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APPENDIX 1
GENERAL CHRONOLOGY OF EVENTS MENTIONED
IN THE TEXT

The following seven appendixes summarize some of the relevant information
appearing in the foregoing chapters. The information contained here has been
gathered from various sources, which are mostly documented in the main text itself.
The most important sources for unpublished material include the manuscripts of
Hilbert’s lecture notes at the Lesezimmer of the mathematical institute in Göttingen
as well as other documents in Hilbert’s Nachlass; miscellaneous announcements in
the JDMV and in the Physikalische Zeitschrift, and source books such as Biermann
1988 or Lorey 1916. I have made the necessary efforts to ensure that the information
appearing here be as comprehensive as possible in the various categories considered,
but it is indeed conceivable that additional sources may add further items to those
appearing here.
1844:
1854:
1859:
1860:
1861:
1862:
1867:
1870:
1871:
1872:

1876:
1877:
1881:
1882:
1883:
1885:
1886:

Grasmann’s Ausdehnungslehre.
Riemann’s “On the Hypotheses which Lie at the Foundations of
Geometry”.
Kirchhoff’s law of emission and absorption.
Maxwell’s first paper on kinetic theory.
Clebsch and Carl Neumann create the Mathematische Annalen.
January 23 – Hilbert is born in Königsberg.
Boltzmann’s first article on kinetic theory.
Carl Neumann’s inaugural lecture in Leipzig, on the basic principles of
physical theories.
Klein, Privatdozent in Göttingen, publishes his first paper on non-Euclidean
geometry.
Klein’s Erlanger Programm.
Dedekind’s Stetigkeit und irrationale Zahlen.
Boltzmann formulates the Boltzmann Equation.
Lodschmidt publishes his objections on kinetic theory and its reliance on
the atomistic hypothesis.
Boltzmann publishes his statistical interpretation of entropy.
Riecke succeeds Weber in Göttingen.
Pasch’s Vorlesungen über neuere Geometrie.
Voigt arrives in Göttingen as professor for theoretical physics.
Hilbert completes his dissertation under Lindemann. Trip to Paris and Leipzig.
Minkowski moves to Bonn (until 1894).
Felix Klein arrives back in Göttingen.

445

446
1888:

1890:
1891:

1892:
1893:
1894:

1895:

1896:

1897:

1898:

1899:

1900:

APPENDIX 1
Hilbert proves the finite basis theorem for the general case.
Dedekind’s Was sind und was sollen die Zahlen?
Poincaré’s Sorbonne lectures on electricity and optics (also in 1890-91).
DMV created by initiative of Cantor.
Hertz’s formulation of Maxwell’s electrodynamics.
Hilbert’s first course on geometry in Königsberg.
DMV meeting in Halle. Wiener lectures on the Foundations of Geometry.
Veronese’s work on non-Archimedean geometries.
Peano’s axioms of arithmetic.
Klein’s failed attempt to bring Hilbert to Göttingen. Weber came instead.
October 12 - Hilbert marries Käthe Jarosch.
Hilbert’s summary article on algebraic invariants.
Mach’s Science of Mechanics.
Early discussions on the EMW project - Meyer, Weber, Klein.
Minkowski returns to Königsberg.
Nernst appointed ordinary professor at Göttingen. He heads the newly
created Institute for Physical Chemistry.
Hertz’s Principles of Mechanics.
March - Hilbert arrives in Göttingen.
Cantor’s Beiträge zur Begründung der tranfiniten Mengenlehre, that
summarized and helped spreading his theory.
Dyck and Burkhardt join the editorial committee of the EMW.
Lorentz’s article on the electrodynamics of moving bodies.
Zermelo’s debate with Boltzmann on kinetic theory.
Minkowski moves to Zurich.
Wien’s law of radiation.
Hilbert’s Zahlbericht.
Boltzmann’s Lectures on the Principles of Mechanics.
Wiechert and Zermelo join the Göttingen faculty.
Hilbert’s first course on mechanics in Göttingen.
Schur’s results on projective geometry.
First articles of the EMW published: Schubert on the foundations of
arithmetic, Netto on combinatorics and Pringsheim on irrational numbers
and convergence.
Hilbert elected head of the DMV.
Hilbert’s first course on geometry in Göttingen.
Weber-Gauss monument unveiled. Grundlagen der Geometrie is published.
Riecke establishes the Physikalische Zeitschrift and acts as its first editor.
September - joint meeting of the DMV-GDNA in Munich. Boltzmann’s
popular lecture on recent developments in physics. Hilbert is present in the
audience.
December – Frege and Hilbert start their correspondence on the meaning of
axiomatization.
Hilbert’s Über den Zahlbegriff.
August – ICM in Paris. Hilbert presents his list of twenty-three problems.
Volkmann’s textbook on theoretical physics.

GENERAL CHRONOLOGY

1901:

1902:

1903:
1904:

1905:

1906:

1907:

1908:

1909:

1910:

1911:
1912:

