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445

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The most important sources for unpublished material include the manuscripts of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: Grasmann’s Ausdehnungslehre.

1854: Riemann’s “On the Hypotheses which Lie at the Foundations of

Geometry”.

1859: Kirchhoff’s law of emission and absorption.

1860: Maxwell’s first paper on kinetic theory.

1861: Clebsch and Carl Neumann create the Mathematische Annalen.

1862: January 23 – Hilbert is born in Königsberg.

1867: Boltzmann’s first article on kinetic theory.

1870: Carl Neumann’s inaugural lecture in Leipzig, on the basic principles of

physical theories.

1871: Klein, Privatdozent in Göttingen, publishes his first paper on non-Euclidean

geometry.

1872: Klein’s Erlanger Programm.

Dedekind’s Stetigkeit und irrationale Zahlen.

Boltzmann formulates the Boltzmann Equation.

1876: Lodschmidt publishes his objections on kinetic theory and its reliance on

the atomistic hypothesis.

1877: Boltzmann publishes his statistical interpretation of entropy.

1881: Riecke succeeds Weber in Göttingen.

1882: Pasch’s Vorlesungen über neuere Geometrie.

1883: Voigt arrives in Göttingen as professor for theoretical physics.

1885: Hilbert completes his dissertation under Lindemann. Trip to Paris and Leipzig.

Minkowski moves to Bonn (until 1894).

1886: Felix Klein arrives back in Göttingen.

446 APPENDIX 1

1888: 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).

1890: DMV created by initiative of Cantor.

Hertz’s formulation of Maxwell’s electrodynamics.

1891: 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.

1892: Klein’s failed attempt to bring Hilbert to Göttingen. Weber came instead.

October 12 - Hilbert marries Käthe Jarosch.

1893: Hilbert’s summary article on algebraic invariants.

Mach’s Science of Mechanics.

1894: 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.

1895: 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.

1896: Zermelo’s debate with Boltzmann on kinetic theory.

Minkowski moves to Zurich.

Wien’s law of radiation.

1897: Hilbert’s Zahlbericht.

Boltzmann’s Lectures on the Principles of Mechanics.

Wiechert and Zermelo join the Göttingen faculty.

1898: 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.

1899: 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.

1900: 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 447

Planck’s law of radiation.

1901: 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.

1902: 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.

1903: Rusell’s paradox published.

1904: 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.

1905: Hilbert’s lectures on axiomatization, including physics.

Hilbert and Minkowski’s seminar on electron theory.

Einstein’s annus mirabilis.

1906: 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.

1907: 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.

1908: 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”.

1909: January 12 – Minkowski’s death.

Hilbert’s proof of Waring’s conjecture.

Landau appointed successor of Minkowski.

1910: 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.

1911: Hilbert’s first course on kinetic theory.

First Solvay Conference in Brussels.

1912: January 9 - Mie’s theory of matter, first installment.

448 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.

1913: 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.

1914: 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.

1915: 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 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.

1916: 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.

1917: 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.

1918: 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.

1921: Pauli completes his EMW article on GTR and moves to Göttingen to work

with Born.

1922: 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.

1923: Heisenberg completes his dissertation under Born in Göttingen.

1924: Hilbert’s GTR papers republished in the Mathematische Annalen.

Hilbert and Courant’s Methoden der mathematischen Physik.

1925: Hilbert contracts pernicious anemia.

1926: Von Neumann arrives in Göttingen.

December – Jordan’s article on the axiomatization of quantum mechanics.

1927: Construction of the new building for the mathematical institute begins.

Hilbert, von Neumann and Nordheim’s paper on the foundations of

quantum mechanics.

1930: Hilbert’s official retirement.

Autumn - Hilbert nominated honorary citizen of Königsberg. Lectures on

Naturerkennen und Logik.

1943: February 14 – Hilbert dies in Göttingen.

450

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 Partial Differential Equations (Notes by Nosse - HLN)

SS 1896 Ordinary Differential Equations (GVV)

SS 1898 Mechanics (DHN)

SS 1899 Variational Calculus (DHN)

WS 1900/01 Partial Differential Equations (DHN)

SS 1901 Linear Partial Differential Equations (Notes by A. Andrae - HLN)

WS 1901/02 Potential Theory (Notes by A. Andrae - HLN)

SS 1902 Selected Topics in Potential Theory (Notes by A. Andrae - HLN)

WS 1902/03 Continuum Mechanics - Part I (Notes by Berkowski - HLN)

SS 1903 Continuum Mechanics - Part II (Notes by Berkowski - HLN)

WS 1903/04 Partial Differential Equations (Notes by Prinz & Tieffenbach-

HLN)

WS 1904/05 Variational Calculus (Notes by E. Hellinger - HLN)

SS 1905 Logical Principles of Mathematical Thinking (and of Physics)

(Notes by E. Hellinger – HLN; Notes by Born - DHN)

SS 1905 Integral Equations (Notes by E. Hellinger - HLN)

WS 1905/06 Partial Differential Equations (Notes by E. Hellinger - HLN)

WS 1905/06 Mechanics (Notes by E. Hellinger - HLN)

