 44, 95 Traktoren, 190 transcendence of S, 13 transfinite cardinals, 100 transformations Galilean, 132, 207, 208, 210 Lorentz, 79, 132, 174, 190-197, 208, 235, 271, 272, 280, 306, 432 Truesdell, Clifford, 178 INDEX Tübingen, 51 Turner, R.S., 176 U Über den Zahlbegriff (Hilbert), 104, 123, 426, 479 ultraviolet catastrophe, 243 unification gravitation and electrodynamics, 172 mechanics and electrodynamics, 153 optics and electromagnetism, 134 unified foundations of physics, 231, 309, 331-333, 351, 397 unimodularity, 348 Urbantke, 365 USSR, 322 V van Dalen, Dirk, 396 van der Waerden, Bartel L. (1903-1996), 420, 459 van Dyck, Walther (1856-1934), 74, 75, 76, 77, 446 variational calculus, 47, 102, 104, 109, 214, 339, 344, 361, 391 variational derivation, 152, 295, 313, 373, 374, 375, 449 variational methods, 295, 353, 404, 414, 436 variational principles, 7, 109, 128, 133, 150, 182, 295, 312-314, 326, 336, 362, 373, 404, 436, 454 Veblen, Oswald (1880-1960), 97, 116 vector, 79, 138-151, 156-157, 178, 181, 189-191, 196-205, 224, 246, 283, 292, 301, 304, 314, 339, 360, 374, 390 contravariant, 360 four-vector, 190-194, 204-205, 301, 447 six-vector, 301 vectorial notation, 153 Veronese, Giusseppe (1854-1917), 25, 44, 86-87, 93, 99, 111, 419, 444 Vienna, 47, 74, 150, 306, 307-308, 316, 323, 448, 470 virtual velocities principle, 93 Voigt, Woldemar (1850-1919), 15, 61, 72, 78-81, 92, 121, 129, 215, 232-234, INDEX 248-249, 297, 317, 319, 321-322, 41, 445, 461 Volkert, Klaus, 12 Volkmann, Paul (1856-1938), 15, 61-63, 68, 81, 103, 106, 126, 180, 182, 446, 461, 462 Vollrath, Hans-Joachim, vi, 66 Volterra, Vito (1860-1940), 228 von Neumann, John (1903-1957), 412, 417-419, 449 von Smoluchowski, Marian (1872-1917), 249-262, 271, 369, 448, 456, 457 von Staudt , Christian (1798-1867), 30, 32, 40, 42, 43, 83-84, 97 Voss, Aurel (1845-1931), 66-71, 75, 92, 129, 132, 138, 143-144, 180, 447, 461462 W Walter, Scott, vi, 49, 133, 189, 192, 205, 211, 212, 224, 322, 411 Waring’s problem, 227-228 Warwick, Andrew C., 75, 92, 130, 132, 364 Was sind und was sollen die Zahlen? (Dedekind), 38, 39, 47, 85, 100, 446 wavelength, 176-177, 242-243, 252-262, 283, 463, 466 wave-mechanics, 414 Weber, Ernst Heinrich (1795-1878), 175 Weber, Heinrich (1842-1913), 12-13, 7274, 175, 446, 461, 463 Weber-Fechner law, 175-176 Weierstrass , Karl (1815-1897), 34, 35, 72, 102, 123, 379 Weyl, Hermann (1885-1955), 3, 4, 17, 20, 22, 89, 183, 215, 324, 359, 364, 373, 374, 392, 395, 431-436, 439, 442, 449, 451-463 Whittaker, Edmund (1873-1956), 75 Wiechert, Emil (1861-1928), 72, 81, 107, 130, 134, 136, 215, 321, 411, 446, 455, 463 Wien, Wilhelm (1864-1928), 49, 70, 129132, 153, 242-252, 299, 363, 369, 371, 446, 455, 460-461 Wiener, Hermann L. (1857-1939), 42, 43, 85, 87, 97, 99, 414-415, 446 Wien's formula, 243 Wightman, A.S., 1 513 Wigner, Eugene (1902-1995), 413, 458 Wilhelm Weber (1804-1891), 11, 78-79, 445-446 Wilkens, Alexander (1881-1968), 130 Wise, Norton, 301 Wolfskehl lectures, 231, 244, 271, 317, 320, 368, 371-372, 411-413, 448-449, 455-457 Wolfskehl, Paul (1856-1906), 231 Woodrow Wilson College, 323 World War I, 75, 319, 322, 370, 409 world-function, 7, 152, 302-303, 313, 315 world-lines, 201-204, 208, 300 world-parameters, 335, 339 world-points, 335 world-postulate, 152, 193, 199, 200, 206, 211-213, 223-225, 235, 402 Wüllner, Adolph (1835-1908), 12 Würzburg, 66, 369 Y Yandell, B.H., 1 Yavetz, Ido, 138 Young, Thomas (1773-1829), 52, 119, 176, 489 Z Zach, Richard, 370 Zahlbericht (Hilbert), 22-24, 71, 418, 446 Zahlkörpersspaziergängen, 89 Zangger, Heinrich (1874-1957), 287, 297, 324-325, 328, 355, 407, 419, 460 Zassenhaus, Hans, 15, 20-22, 105, 129 Zeeman effect, 79, 136 Zeeman, Pieter (1865-1943), 79, 130, 136 Zeitschrift für Mathematik und Physik, 73, 142 Zermelo, Ernst (1871-1953), 2, 47-48, 120-121, 215, 296, 319, 369, 398, 446447, 455 Ziegler, R., 30 Zippin, L., 106 Zsigmondy, Richard A. (1865-1927), 369 Zurich, 12-15, 129, 289, 297, 317, 318, 324, 369, 370, 406, 446, 448
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