447

Planck’s law of radiation.
September 18 - 150th anniversary of the GWG. In the keynote address,
Hilbert analyzes the conditions of validity of the Dirichlet Principle.
November 18 – Hilbert presents his solution of the fifth problem for the
plane.
Schwarzschild appointed professor of astronomy and director of the
observatory in Göttingen.
Voss’s EMW article on the principles of mechanics.
Husserl comes to Göttingen.
Hilbert refuses an offering to take Fuchs’ chair in Berlin. Minkowski comes
to Göttingen.
Hilbert starts working on linear integral equations.
Moore teaches GdG in Chicago opening the way to postulational analysis in
USA.
Rusell’s paradox published.
ICM in Heidelberg. Hilbert’s “On the Foundations of Logic and
Arithmetic”.
Runge, Prandtl and Herglotz arrive in Göttingen.
Lorentz’s EMW article on electron theory.
Hilbert’s lectures on axiomatization, including physics.
Hilbert and Minkowski’s seminar on electron theory.
Einstein’s annus mirabilis.
January - Poincaré’s article on the dynamics of the electron, including a
section on gravitation.
New building of the physics institute inaugurated in Göttingen.
Planck’s textbook on radiation.
Boltzmann and Nabl’s EMW article on kinetic theory.
Einstein adopts the “equivalence principle” as fundamental for any
relativistic treatment of gravitation.
November - Minkowski’s first talk on electrodynamics at the GMG.
December 21 - Minkowski’s second talk on electrodynamics at the GMG.
Sketch of a relativistic theory of gravitation.
Zermelo’s proof of the well-ordering theorem.
ICM in Rome: Hilbert calls for a “methodologically unified reorganization
of algebra and analysis”, using his theory of integral equations. Lorentz
lectures on black body radiation.
September 21 - GDNA meeting in Köln. Minkowski’s “Space and Time”.
January 12 – Minkowski’s death.
Hilbert’s proof of Waring’s conjecture.
Landau appointed successor of Minkowski.
Hilbert is awarded the second Bolyai Prize.
Born’s articles on rigidity in STR (partly based on Minkowski’s ideas).
Sommerfeld’s two-part article on Minkowski’s four-vectors and relativity.
Hilbert’s first course on kinetic theory.
First Solvay Conference in Brussels.
January 9 - Mie’s theory of matter, first installment.

448

1913:

1914:

1915:

APPENDIX 1
June 7 - Mie’s theory of matter, second installment.
Hilbert publishes his article on kinetic theory.
Paul and Tatyana Ehrenfest’s EMW article on statistical mechanics.
Ewald appointed as Hilbert’s first assistant for physics.
August: Einstein takes his position at the ETH Zurich. Reencounters with
Grossman and starts working seriously on general relativity.
Hilbert’s first course on radiation theory.
September – GDNA meeting in Münster. Hilbert lectures on radiation
theory
November 2 – Mie’s theory of matter, third installment.
December – Born and Carathéodory discuss with Pringsheim the contents
and implications of Hilbert’s work on radiation theory.
Hilbert publishes several versions of his approach to radiation theory.
Pringsheim publishes two critical articles.
April – Hilbert corresponds with Planck on radiation theory.
May-June – Einstein and Grossmann publish their Entwurf theory.
September – 85th GDNA meeting in Vienna. Einstein discusses several
existing theories of gravitation.
December 16 – Born’s version of Mie´s theory.
Hilbert’s publishes the final version of his radiation theory.
April – Einstein moves to Berlin.
April – Kinetic theory week in Göttingen. Lectures by Planck, Debye,
Nernst, Von Smoluchowski, Sommerfeld.
August – The Great War breaks out.
October – Aufruf an die Kulturwelt - Neither Einstein nor Hilbert among
the signees.
November – Einstein’s “On the Formal Foundations of the General Theory
of Relativity”. An elaborate, comprehensive version of the Entwurf theory.
Spring – Emmy Noether arrives in Göttingen.
June 29 to July 7 – Einstein’s Wolfskehl lectures.
Summer – Einstein corresponds with Paul Hertz on the ‘hole argument’.
July-November – No known contact between Hilbert and Einstein. The two
may have coincided for a short time at Rügen. Over the month of October,
Einstein became increasingly dissatisfied with his theory, and increasingly
convinced of the need to return to generally covariant field equations.
November – In four successive sessions of the Berlin academy Einstein
reads four papers on gravitation and relativity.
November 7 – Beginning of the Hilbert-Einstein correspondence.
November 18 – Einstein’s third Academy talk, with an explanation of
Mercury’s perihelion deviation.
November 20 – Hilbert’s lecture at the GWG on the “Foundations of
Physics”.
November 25 – Einstein present the final version of his gravitational field
equations.

GENERAL CHRONOLOGY

1916:

1917:

1918:

1921:
1922:

1923:
1924:
1925:
1926:
1927:

1930:

1943:

449

December 6 – Hilbert receive the galley proofs of his article on the
proceedings of the GWG.
December 20 – After a brief tension against the background of a possible
priority issue over the formulation of the equation, Einstein writes a
conciliatory letter to Hilbert.
January – First solution of the gravitational field equations of GTR,
formulated by Schwarschild’s for a special case, is communicated by
Einstein at the Berlin Academy.
March – First published version of Hilbert’s communication.
April – Hilbert start corresponding with Russell on foundations of
arithmetic.
May – Einstein’s first systematic presentation of GTR published in Annalen
der Physik.
Hilbert teaches GTR at Göttingen.
October – Einstein publishes his variational derivation of the gravitational
field equations.
December 23 – Hilbert’s second communication at the GWG.
Spring – Einstein publishes the first semi-popular presentation of GTR
Einstein’s first cosmological paper.
Mathematische Zeitschrift created through the efforts of Courant and
Ferdinand Springer.
January – Klein lectures on the status of energy conservation in Hilbert’s
theory and GTR. This is followed by a series of related lectures by Hilbert,
Noether and others.
Easter – Weyl’s Raum-Zeit-Materie.
Bernays arrives in Göttingen to work with Hilbert on the foundations of
arithmetic
December – Discharged soldiers start returning from the front.
Pauli completes his EMW article on GTR and moves to Göttingen to work
with Born.
June – Bohr’s Wolfskehl lectures on atomic structure.
Hilbert’s “New Foundations of Mathematics”.
Hilbert teaches a course on the mathematical foundations of quantum theory.
Heisenberg completes his dissertation under Born in Göttingen.
Hilbert’s GTR papers republished in the Mathematische Annalen.
Hilbert and Courant’s Methoden der mathematischen Physik.
Hilbert contracts pernicious anemia.
Von Neumann arrives in Göttingen.
December – Jordan’s article on the axiomatization of quantum mechanics.
Construction of the new building for the mathematical institute begins.
Hilbert, von Neumann and Nordheim’s paper on the foundations of
quantum mechanics.
Hilbert’s official retirement.
Autumn - Hilbert nominated honorary citizen of Königsberg. Lectures on
Naturerkennen und Logik.
February 14 – Hilbert dies in Göttingen.