SS 1906 Integral Equations (Notes by E. Hellinger - HLN)

COURSES ON PHYSICS 451

WS 1906/07 Continuum Mechanics (Notes by E. Hellinger - HLN)

SS 1907 Differential Equations (Notes by E. Hellinger - HLN)

WS 1909/10 Partial Differential Equations (Notes by R. Courant - HLN)

SS 1910 Selected Chapters in the Theory of Partial Differential Equations

(Notes by R. Courant - HLN)

WS 1910/11 Mechanics (Notes by F. Frankfurther, W. Behrens - HLN)

SS 1911 Continuum Mechanics (Notes by E. Hecke - HLN)

WS 1911/12 Statistical Mechanics (Notes by E. Hecke - HLN)

SS 1912 Radiation Theory (HLN)

SS 1912 Ordinary Differential Equations (HLN)

SS 1912 Mathematical Foundations of Physics (GVV)

WS 1912/13 Molecular Theory of Matter (HLN)

WS 1912/13 Partial Differential Equations (Notes by B. Baule - HLN)

WS 1912/13 Mathematical Foundations of Physics (GVV)

SS 1913 Foundations of Mathematics (and the axiomatization of Physics)

(GVV)

Electron Theory (HLN)

WS 1913/14 Electromagnetic Oscillations (HLN)

Analytical Mechanics (GVV)

Exercises in Mechanics (together with H. Weyl) (GVV)

SS 1914 Statistical Mechanics (Notes by L.Lange - HLN)

Differential Equations (GVV)

WS 1914/15 Lectures on the Structure of Matter (GVV)

SS 1915 Structure of Matter (Born’s Theory of Crystals) (HLN)

WS 1915/16 Differential Equations (HLN)

SS 1916 Partial Differential Equations (HLN)

Foundations of Physics I (General Relativity) (HLN)

WS 1916/17 Foundations of Physics II (General Relativity) (Notes by R. Bär –

HLN; Hückel - EHN)

SS 1917 Electron Theory (Notes by H. Humm - HLN)

SS 1918 Ordinary Differential Equations (GVV)

WS 1918/19 Space and Time (Notes by P. Bernays – HLN; E. Hückel - EHN)

Partial Differential and Integral Equations (GVV)

HS 1919 Nature and Mathematical Knowledge (Notes by P. Bernays –

HLN. Special Autumn Semester)

WS 1920 Mechanics (GVV)

SS 1920 Higher Mechanics and the New Theory of Gravitation (Notes by

A. Kratzer – HLN; E. Hückel - EHN)

WS 1920-21 Mechanics and the New Theory of Gravitation (Notes by A.

Kratzer – HLN; E. Hückel - EHN)

SS 1921 Einstein’s Gravitation Theory (GVV)

Basic Principles of the Theory of Relativity (Notes by P. Bernays -

HLN) – for students of all faculties

SS 1921 On Geometry and Physics (Partial Notes by E. Hückel – EHN)

SS 1922 Statistical Mechanics (Notes by L. Nordheim - HLN)

452 APPENDIX 2

WS 1922/23 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

SS 1923 Our Conception of Gravitation and Electricity (generally

understood) (GVV)

WS 1923/24 On the Unity of Science (HLN)

SS 1924 Mechanics and Relativity Theory (Notes by L. Nordheim - HLN)

WS 1926/27 Mathematical Methods of Quantum Theory (Notes by L.

Nordheim - HLN)

SS 1930 Mathematical Methods of Modern Physics

WS 1930/31 Nature and Thought

WS 1931/32 Philosophical Foundations of Modern Natural Science

453

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. Mechanics (with Klein) 1896 (?)

2. Stability Theory (with Minkowski) SS 1903

3. Exercises in Mechanics (with Minkowski) SS 1904

4. Mechanics WS 1904-05

5. Electron Theory (with Minkowski et al) SS 1905

6. The Equations of Electrodynamics (with Minkowski) SS 1907

7. Hydrodynamics ???

8. Electrodynamics ???

9. Kinetic Theory of Gases 1912

10. Structure of Matter (with Debye) WS 1914-15 to SS 1920

11. Structure of Matter WS 1920-21

12. Structure of Matter (with Born) SS 1921 to SS 1928

13. Theoretical and Math. Physics (with Born and Herglotz) WS 1927/28

3.B. PUBLIC LECTURES BY HILBERT:

1. Stability Theory (Kassel) 1903

2. Maxwell’s Theory of Gases 1912

3. Statistical Mechanics 1912

4. On Nernst’s Law of Heat 1913

5. Space and Time (Bucharest) 1918

6. On the Laws of Chance 1920

7. Nature and Mathematical Knowledge (Copenhagen) 1921

8. The Knowledge of Nature and Logic (Königsberg) 1930

454 APPENDIX 3

3.C. PHYSICAL LECTURES AT THE GMG AND GWG BY HILBERT:

1. Continuum Mechanics Feb. 24, 1903

2. Continuum Mechanics Aug. 4, 1903

3. The relations between variational principles and the theory of partial

differential equations, with applications to the integral principles of

mechanics. Jan. 18, 1910

4. Kinetic theory of gases Dec 19, 1911

5. Axiomatic Foundations of Physics (Ferienkurs for high-school

teachers) April 15-27, 1912

6. Theory of Radiation July 30, 1912

7. Theory of Radiation Jan. 21, 1913

8. Theory of Radiation July 28, 1914

9. The Fundamental Equations of Physics (General Relativity) Nov. 16, 1915

10. Foundations of Physics – First Part November 20, 1916

11. Foundations of Physics December 4, 1915

12. Theory of Invariants and the Energy Principle Jan. 25, 1916

13. The Causality Principle in Physics Nov. 21 & 28, 1916

14. Foundations of Physics – Second Part Dec. 23, 1916

15. Non-Euclidean Geometry and the new Gravitation Theory Jan. 23, 1917

16. Laue’s Theorem June 12, 1917

17. Reply to Klein’s “On Hilbert’s first note on the

Foundations of Physics” Jan. 29, 1918

18. The Energy Principle for the Motion of Planets in the New

Theory of Gravitation June 4, 1918

19. 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. On the Axioms of Vector Addition (R. Schimmack) June 9, 1903