APPENDIX 2
HILBERT’S GÖTTINGEN COURSES ON PHYSICS
(and related fields): 1895-1927

In compiling the following list I have relied on several documents, mainly the
Nachlassverzeichnisse at the mathematical institute (HLN) and at the
Handschriftenabteilung, SUB Göttingen (DHN). These documents, however, omit
several items registered in the printed version of the Göttingen
Vorlesungsverzeichnisse (GVV) for the years in question. In addition, DHN 520
contains another list of Hilbert’s courses over 46 years, between 1886 and 1932.
This list is complied in Hilbert’s own handwriting until WS 1917-18. It indicates, in
particular, that while at Königsberg, Hilbert taught one course on Hydrodynamics in
SS 1887 (notes preserved in DHN 522). Needless to say, there are also many
additional lectures throughout the years on more purely mathematical topics not
included here, and ranging from geometry, to integral and differential calculus, to
invariants, number theory, set theory and logic.
I have added in parentheses a reference to the existing notes for the lecture notes
of most courses and their locations.
WS 1895/96
SS 1896
SS 1898
SS 1899
WS 1900/01
SS 1901
WS 1901/02
SS 1902
WS 1902/03
SS 1903
WS 1903/04
WS 1904/05
SS 1905
SS 1905
WS 1905/06
WS 1905/06
SS 1906

Partial Differential Equations (Notes by Nosse - HLN)
Ordinary Differential Equations (GVV)
Mechanics (DHN)
Variational Calculus (DHN)
Partial Differential Equations (DHN)
Linear Partial Differential Equations (Notes by A. Andrae - HLN)
Potential Theory (Notes by A. Andrae - HLN)
Selected Topics in Potential Theory (Notes by A. Andrae - HLN)
Continuum Mechanics - Part I (Notes by Berkowski - HLN)
Continuum Mechanics - Part II (Notes by Berkowski - HLN)
Partial Differential Equations (Notes by Prinz & TieffenbachHLN)
Variational Calculus (Notes by E. Hellinger - HLN)
Logical Principles of Mathematical Thinking (and of Physics)
(Notes by E. Hellinger – HLN; Notes by Born - DHN)
Integral Equations (Notes by E. Hellinger - HLN)
Partial Differential Equations (Notes by E. Hellinger - HLN)
Mechanics (Notes by E. Hellinger - HLN)
Integral Equations (Notes by E. Hellinger - HLN)

450

COURSES ON PHYSICS
WS 1906/07
SS 1907
WS 1909/10
SS 1910
WS 1910/11
SS 1911
WS 1911/12
SS 1912
SS 1912
SS 1912
WS 1912/13
WS 1912/13
WS 1912/13
SS 1913

WS 1913/14

SS 1914
WS 1914/15
SS 1915
WS 1915/16
SS 1916
WS 1916/17
SS 1917
SS 1918
WS 1918/19
HS 1919
WS 1920
SS 1920
WS 1920-21
SS 1921

SS 1921
SS 1922

451

Continuum Mechanics (Notes by E. Hellinger - HLN)
Differential Equations (Notes by E. Hellinger - HLN)
Partial Differential Equations (Notes by R. Courant - HLN)
Selected Chapters in the Theory of Partial Differential Equations
(Notes by R. Courant - HLN)
Mechanics (Notes by F. Frankfurther, W. Behrens - HLN)
Continuum Mechanics (Notes by E. Hecke - HLN)
Statistical Mechanics (Notes by E. Hecke - HLN)
Radiation Theory (HLN)
Ordinary Differential Equations (HLN)
Mathematical Foundations of Physics (GVV)
Molecular Theory of Matter (HLN)
Partial Differential Equations (Notes by B. Baule - HLN)
Mathematical Foundations of Physics (GVV)
Foundations of Mathematics (and the axiomatization of Physics)
(GVV)
Electron Theory (HLN)
Electromagnetic Oscillations (HLN)
Analytical Mechanics (GVV)
Exercises in Mechanics (together with H. Weyl) (GVV)
Statistical Mechanics (Notes by L.Lange - HLN)
Differential Equations (GVV)
Lectures on the Structure of Matter (GVV)
Structure of Matter (Born’s Theory of Crystals) (HLN)
Differential Equations (HLN)
Partial Differential Equations (HLN)
Foundations of Physics I (General Relativity) (HLN)
Foundations of Physics II (General Relativity) (Notes by R. Bär –
HLN; Hückel - EHN)
Electron Theory (Notes by H. Humm - HLN)
Ordinary Differential Equations (GVV)
Space and Time (Notes by P. Bernays – HLN; E. Hückel - EHN)
Partial Differential and Integral Equations (GVV)
Nature and Mathematical Knowledge (Notes by P. Bernays –
HLN. Special Autumn Semester)
Mechanics (GVV)
Higher Mechanics and the New Theory of Gravitation (Notes by
A. Kratzer – HLN; E. Hückel - EHN)
Mechanics and the New Theory of Gravitation (Notes by A.
Kratzer – HLN; E. Hückel - EHN)
Einstein’s Gravitation Theory (GVV)
Basic Principles of the Theory of Relativity (Notes by P. Bernays HLN) – for students of all faculties
On Geometry and Physics (Partial Notes by E. Hückel – EHN)
Statistical Mechanics (Notes by L. Nordheim - HLN)

452
WS 1922/23

SS 1923
WS 1923/24
SS 1924
WS 1926/27
SS 1930
WS 1930/31
WS 1931/32

APPENDIX 2
Mathematical Foundations of Quantum Theory (Notes by L.
Nordheim, G. Heckhausen - HLN)
Knowledge and Mathematical Thought (Notes by W. Ackermann HLN) – for students of all faculties
Our Conception of Gravitation and Electricity (generally
understood) (GVV)
On the Unity of Science (HLN)
Mechanics and Relativity Theory (Notes by L. Nordheim - HLN)
Mathematical Methods of Quantum Theory (Notes by L.
Nordheim - HLN)
Mathematical Methods of Modern Physics
Nature and Thought
Philosophical Foundations of Modern Natural Science

APPENDIX 3
SEMINARS, MISCELLANEOUS LECTURES

The main sources of information for lists 3.C and 3.D are the periodical
announcements of mathematical courses and activities at the various German
universities reported in the relevant sections of the JDMV. Additional information
concerning these, as well as the other two sections, appears in various documents in
DHN, some journals quoted in the text, and in the Vorlesungsverzeichnisse of the
University of Göttingen.
3.A. ADVANCED SEMINARS TAUGHT BY HILBERT:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.

Mechanics (with Klein)
1896 (?)
Stability Theory (with Minkowski)
SS 1903
Exercises in Mechanics (with Minkowski)
SS 1904
Mechanics
WS 1904-05
Electron Theory (with Minkowski et al)
SS 1905
The Equations of Electrodynamics (with Minkowski)
SS 1907
Hydrodynamics
???
Electrodynamics
???
Kinetic Theory of Gases
1912
Structure of Matter (with Debye)
WS 1914-15 to SS 1920
Structure of Matter
WS 1920-21
Structure of Matter (with Born)
SS 1921 to SS 1928
Theoretical and Math. Physics (with Born and Herglotz)
WS 1927/28
3.B. PUBLIC LECTURES BY HILBERT:

1.
2.
3.
4.
5.
6.
7.
8.

Stability Theory
Maxwell’s Theory of Gases
Statistical Mechanics
On Nernst’s Law of Heat
Space and Time
On the Laws of Chance
Nature and Mathematical Knowledge
The Knowledge of Nature and Logic

453

(Kassel) 1903
1912
1912
1913
(Bucharest) 1918
1920
(Copenhagen) 1921
(Königsberg) 1930

454

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

1.
2.
3.

4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.

Continuum Mechanics
Feb. 24, 1903
Continuum Mechanics
Aug. 4, 1903
The relations between variational principles and the theory of partial
differential equations, with applications to the integral principles of
mechanics.
Jan. 18, 1910
Kinetic theory of gases
Dec 19, 1911
Axiomatic Foundations of Physics (Ferienkurs for high-school
teachers)
April 15-27, 1912
Theory of Radiation
July 30, 1912
Theory of Radiation
Jan. 21, 1913
Theory of Radiation
July 28, 1914
The Fundamental Equations of Physics (General Relativity) Nov. 16, 1915
Foundations of Physics – First Part
November 20, 1916
Foundations of Physics
December 4, 1915
Theory of Invariants and the Energy Principle
Jan. 25, 1916
The Causality Principle in Physics
Nov. 21 & 28, 1916
Foundations of Physics – Second Part
Dec. 23, 1916
Non-Euclidean Geometry and the new Gravitation Theory
Jan. 23, 1917
Laue’s Theorem
June 12, 1917
Reply to Klein’s “On Hilbert’s first note on the
Foundations of Physics”
Jan. 29, 1918
The Energy Principle for the Motion of Planets in the New
Theory of Gravitation
June 4, 1918
On Weyl’s Communication (May 2, 1918) to the Berlin
Academy “The Energy Principle in the General Theory of
Relativity”
July 15, 1918

3.D. LECTURES ON PHYSICAL ISSUES AT THE GMG BY OTHERS:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

On the Axioms of Vector Addition (R. Schimmack)
Molecular Theory of Heat Conduction (G. Prasad)
Capillarity (H. Minkowski)
Linear Heat Conduction in Surfaces (G. Prasad)
Maxwell’s Work on Stress Systems (Klein)
Euler’s Equations of Hydrodynamics (Minkowski)
Electromagnetic Quantity of Motion (Abraham)
Gibb’s Thermodynamical Surfaces (H. Happel)
Variational Principles in Electrodynamics (Schwarzschild)
Can the Electron Reach the Speed of Light (P. Hertz)
On a Seminar on Hydrodynamics and Hydraulics (Klein)
Motion of a Material Particle on a Uniformly Moving
Plane (P. Ceresole)

June 9, 1903
June 9, 1903
June 23, 1903
June 23, 1903
June 23, 1903
June 28, 1903
July 14, 1903
Dec. 8, 1903
Jan. 26, 1904
Jan. 26, 1904
Feb. 9, 1904
May 17, 1904

SEMINARS ON PHYSICS
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.