2. Molecular Theory of Heat Conduction (G. Prasad) June 9, 1903

3. Capillarity (H. Minkowski) June 23, 1903

4. Linear Heat Conduction in Surfaces (G. Prasad) June 23, 1903

5. Maxwell’s Work on Stress Systems (Klein) June 23, 1903

6. Euler’s Equations of Hydrodynamics (Minkowski) June 28, 1903

7. Electromagnetic Quantity of Motion (Abraham) July 14, 1903

8. Gibb’s Thermodynamical Surfaces (H. Happel) Dec. 8, 1903

9. Variational Principles in Electrodynamics (Schwarzschild) Jan. 26, 1904

10. Can the Electron Reach the Speed of Light (P. Hertz) Jan. 26, 1904

11. On a Seminar on Hydrodynamics and Hydraulics (Klein) Feb. 9, 1904

12. Motion of a Material Particle on a Uniformly Moving

Plane (P. Ceresole) May 17, 1904

SEMINARS ON PHYSICS 455

13. On the Elasticity of the Earth (G. Herglotz) June 28, 1904

14. On Sommerfeld’s Works on Electron Theory (G. Herglotz) Dec. 6, 1904

15. Motion of a Fluid with Little Friction (L. Prandtl) Dec. 13, 1904

16. On a Talk by Poincaré on n the Future of Mathematical

Physics (C.H. Müller) Jan. 24, 1905

17. On Gases ans Vapors (L. Prandtl) May 23, 1905

18. On Poincaré’s Published Lectures on Mathematical

Physics (M. Abraham) Feb. 6, 1906

19. Poincaré’s Research on Rotating Fluid Masses (H. Müller) Feb. 13, 1906

20. On Gibb’s Book on Statistical Mechanics (Zermelo) Feb. 20, 1906

21. Graphical Methods in Mechanics and Physics (C. Runge) Feb. 27, 1906

22. On Painlevé’s Work on the Foundations of Mechanics

(Carathéodory) May 28, 1906

23. On W. Nernst’s “On Chemical Equilibrium” (Minkowski) June 26, 1906

24. Problems of Aeronavigation (Prandtl & Wiechert) Oct. 30, 1906

25. The Mathematical Theory of Elasticity (C.H. Müller) Nov. 6, 1906

26. On Botzmann’s H-Theorem (P. Ehrenfest) Nov. 13, 1906

27. The Evolution of the Theory of Radiation through the Works of

Lorentz, Rayleigh, W. Wien and Planck (Minkowski) Dec 1, 1906

28. On H. Witte’s “On the Possibility of a Mechanical

Explanation of Electromagnetic Phenomena” (Abraham) Dec. 18, 1906

29. On the Application of Probability Calculus to Astronomy

(Schwarzschild) Jan. 8, 1907

30. Theories of the Effects of Air Resistance (L. Prandtl) Jan. 22, 1907

31. Seismic Waves (E. Wiechert) Jan. 29, 1907

32. Statistical Stellar Astronomy (Schwarzschild) Feb. 19, 1907

33. Seismic Rays (G. Herglotz) May 14, 1907

34. Solutions of Differential Equations for Gas Spheres

(Gaskügeln) (K. Schwarzschild) July 30, 1907

35. On the Equations of Electrodynamics (Minkowski) Nov. 5, 1907

36. Graphical Methods in Fluid Mechanics (C. Runge) Nov. 26, 1907

37. Applications of Quaternions to Electron Theory (Klein) Dec. 10, 1907

38. A New, Simple General Proof of the Second Law of

Thermodynamics (Carathéodory) Dec. 17, 1907

39. An Overview of Man’s Attempts to Fly (C. Runge) March 3, 1908

40. Report on a Joint Seminar on Hydrodynamics (F. Klein,

L. Prandtl, C. Runge, E. Wiechert) May 5, 1908

41. An Experiment on Stabilization of Air Balloons (L. Prandtl) May 12, 1908

42. On Lanchester’s Book “Aerodynamics” (C. Runge) May 12, 1908

43. On the Equations of Electrodynamics (Minkowski) July 28, 1908

44. On Recent French Research on Aviation (C. Runge) Nov. 3, 1908

45. Recent Works on Earth Pressure (Th. Van Kármán) Nov. 24, 1908

46. Theory of Earth Pressure (A. Haar & Th. Van Kármán) Dec. 8, 1908

47. The New Mechanics (Poincaré, Wolfskehl Lectures) April 22-28, 1909

48. Position Determination from and Air Balloon (Runge) May 11 & 18, 1909

456 APPENDIX 3

49. Defintion of a Rigid Body on the “Einstein-Minkowski”

System of Electrodynamics (M. Born) June 8 & 15, 1909

50. Average Motion in the Theory of Perturbations and

Applications of Probability to Astronomy (F. Bernstein) June 22, 1909

51. On Minkowski’s Nachlass (Electrodynamics) (M. Born) Feb. 8, 1910

52. On the Definition of a Rigid Body (M. Born) Juni 21, 1910

53. Old and New Problems in Physics (Lorentz, Wolfskehl

Lectures) Summer 1910

54. Stable Orderings of Electrons in the Atom

(L. Föppl - PhD Dissertation supervised by Hilbert) Nov. 21, 1911

55. On Herglotz Work on Deformable Bodies in the

Theory of Relativity (M. Born) Dec. 12, 1911

56. The Behavior of Solid Bodies and Hooke’s Law (L. Prandtl) Jan. 16, 1912

57. A Newly Discovered Relation Between Elasticity of

Crystals and Optical Oscillations (M. Born & Th. van

Kármán) Feb. 13, 1912

58. Molecular Oscillations and Specific Heat (Born & van

Kármán) May 14, 1912

59. Theory of Dispersion in Crystals (P.P. Ewald - PhD Diss.) June 4, 1912

60. New Works of Poincaré and Ehrenfest on the Axiomatic