455

On the Elasticity of the Earth (G. Herglotz)
June 28, 1904
On Sommerfeld’s Works on Electron Theory (G. Herglotz)
Dec. 6, 1904
Motion of a Fluid with Little Friction (L. Prandtl)
Dec. 13, 1904
On a Talk by Poincaré on n the Future of Mathematical
Physics (C.H. Müller)
Jan. 24, 1905
On Gases ans Vapors (L. Prandtl)
May 23, 1905
On Poincaré’s Published Lectures on Mathematical
Physics (M. Abraham)
Feb. 6, 1906
Poincaré’s Research on Rotating Fluid Masses (H. Müller) Feb. 13, 1906
On Gibb’s Book on Statistical Mechanics (Zermelo)
Feb. 20, 1906
Graphical Methods in Mechanics and Physics (C. Runge)
Feb. 27, 1906
On Painlevé’s Work on the Foundations of Mechanics
(Carathéodory)
May 28, 1906
On W. Nernst’s “On Chemical Equilibrium” (Minkowski)
June 26, 1906
Problems of Aeronavigation (Prandtl & Wiechert)
Oct. 30, 1906
The Mathematical Theory of Elasticity (C.H. Müller)
Nov. 6, 1906
On Botzmann’s H-Theorem (P. Ehrenfest)
Nov. 13, 1906
The Evolution of the Theory of Radiation through the Works of
Lorentz, Rayleigh, W. Wien and Planck (Minkowski)
Dec 1, 1906
On H. Witte’s “On the Possibility of a Mechanical
Explanation of Electromagnetic Phenomena” (Abraham)
Dec. 18, 1906
On the Application of Probability Calculus to Astronomy
(Schwarzschild)
Jan. 8, 1907
Theories of the Effects of Air Resistance (L. Prandtl)
Jan. 22, 1907
Seismic Waves (E. Wiechert)
Jan. 29, 1907
Statistical Stellar Astronomy (Schwarzschild)
Feb. 19, 1907
Seismic Rays (G. Herglotz)
May 14, 1907
Solutions of Differential Equations for Gas Spheres
(Gaskügeln) (K. Schwarzschild)
July 30, 1907
On the Equations of Electrodynamics (Minkowski)
Nov. 5, 1907
Graphical Methods in Fluid Mechanics (C. Runge)
Nov. 26, 1907
Applications of Quaternions to Electron Theory (Klein)
Dec. 10, 1907
A New, Simple General Proof of the Second Law of
Thermodynamics (Carathéodory)
Dec. 17, 1907
An Overview of Man’s Attempts to Fly (C. Runge)
March 3, 1908
Report on a Joint Seminar on Hydrodynamics (F. Klein,
L. Prandtl, C. Runge, E. Wiechert)
May 5, 1908
An Experiment on Stabilization of Air Balloons (L. Prandtl) May 12, 1908
On Lanchester’s Book “Aerodynamics” (C. Runge)
May 12, 1908
On the Equations of Electrodynamics (Minkowski)
July 28, 1908
On Recent French Research on Aviation (C. Runge)
Nov. 3, 1908
Recent Works on Earth Pressure (Th. Van Kármán)
Nov. 24, 1908
Theory of Earth Pressure (A. Haar & Th. Van Kármán)
Dec. 8, 1908
The New Mechanics (Poincaré, Wolfskehl Lectures)
April 22-28, 1909
Position Determination from and Air Balloon (Runge) May 11 & 18, 1909

456
49.
50.
51.
52.
53.
54.
55.
56.
57.

58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.

APPENDIX 3
Defintion of a Rigid Body on the “Einstein-Minkowski”
System of Electrodynamics (M. Born)
June 8 & 15, 1909
Average Motion in the Theory of Perturbations and
Applications of Probability to Astronomy (F. Bernstein)
June 22, 1909
On Minkowski’s Nachlass (Electrodynamics) (M. Born)
Feb. 8, 1910
On the Definition of a Rigid Body (M. Born)
Juni 21, 1910
Old and New Problems in Physics (Lorentz, Wolfskehl
Lectures)
Summer 1910
Stable Orderings of Electrons in the Atom
(L. Föppl - PhD Dissertation supervised by Hilbert)
Nov. 21, 1911
On Herglotz Work on Deformable Bodies in the
Theory of Relativity (M. Born)
Dec. 12, 1911
The Behavior of Solid Bodies and Hooke’s Law (L. Prandtl) Jan. 16, 1912
A Newly Discovered Relation Between Elasticity of
Crystals and Optical Oscillations (M. Born & Th. van
Kármán)
Feb. 13, 1912
Molecular Oscillations and Specific Heat (Born & van
Kármán)
May 14, 1912
Theory of Dispersion in Crystals (P.P. Ewald - PhD Diss.)
June 4, 1912
New Works of Poincaré and Ehrenfest on the Axiomatic
Foundation of Quantum Theory (Th. van Kármán)
Juli 16, 1912
Statistical Mechanics (P. Hertz)
Nov. 26, 1912
On Sommerfeld’s Article on the Theory of
Oscillating Equations (H. Weyl)
Dec. 10, 1912
Mie’s Theory of Matter (M. Born)
Dec. 17, 1912
Motion of Fluids (L. Prandtl)
Feb. 4, 1913
Reports on the Solvay Conference, Brussels 1911
(Born & van Kármán)
Feb. 25 & March 4, 1913
Kinetic Theory Week (Debye, Nernst, Von Smoluchowski,
Lorentz, Sommerfeld, Planck - Wolfskehl Lectures)
May 1913
An Application of Diophantine Approximations to a
Question in Statistical Mechanics (E. Hecke)
May 20, 1913
On the Structure of Crystals (M. Born)
June 7, 1913
Recent Work of J.J. Thomson on Canal Waves
(Kanalstrahlen) (C. Runge)
Juni 24, 1913
An Application of Quantum Theory to Capillarity
(M. Born & R. Courant)
July 1, 1913
On a Recent Work of E. Noether on Turbulences in a
Fluid (Th. van Kármán)
July 30, 1913
On Poincaré’s Book on Cosmogonic Hypotheses (L. Föppl) July 30, 1913
Propagation of Light in Transparent Media (W. Behrens)
Nov. 4, 1913
On Mie’s theory of Matter (M. Born)
Nov. 25, 1913
The Solution of an Equation of Spectroscopy (C. Runge)
Dec. 2, 1913
Recent Work of Einstein and Grossmann on
Gravitation (F. Böhm)
Dec. 9, 1913
On Mie’s Theory of Matter (M. Born)
Dec. 16, 1913

SEMINARS ON PHYSICS
78.
79.

80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.

457

Theoretical Treatment of Phenomena in Diluted Gases
(B. Baule - PhD Dissertation Supervised by Hilbert)
Feb 24, 1914
Review of Recently Published Works by von
Smoluchowski (Brownian Movement), and Einstein (On
Light Deflection; On the Determination of Molecular
Dimensions) (P. Hertz)
Feb. 24, 1914
Lattice Theory of Diamonds (M. Born)
March 3, 1914
Intensity Distribution in Spectral Lines (P. Debye)
Dec. 18, 1914
Foundation and Problems of Quantum Theory (P. Debye)
Feb. 23, 1915
Dynamics of Crystal Lattices (M. Born)
Feb. 25, 1915
Structure of Crystals (F. Klein, with Hilbert and Mügge)
May 18, 1915
On Herglotz’s Research on Potentials in the Interior of
Attracting Masses (Wiarda)
June 1, 1915
On Modern Physics (A. Sommerfeld)
June 15, 1915
On Gravitation (A. Einstein, Wolfskehl Lectures)
June 29 – July 7, 1915
Theory of Distant Forces (Uhlich-Pirna)
July 20, 1915
History of Mechanics up until Galileo (C. Müller,
Wolfskehl Lectures)
March 2-4, 1916
Diffusion, Brownian Movement, Colloidal Particles
(Von Smoluchowski, Wolfskehl Lectures)
June 20-22, 1916
Four-dimensional Vectorial Analysis (C. Runge)
Dec. 5, 1916
Foundations of a Theory of Matter (G. Mie, Wolfskhel
Lectures)
June 5-8, 1917
On the Riemannian Curvature (Klein)
Oct. 30, 1917
On the Riemannian Curvature (Klein)
Nov. 6, 1917
On G. Herglotz’s Paper on Curvature and Gravitation (Klein) Dec. 4, 1917
On Liquid Crystals (M. Born)
Dec. 11, 1917
On Invariants of Arbitrary Differential Expressions (E.
Noether)
Jan. 15, 1918
On Hilbert’s First Note on the Foundations of Physics (Klein) Jan. 22, 1918
On Einstein’s Cosmological Ideas of 1917 (F. Klein)
May 7, 1918
On Quantum Theory (M. Planck, Wolfskehl Lectures)
May 13-17, 1918
On Einstein’s “On Gravitational Waves” (C. Runge)
Jun. 31, 1918
On Einstein’s Cosmological Ideas of 1917 (Klein)
June 11, 1918
On the Three-body Problem (C. Carathéodory)
June 24, 1918
Einstein’s “Energy Principle in General Relatitvity” (Klein)
July 4, 1918
Hilbert’s Energy Vector (Klein)
July 22, 1918
Invariant Variational Problems (E. Noether)
July 23, 1918
Organic Causality (Hans Driesch, Wolfskhel Lectures)
Dec. 16-19, 1918
On the Structure of the Atom (N. Bohr, Wolfskehl Lectures)
June 1922

APPENDIX 4
HILBERT’S PHYSICS ASSISTANTS AND DOCTORAL
STUDENTS

4.A. ASSISTANTS FOR PHYSICS:
Some of the persons listed below worked with Hilbert officially under this
denomination (e.g., Ewald and Landé). Others (e.g., Bernays) may be classified as
such simply for having actually fulfilled this role (e.g., by maintaining Hilbert
updated on recent developments on physics, by preparing the notes for his physical
courses, etc.) in the period mentioned.
1.
2.
3.
4.
5.
6.
7.
8.
9.

1912-13: Paul P. Ewald
1913-14: Alfred Landé
1914-16: Louise Lange
1916-17: Richard Bär
1918-19: Paul Bernays
1920-21: Adolf Kratzer
1921-22: Erich Hückel
1922-27: Lothar Nordheim
1927-28: Eugene Wigner
4.B. DOCTORAL STUDENTS ON PHYSICAL TOPICS:

1.
2.
3.
4.
5.

As listed in HGA Vol. 3, 430-432.
Ludwig Föppl: “Stabile Anordnungen von Elektronen im Atom” (March 1,
1912)
Hans Bolza: “Anwendungen der Theorie der Integralrechnungen auf die
Elektronentheorie und die Theorie der verdünnten Gasen.” (July 2, 1913)
Bernhard Baule: “Theoretische Behandlung der Erscheinungen in
verdünnten Gasen.” (Feb. 18, 1914)
Kurt Schelenberg: “Anwendungen der Integralgleichung auf die Theories
der Elektrolysie.” (June 24, 1914)
Hellmuth Kneser: “Untersuchungen zur Quantentheorie.” (July 22, 1921)

458

APPENDIX 5
LETTERS QUOTED IN THE BOOK

Numbers for each entry indicate the chapter and footnote where a letter is quoted
in the book, and where its exact reference can be found.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.

Abraham to Stark
Apelt to Grassmann
Birkhoff to van der Waerden
Born to Hilbert
Born to Hilbert
Born to Hilbert
Born to Hilbert
Born to Hilbert
Born to Hilbert
Cantor to Hilbert
Carathéodory to Hilbert
Carathéodory to Hilbert
Dedekind to du Bois-Reymond
Dingler to Hilbert
Einstein to Besso
Einstein to Besso
Einstein to Besso
Einstein to Ehrenfest
Einstein to Ehrenfest
Einstein to Ehrensfest
Einstein to Freundlich
Einstein to Freundlich
Einstein to Habitch
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Hilbert
Einstein to Klein

Oct. 10, 1914
Sept. 3, 1845
Nov. 1, 1973
April 4, 1916
Aug. 24, 1916
Nov. 23, 1915
Aug. 3, 1909
Jan. 7, 1913
Oct. 28, 1915
Jan. 1, 1900
Dec. 12, 1912
April 4, 1913
March, 1888
Jan. 2, 1915
Dec. 10, 1915
Jan. 1, 1916
Jan. 3, 1916
Undated, 1914
April 1, 1914
Dec. 26, 1915
Aug. 1, 1913
Jan. 1, 1914
Dec. 24, 1907
Nov. 7, 1915
Nov. 12, 1915
Nov. 14, 1915
March 16, 1916
May 30, 1916
May 30, 1916
June 2, 1916
June 2, 1916
May 19, 1917
Nov. 15, 1915
Nov. 18, 1915
Dec. 15, 1917

459

(Ch. 6, # 62)
(Ch. 1, # 85)
(Ch. 9, # 41)
(Ch. 8, # 23)
(Ch. 8, # 26)
(Ch. 7, # 116)
(Ch. 4, # 67)
(Ch. 5, # 94)
(Ch. 7, # 100)
(Ch. 2, # 60)
(Ch. 5, # 91)
(Ch. 5, # 106)
(Ch. 2, # 10)
(Ch. 8, # 40)
(Ch. 7, # 50, 94)
(Ch. 4, # 85)
(Ch. 7, # 95)
(Ch. 6, # 20)
(Ch. 6, # 26)
(Ch. 7, # 95)
(Ch. 6, # 58)
(Ch. 6, # 54)
(Ch. 6, # 10)
(Ch. 7, # 98)
(Ch. 7, # 101, 104)
(Ch. 7, # 56)
(Ch. 7, # 108)
(Ch. 8, # 30)
(Ch. 8, # 76)
(Ch. 8, # 30)
(Ch. 8, # 93)
(Ch. 8, # 55)
(Ch. 7, # 108)
(Ch. 7, # 111)
(Ch. 9, # 97)

460
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.