Foundation of Quantum Theory (Th. van Kármán) Juli 16, 1912

61. Statistical Mechanics (P. Hertz) Nov. 26, 1912

62. On Sommerfeld’s Article on the Theory of

Oscillating Equations (H. Weyl) Dec. 10, 1912

63. Mie’s Theory of Matter (M. Born) Dec. 17, 1912

64. Motion of Fluids (L. Prandtl) Feb. 4, 1913

65. Reports on the Solvay Conference, Brussels 1911

(Born & van Kármán) Feb. 25 & March 4, 1913

66. Kinetic Theory Week (Debye, Nernst, Von Smoluchowski,

Lorentz, Sommerfeld, Planck - Wolfskehl Lectures) May 1913

67. An Application of Diophantine Approximations to a

Question in Statistical Mechanics (E. Hecke) May 20, 1913

68. On the Structure of Crystals (M. Born) June 7, 1913

69. Recent Work of J.J. Thomson on Canal Waves

(Kanalstrahlen) (C. Runge) Juni 24, 1913

70. An Application of Quantum Theory to Capillarity

(M. Born & R. Courant) July 1, 1913

71. On a Recent Work of E. Noether on Turbulences in a

Fluid (Th. van Kármán) July 30, 1913

72. On Poincaré’s Book on Cosmogonic Hypotheses (L. Föppl) July 30, 1913

73. Propagation of Light in Transparent Media (W. Behrens) Nov. 4, 1913

74. On Mie’s theory of Matter (M. Born) Nov. 25, 1913

75. The Solution of an Equation of Spectroscopy (C. Runge) Dec. 2, 1913

76. Recent Work of Einstein and Grossmann on

Gravitation (F. Böhm) Dec. 9, 1913

77. On Mie’s Theory of Matter (M. Born) Dec. 16, 1913

SEMINARS ON PHYSICS 457

78. Theoretical Treatment of Phenomena in Diluted Gases

(B. Baule - PhD Dissertation Supervised by Hilbert) Feb 24, 1914

79. 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

80. Lattice Theory of Diamonds (M. Born) March 3, 1914

81. Intensity Distribution in Spectral Lines (P. Debye) Dec. 18, 1914

82. Foundation and Problems of Quantum Theory (P. Debye) Feb. 23, 1915

83. Dynamics of Crystal Lattices (M. Born) Feb. 25, 1915

84. Structure of Crystals (F. Klein, with Hilbert and Mügge) May 18, 1915

85. On Herglotz’s Research on Potentials in the Interior of

Attracting Masses (Wiarda) June 1, 1915

86. On Modern Physics (A. Sommerfeld) June 15, 1915

87. On Gravitation (A. Einstein, Wolfskehl Lectures) June 29 – July 7, 1915

88. Theory of Distant Forces (Uhlich-Pirna) July 20, 1915

89. History of Mechanics up until Galileo (C. Müller,

Wolfskehl Lectures) March 2-4, 1916

90. Diffusion, Brownian Movement, Colloidal Particles

91. (Von Smoluchowski, Wolfskehl Lectures) June 20-22, 1916

92. Four-dimensional Vectorial Analysis (C. Runge) Dec. 5, 1916

93. Foundations of a Theory of Matter (G. Mie, Wolfskhel

Lectures) June 5-8, 1917

94. On the Riemannian Curvature (Klein) Oct. 30, 1917

95. On the Riemannian Curvature (Klein) Nov. 6, 1917

96. On G. Herglotz’s Paper on Curvature and Gravitation (Klein) Dec. 4, 1917

97. On Liquid Crystals (M. Born) Dec. 11, 1917

98. On Invariants of Arbitrary Differential Expressions (E.

Noether) Jan. 15, 1918

99. On Hilbert’s First Note on the Foundations of Physics (Klein) Jan. 22, 1918

100. On Einstein’s Cosmological Ideas of 1917 (F. Klein) May 7, 1918

101. On Quantum Theory (M. Planck, Wolfskehl Lectures) May 13-17, 1918

102. On Einstein’s “On Gravitational Waves” (C. Runge) Jun. 31, 1918

103. On Einstein’s Cosmological Ideas of 1917 (Klein) June 11, 1918

104. On the Three-body Problem (C. Carathéodory) June 24, 1918

105. Einstein’s “Energy Principle in General Relatitvity” (Klein) July 4, 1918

106. Hilbert’s Energy Vector (Klein) July 22, 1918

107. Invariant Variational Problems (E. Noether) July 23, 1918

108. Organic Causality (Hans Driesch, Wolfskhel Lectures) Dec. 16-19, 1918

109. On the Structure of the Atom (N. Bohr, Wolfskehl Lectures) June 1922

458

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. 1912-13: Paul P. Ewald

2. 1913-14: Alfred Landé

3. 1914-16: Louise Lange

4. 1916-17: Richard Bär

5. 1918-19: Paul Bernays

6. 1920-21: Adolf Kratzer

7. 1921-22: Erich Hückel

8. 1922-27: Lothar Nordheim

9. 1927-28: Eugene Wigner

4.B. DOCTORAL STUDENTS ON PHYSICAL TOPICS:

As listed in HGA Vol. 3, 430-432.

1. Ludwig Föppl: “Stabile Anordnungen von Elektronen im Atom” (March 1,

1912)

2. Hans Bolza: “Anwendungen der Theorie der Integralrechnungen auf die

Elektronentheorie und die Theorie der verdünnten Gasen.” (July 2, 1913)

3. Bernhard Baule: “Theoretische Behandlung der Erscheinungen in

verdünnten Gasen.” (Feb. 18, 1914)

4. Kurt Schelenberg: “Anwendungen der Integralgleichung auf die Theories

der Elektrolysie.” (June 24, 1914)

5. Hellmuth Kneser: “Untersuchungen zur Quantentheorie.” (July 22, 1921)

459

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. Abraham to Stark Oct. 10, 1914 (Ch. 6, # 62)