APPENDIX 5
Einstein to Klein
Einstein to Kleiner
Einstein to Lorentz
Einstein to Lorentz
Einstein to Lorentz
Einstein to Mie
Einstein to Mie
Einstein to Sommerfeld
Einstein to Sommerfeld
Einstein to Sommerfeld
Einstein to Sommerfeld
Einstein to Stark
Einstein to Weyl
Einstein to Wien
Einstein to Zangger
Einstein to Zannger
Einstein to Zannger
Ewald to Hilbert
Frege to Hilbert
Hecke to Hilbert
Hilbert to Einstein
Hilbert to Einstein
Hilbert to Einstein
Hilbert to Einstein
Hilbert to Einstein
Hilbert to Einstein
Hilbert to Frege
Hilbert to Frege
Hilbert to Frege
Hilbert to Hurwitz
Hilbert to Klein
Hilbert to Klein
Hilbert to Klein
Hilbert to Poincaré
Hilbert to Poincaré
Hilbert to Poincaré
Hilbert to Poincaré
Hilbert to Russell
Hilbert to Schwarzschild
Hilbert to Schwarzschild
Hilbert to Sommerfeld
Hilbert to Weyl
Klein to Pauli
Klein to Pauli
Klein to Pauli
Mie to Hilbert

April 12, 1917
(Ch. 8, # 61)
April 3, 1912
(Ch. 4, # 86)
Aug. 16, 1913
(Ch. 6, # 18)
Oct. 12, 1915
(Ch. 7, # 92)
Jan. 17, 1916
(Ch. 8, # 2)
May 1, 1917
(Ch. 6, # 58)
June 1, 1917
(Ch. 6, # 58)
July 15, 1915
(Ch. 7, # 17, 89)
Nov. 28, 1915
(Ch. 7, # 93, 118)
Dec. 9, 1915
(Ch. 7, # 119)
Summer 1910
(Ch. 4, # 85)
Nov. 1, 1907
(Ch. 4, # 58)
Nov. 23, 1916
(Ch. 8, # 53)
Oct. 10, 1915
(Ch. 8, # 42)
April, 1915
(Ch. 6, # 1, 30)
July 7, 1915
(Ch. 7, # 36)
Aug. 7, 1915
(Ch. 7, # 40)
April 11, 1912
(Ch. 5, # 80)
Jan. 6, 1900
(Ch. 2, # 95)
March 7, 1916
(Ch. 2, # 86)
Nov. 19, 1915
(Ch. 7, # 114)
May 27, 1916
(Ch. 8, # 40)
Nov. 13, 1915
(Ch. 7, # 106)
May 25, 1916
(Ch. 8, # 93)
March 30, 1912
(Ch. 5, # 77)
Oct. 3, 1912
(Ch. 5, # 145)
Jan. 15, 1900
(Ch. 2, # 96)
Nov. 7, 1903
(Ch. 3, # 5)
Dec. 29, 1899
(Ch.2, 93,94,98, 99)
June 6, 1894
(Ch. 2, # 25)
May 23, 1893
(Ch. 2, # 12)
Nov. 15, 1893
(Ch. 2, # 13)
Sept. 14, 1892
(Ch. 1, # 38)
Nov. 6, 1908
(Ch. 5, # 13)
Nov. 19, 1908
(Ch. 5, # 13)
Nov. 25, 1908
(Ch. 5, # 13)
May 6, 1912
(Ch. 5, # 62)
April 12, 1916
(Ch. 8, # 40)
July 17, 1915
(Ch. 7, # 37)
Oct. 23, 1915
(Ch. 7, # 46)
April 5, 1912
(Ch. 5, # 63)
April 22, 1918
(Ch. 9, # 78)
May 8, 1921
(Ch. 7, # 84, 87)
May 8, 1921
(Ch. 8, # 129)
May 8, 1921
(Ch. 8, # 49)
Feb. 13, 1916 (Ch. 6, # 66; Ch. 8, # 43)

LETTERS QUOTED
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.

Mie to Hilbert
Mie to Hilbert
Mie to Hilbert
Mie to Hilbert
Mie to Hilbert
Mie to Hilbert
Mie to Stark
Mie to Wien
Mie to Wien
Minkowski to Einstein
Minkowski to Hilbert
Minkowski to Hilbert
Planck to Hilbert
Planck to Hilbert
Planck to Hilbert
Planck to Hilbert
Planck to Hilbert
Planck to Hilbert
Runge to Hilbert
Sommerfeld to Hilbert
Voigt to Lorentz
Volkmann to Hilbert
Voss to Hilbert
Weber to Dedekind

Feb. 29, 1916
May 8, 1917
May 16, 1917
June 10, 1917
July 2, 1917
Dec. 26, 1917
Dec. 10, 1913
Oct, 10, 1915
Feb. 6, 1916
Oct. 9, 1907
March 31, 1896
Dec. 20, 1890
Jan. 12, 1917
Feb. 8, 1917
Jan. 20, 1918
Jan. 27, 1918
April 4, 1913
April 15, 1913
May 8, 1918
May 4, 1916
May 19, 1911
Jan. 1, 1900
July 19, 1899
End of 1879

461
(Ch. 8, # 46)
(Ch. 8, # 48)
(Ch. 8, # 48)
(Ch. 8, # 50)
(Ch. 8, # 51, 52)
(Ch. 8, # 50)
(Ch. 6, # 62)
(Ch. 8, # 42)
(Ch. 8, # 42)
(Ch. 4, # 5)
(Ch. 1, # 46)
(Ch. 1, # 18)
(Ch. 8, # 33)
(Ch. 8, # 31, 33)
(Ch. 8, # 31)
(Ch. 8, # 31)
(Ch. 5, # 108)
(Ch. 5, # 109)
(Ch. 8, # 102)
(Ch. 8, # 24)
(Ch. 5, # 17)
(Ch. 1, # 158)
(Ch. 1, # 176)
(Ch. 1, # 14)

APPENDIX 6
ITEMS FROM THE HILBERT NACHLASS REFERRED TO
IN THE BOOK

Numbers for each entry indicate the chapter and footnote where an item is
referred to in the book.
DHN 40A, 1. 19091918.