2. Apelt to Grassmann Sept. 3, 1845 (Ch. 1, # 85)

3. Birkhoff to van der Waerden Nov. 1, 1973 (Ch. 9, # 41)

4. Born to Hilbert April 4, 1916 (Ch. 8, # 23)

5. Born to Hilbert Aug. 24, 1916 (Ch. 8, # 26)

6. Born to Hilbert Nov. 23, 1915 (Ch. 7, # 116)

7. Born to Hilbert Aug. 3, 1909 (Ch. 4, # 67)

8. Born to Hilbert Jan. 7, 1913 (Ch. 5, # 94)

9. Born to Hilbert Oct. 28, 1915 (Ch. 7, # 100)

10. Cantor to Hilbert Jan. 1, 1900 (Ch. 2, # 60)

11. Carathéodory to Hilbert Dec. 12, 1912 (Ch. 5, # 91)

12. Carathéodory to Hilbert April 4, 1913 (Ch. 5, # 106)

13. Dedekind to du Bois-Reymond March, 1888 (Ch. 2, # 10)

14. Dingler to Hilbert Jan. 2, 1915 (Ch. 8, # 40)

15. Einstein to Besso Dec. 10, 1915 (Ch. 7, # 50, 94)

16. Einstein to Besso Jan. 1, 1916 (Ch. 4, # 85)

17. Einstein to Besso Jan. 3, 1916 (Ch. 7, # 95)

18. Einstein to Ehrenfest Undated, 1914 (Ch. 6, # 20)

19. Einstein to Ehrenfest April 1, 1914 (Ch. 6, # 26)

20. Einstein to Ehrensfest Dec. 26, 1915 (Ch. 7, # 95)

21. Einstein to Freundlich Aug. 1, 1913 (Ch. 6, # 58)

22. Einstein to Freundlich Jan. 1, 1914 (Ch. 6, # 54)

23. Einstein to Habitch Dec. 24, 1907 (Ch. 6, # 10)

24. Einstein to Hilbert Nov. 7, 1915 (Ch. 7, # 98)

25. Einstein to Hilbert Nov. 12, 1915 (Ch. 7, # 101, 104)

26. Einstein to Hilbert Nov. 14, 1915 (Ch. 7, # 56)

27. Einstein to Hilbert March 16, 1916 (Ch. 7, # 108)

28. Einstein to Hilbert May 30, 1916 (Ch. 8, # 30)

29. Einstein to Hilbert May 30, 1916 (Ch. 8, # 76)

30. Einstein to Hilbert June 2, 1916 (Ch. 8, # 30)

31. Einstein to Hilbert June 2, 1916 (Ch. 8, # 93)

32. Einstein to Hilbert May 19, 1917 (Ch. 8, # 55)

33. Einstein to Hilbert Nov. 15, 1915 (Ch. 7, # 108)

34. Einstein to Hilbert Nov. 18, 1915 (Ch. 7, # 111)

35. Einstein to Klein Dec. 15, 1917 (Ch. 9, # 97)

460 APPENDIX 5

36. Einstein to Klein April 12, 1917 (Ch. 8, # 61)

37. Einstein to Kleiner April 3, 1912 (Ch. 4, # 86)

38. Einstein to Lorentz Aug. 16, 1913 (Ch. 6, # 18)

39. Einstein to Lorentz Oct. 12, 1915 (Ch. 7, # 92)

40. Einstein to Lorentz Jan. 17, 1916 (Ch. 8, # 2)

41. Einstein to Mie May 1, 1917 (Ch. 6, # 58)

42. Einstein to Mie June 1, 1917 (Ch. 6, # 58)

43. Einstein to Sommerfeld July 15, 1915 (Ch. 7, # 17, 89)

44. Einstein to Sommerfeld Nov. 28, 1915 (Ch. 7, # 93, 118)

45. Einstein to Sommerfeld Dec. 9, 1915 (Ch. 7, # 119)

46. Einstein to Sommerfeld Summer 1910 (Ch. 4, # 85)

47. Einstein to Stark Nov. 1, 1907 (Ch. 4, # 58)

48. Einstein to Weyl Nov. 23, 1916 (Ch. 8, # 53)

49. Einstein to Wien Oct. 10, 1915 (Ch. 8, # 42)

50. Einstein to Zangger April, 1915 (Ch. 6, # 1, 30)

51. Einstein to Zannger July 7, 1915 (Ch. 7, # 36)

52. Einstein to Zannger Aug. 7, 1915 (Ch. 7, # 40)

53. Ewald to Hilbert April 11, 1912 (Ch. 5, # 80)

54. Frege to Hilbert Jan. 6, 1900 (Ch. 2, # 95)

55. Hecke to Hilbert March 7, 1916 (Ch. 2, # 86)

56. Hilbert to Einstein Nov. 19, 1915 (Ch. 7, # 114)

57. Hilbert to Einstein May 27, 1916 (Ch. 8, # 40)

58. Hilbert to Einstein Nov. 13, 1915 (Ch. 7, # 106)

59. Hilbert to Einstein May 25, 1916 (Ch. 8, # 93)

60. Hilbert to Einstein March 30, 1912 (Ch. 5, # 77)

61. Hilbert to Einstein Oct. 3, 1912 (Ch. 5, # 145)

62. Hilbert to Frege Jan. 15, 1900 (Ch. 2, # 96)

63. Hilbert to Frege Nov. 7, 1903 (Ch. 3, # 5)

64. Hilbert to Frege Dec. 29, 1899 (Ch.2, 93,94,98, 99)

65. Hilbert to Hurwitz June 6, 1894 (Ch. 2, # 25)

66. Hilbert to Klein May 23, 1893 (Ch. 2, # 12)

67. Hilbert to Klein Nov. 15, 1893 (Ch. 2, # 13)

68. Hilbert to Klein Sept. 14, 1892 (Ch. 1, # 38)

69. Hilbert to Poincaré Nov. 6, 1908 (Ch. 5, # 13)

70. Hilbert to Poincaré Nov. 19, 1908 (Ch. 5, # 13)

71. Hilbert to Poincaré Nov. 25, 1908 (Ch. 5, # 13)

72. Hilbert to Poincaré May 6, 1912 (Ch. 5, # 62)

73. Hilbert to Russell April 12, 1916 (Ch. 8, # 40)

74. Hilbert to Schwarzschild July 17, 1915 (Ch. 7, # 37)

75. Hilbert to Schwarzschild Oct. 23, 1915 (Ch. 7, # 46)

76. Hilbert to Sommerfeld April 5, 1912 (Ch. 5, # 63)

77. Hilbert to Weyl April 22, 1918 (Ch. 9, # 78)

78. Klein to Pauli May 8, 1921 (Ch. 7, # 84, 87)

79. Klein to Pauli May 8, 1921 (Ch. 8, # 129)

80. Klein to Pauli May 8, 1921 (Ch. 8, # 49)

81. Mie to Hilbert Feb. 13, 1916 (Ch. 6, # 66; Ch. 8, # 43)

LETTERS QUOTED 461

82. Mie to Hilbert Feb. 29, 1916 (Ch. 8, # 46)

83. Mie to Hilbert May 8, 1917 (Ch. 8, # 48)

84. Mie to Hilbert May 16, 1917 (Ch. 8, # 48)

85. Mie to Hilbert June 10, 1917 (Ch. 8, # 50)

86. Mie to Hilbert July 2, 1917 (Ch. 8, # 51, 52)

87. Mie to Hilbert Dec. 26, 1917 (Ch. 8, # 50)

88. Mie to Stark Dec. 10, 1913 (Ch. 6, # 62)

89. Mie to Wien Oct, 10, 1915 (Ch. 8, # 42)

90. Mie to Wien Feb. 6, 1916 (Ch. 8, # 42)

91. Minkowski to Einstein Oct. 9, 1907 (Ch. 4, # 5)

92. Minkowski to Hilbert March 31, 1896 (Ch. 1, # 46)

93. Minkowski to Hilbert Dec. 20, 1890 (Ch. 1, # 18)

94. Planck to Hilbert Jan. 12, 1917 (Ch. 8, # 33)

95. Planck to Hilbert Feb. 8, 1917 (Ch. 8, # 31, 33)

96. Planck to Hilbert Jan. 20, 1918 (Ch. 8, # 31)

97. Planck to Hilbert Jan. 27, 1918 (Ch. 8, # 31)

98. Planck to Hilbert April 4, 1913 (Ch. 5, # 108)

99. Planck to Hilbert April 15, 1913 (Ch. 5, # 109)

100. Runge to Hilbert May 8, 1918 (Ch. 8, # 102)

101. Sommerfeld to Hilbert May 4, 1916 (Ch. 8, # 24)

102. Voigt to Lorentz May 19, 1911 (Ch. 5, # 17)

103. Volkmann to Hilbert Jan. 1, 1900 (Ch. 1, # 158)

104. Voss to Hilbert July 19, 1899 (Ch. 1, # 176)

105. Weber to Dedekind End of 1879 (Ch. 1, # 14)

462

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. 1909-

1918.

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. 1912-

1917.

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.

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 1898-

99.

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 1915-

1916.

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.

465

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

, the absorption coefficient

, 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

and refraction

capacity are such that the quotient

/q2 falls short of the wavelength

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,

): The characteristic

magnitudes of radiation for any given wavelength (speed of light q, emission

coefficient

, absorption coefficient

) 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.

466 AXIOMS OF RADIATION THEORY

Axiom 5 (Axiom of the existence of certain diversities in matter): There exist

substances whose absorptions coefficient

and refraction capacity are such that the

quotient

/q2 falls short of the wavelength

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.

467

REFERENCES

COMMONLY USED ABBREVIATIONS

AHES Archive for History of Exact Sciences

AIHS Archives int. d’histoire des sciences

AJP American Journal of Physics

AM Annals of Mathematics

AMP Archiv für Mathematik und Physik

AMS American Mathematical Society

AP Annalen der Physik

ASN Nachlass Arnold Sommerfeld, Deutsches Museum, Munich.

BSL The Bulletin of Symbolic Logic

BSPS Boston Studies in the Philosophy of Science

CPAE The Collected Papers of Albert Einstein (Princeton, Princeton

University Press).

CRN Nachlass Runge – Du Bois Reymond, Staatsbibliothek Berlin,

Preußischer Kulturbesitz

DHN Nachlass David Hilbert – Niedersächsische Staats- und

Universitätsbibliothek Göttingen, Abteilung Handschriften und Seltene

Drucke, Nachlass Hilbert (Cod. Ms. D. Hilbert).

DMV Deutschen Mathematiker-Vereiningung

DSB Dictionary of Scientific Biography

EHN Nachlass Erich Hückel, Staatsbibliothek Berlin, Preußischer

Kulturbesitz

EMV Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer

Anwendungen

ES Einstein Studies

GdG Grundlagen der Geometrie

GDNA Gesellschaft Deutscher Naturforscher und Ärzte

GMG Göttingen Mathematische Gesellschaft

GN Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu

Göttingen, Mathematische-Physikalische Klasse

GTR General Theory of Relavitity

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GWG Königlichen Gesellschaft der Wissenschaften zu Göttingen

HGA David Hilbert – Gesammelte Abhandlungen

HLN Manuscript/Typescript of Hilbert Lecture Notes. Bibliothek des

Mathematisches Insititut, Universität Göttingen

HM Historia Mathematica

HPL History and Philosophy of Logic

HSPS Historical Studies in the Physical Sciences

ICM International Congress of Mathematicians

JDMV Jahresbericht der Deutschen Mathematiker-Vereiningung

JRAM Journal für die reine und angewandte Mathematik

JRE Jahrbuch der Radioaktivität und Elektronik

JSHS Japanese Studies in the History of Science

JSL Journal of Symbolic Logic

JSN Nachlass Johannes Stark – Staatsbibliothek Berlin, Preußischer

Kulturbesitz.

LCP Collected Papers of Hendrik Anton Lorentz

MA Mathematische Annalen

MBN Nachlass Max Born, Staatsbibliothek Berlin, Preußischer Kulturbesitz

MPIWG Max Planck Institut für Wissenschaftgeschichte, Berlin

MZ Mathematische Zeitschrift

PAWS Königlich Preussische Akademie der Wissenchaften (Berlin)

Sitzungsberichte

PB Physikalische Blätter

PiP Physics in Perspective

PZ Physikalische Zeitschrift

SHPMP Studies in History and Philosophy of Modern Physics

SHPS Studies in History and Philosophy of Science

SiC Science in Context

SN Science Networks

STR Special Theory of Relativity

SUB Göttingen Niedersächsische Staats- und Universitätsbibliothek, Göttingen.

Trans. AMS Transactions of the AMS

VDPG Verhandlungen der Deutsche Physikalische Gesellschaft

VGDNA Verhandlungen GDNA

ZMP Zeitschrift für Mathematik und Physik

ZP Zeitschrift für Physik

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497

INDEX

Aachen, 136

Abraham, Max (1875-1922), 8, 49, 133-

136, 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

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, 94-

106, 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, 120-

123, 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, 166-

168, 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 (Vollständigkeits-

axiom), 97, 100, 121

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, 177-

178, 198, 230, 239, 262, 266-278, 334,

344, 350-351, 357, 373-374, 397, 403,

418, 442

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, 164-

166, 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, 46-

50, 60-65, 76, 77, 80, 92, 106-107,

129, 140, 141, 148-153, 168-171, 179-

180, 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 499

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, 447-

463

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

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

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, 381-

386, 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, 164-

167, 171

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, 185-

186, 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

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 (1876-

1964), 47, 76, 77, 150, 179, 265, 440,

448

Einstein, Albert (1879-1956), v, vii, 2, 7,

8, 81, 132, 136, 149, 168, 182, 186-

195, 205-206, 211-226, 235-236, 243,

249, 271, 284-297, 300, 302-317, 320-

462

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 501

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, 178-

200, 205, 210-225, 239, 246-248, 272-

281, 300, 304-305, 311-316, 324, 333-

337, 342-345, 350, 356-357, 362, 367,

375-376, 387, 390-391, 397, 401, 432-

434, 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, 132-

134, 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

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, 254-

257, 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

Fachwerk von Begriffen, 123, 124, 393,

396, 425

Fano, Gino (1871-1952), 34, 44, 75, 77,

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

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, 85-

89, 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, 290-

291, 296, 306, 378-388, 396, 423-

427, 454

foundations, 1, 3, 6, 7, 11, 19- 25, 28-

29, 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 503

Goenner, Hubert, 364

Goethe, Johann Wolfgang von (1749-

1832), 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,

Grassmann, Hermann Gunther (1809-

1877), 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, 289-

302, 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

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), 289-

295, 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.

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, 371-

374, 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 INDEX

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, 86-

96, 106-107, 113, 136, 140-144, 147-

150, 153-154, 179-181, 221, 235, 273,

277-278, 299, 321, 326, 424-446, 454-

457

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, 339-

340, 360, 402

energy concept, 338, 342-344, 351,

356, 360, 389, 422

first communication, 352

first printed version, 343, 353, 355,

361, 402-405

Proofs version, 330, 334-345, 357-

361, 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

ideal oscillator, 242

Immanuel Kant (1724-1804), 12, 57, 69-

70, 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,

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 505

inertial properties of matter, 49, 213

infinite matrices, 414

infinitesimal element, 27, 201

Ingrao, Bruna, 75

insurance mathematics, 107, 164, 171-

173, 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

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, 414-

418, 437, 440

Jungnickel, Christa, 13, 45, 48, 49, 51,

54, 61, 79, 92, 132, 134, 232, 234, 297,

317, 321

Kahle, R., 104, 121

Karachalios, Andreas, 411

Kármán, Theodor von (1881-1963), 241,

265, 455, 456

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, 78-

83, 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, 21-

24, 72, 102-104, 123, 379, 417

Kuhn, Thomas .S., 46-48, 79, 154, 168,

242-247

Kummer, Edward E. (1810-1893), 21-24

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, 187-

235, 243, 244, 271-273, 280-289, 291-

293, 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

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 507

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

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, 298-

319, 324, 333-382, 404-407, 421, 433-

436, 447-448, 456-462

Mie’s electromagnetic theory of matter,

234, 298-319, 333-382, 405, 421, 435-

436, 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

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, 413-

418, 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

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,

Oxford, England, 13, 441

Oxford, Ohio, 323

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 509

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

mechanics, 66

Principles of Mechanics (Hertz), 221

Pringsheim, Alfred (1850-1941), 75-76

Pringsheim, Ernst (1859-1917), 75, 247-

266, 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-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

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 INDEX

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, 220-

221, 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,

292-293, 309, 324, 337, 341, 346, 352-

353, 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),

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

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 511

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, 87-

90, 95, 97-99, 115, 138, 140-142, 297,

446

Schur, Issai (1875-1941), 297

Schwarz, Hermann Amandus (1843-

1921), 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),

Segre, Michael, 34-36, 43, 75

set theory, 21, 45, 47, 101-102, 104, 120-

122, 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,

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),

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,

symmetric function, 149, 228

Szanton, A., 411

tensor

contravariant, 335

gravitational, 293

512 INDEX

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, 226-

228, 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,

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

Tübingen, 51

Turner, R.S., 176

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

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 513

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, 461-

462

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, 72-

74, 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, 129-

132, 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

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

Yandell, B.H., 1

Yavetz, Ido, 138

Young, Thomas (1773-1829), 52, 119,

176, 489

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, 446-

447, 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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