Correspondence Born-Hilbert

Passim.

DHN 55, 4-5. Dec. 12,
1912, Apr. 4, 1913.

Letters Carathéodory to Hilbert

Ch. 5, # 91, #106.

DHN 98, 1. April 11,
1912.

Letter Ewald to Hilbert

Ch. 5, # 80.

DHN 141, 7. March 7,
1916.

Letter Hecke to HIlbert

Ch. 7, #86.

DHN 254. 1913-1917.

Correspondence Mie-Hilbert

Passim.

DHN 308A, 4. 19121917.

Correspondence Planck-Hilbert

Ch. 5, # 108, 109;
Ch. 8, # 31, 33.

DHN 379A. May 14,
1916.

Letter Sommerfeld to Hilbert

Ch. 8, # 24.

DHN 416. 1886-1913.

Correspondence Hilbert-Volkmann

Ch. 1, #158, #163.

DHN 418, 1. July 19,
1899.

Letter Voss to Hilbert

Ch. 1, #176.

462

ITEMS FROM HILBERT’S NACHLASS

463

DHN 457, 17. April
22, 1918.

Letter Hilbert to Weyl

Ch. 9, # 78.

DHN 504. SS 1882.

Lecture notes of a course on
number theory taught by Weber
(Annotated by Hilbert)

Ch 1, #4.

DHN 505-519.
Undated, probably
around 1880.

Hilbert’s student notebooks

Ch. 1, # 6-7; 11.

DHN 520. Undated.

A list of Hilbert’s courses over 46
years, between 1886 and 1932. This
list is complied in Hilbert’s own
handwriting until WS 1917-18

Ch.1, # 38, Ch. 2, #
30, Ch. 5 # 158.

DHN 522. SS 1887.

Hydrodynamics – Lecture Notes

Ch. 1, # 20, Ch. 2, #
30.

DHN 535. SS 1891.

Projective Geometry – Lecture
Notes

Ch. 2, # 3.

DHN 553. WS 189899.

Mechanics – Lecture Notes

Ch. 9, # 44-47.

DHN 558a. SS 1905.

Logical Principles of Mathematical
Thought – Lecture Notes
(Annotated by Max Born)

Ch. 3.

DHN 570, 9. 1905.

Notes from a seminar on electron
theory taught by Hilbert,
Minkowski, Wiechert, and Herglotz

Ch. 3, # 43.

DHN 570, 1. Undated.

Random collection of handwritten
notes related to many different
courses and seminars of Hilbert

Ch. 3, # 36.

464

APPENDIX 6

DHN 570, 5. 1907.

Notes by Hermann Mierendorff
from a seminar on electrodynamics
taught by Hilbert and Minkowski,

Ch. 4, #15.

DHN 586. August
1912.

Notes of a talk on radiation theory

Ch. 5, # 73, 82.

DHN 590. January
1913.

Notes of a lecture on Nernst’s law
of heat

Ch. 5, #144.

DHN 593. Undated.
Probably 1903.

Notes of a talk on stability theory

Ch. 2, #78; Ch. 3, #
37.

DHN 596. July 26, 27,
28, 1923.

Notes on three talks about
“Foundations of Physics”

Ch. 8, #121.

DHN 600. Undated.
Probably before 1900.

Tagebuch

Ch. 3, #1.

DHN 634, 15-22.
Undated. Around
1916.

Manuscripts with notes related to
Hilbert 1917

Ch. 8, # 21, # 22.

DHN 634. Before or
on Dec 6, 1915.

Galley proofs of Hilbert 1916

Ch. 7, # 63.

DHN 642. Undated.
Around late 19151916.

Talk on the causality principle

Ch. 7, # 65.

DHN 696. Undated.

Random collection of handwritten
notes related to many different
courses and seminars of Hilbert

Ch. 3, # 36.

DHN 707. SS 1907.

Radiation Heath – Minkowski’s
Lecture Notes

Ch. 4, #3.

DHN 742. June 1915.

Lecture of Einstein on GTR

Ch. 7, # 33.

APPENDIX 7
HILBERT’S AXIOMS FOR RADIATION THEORY

The precise context of Hilbert’s various systems of axioms for radiation theory is
discussed in § 5.3.
1. FIRST VERSION (HILBERT 1913):
Axiom I: In a state of thermal equilibrium of radiation no interchange of energy
among colors takes place for a given portion of matter. Moreover, the radiation of
each color is itself in a state of equilibrium.
Axiom II: The values of the three characteristic magnitudes of any wavelength at a
given temperature (the emission coefficient K, the absorption coefficient D, and the
speed of light q) are uniquely determined by the physical properties of matter at the
given position in space where that matter is currently found.
Axiom III: There exist substances whose absorptions coefficient D and refraction
capacity are such that the quotient D/q2 falls short of the wavelength O by a function
which is arbitrarily prescribed in advance.

2. SECOND VERSION (HILBERT 1913A):
Axiom 1 (Axiom of the compensation of the total energy): In a state of thermal
equilibrium of radiation the total amount of energy emitted by any given volume
element for all colors equals the amount energy absorbed by it.
Axiom 2 (Axiom of the compensation of energy for each individual color): In a state
of thermal equilibrium of radiation there is no exchange of radiant energy across
different colors at any given region of matter. Moreover, the radiation corresponding
to each color is itself in a state of independent equilibrium.
Axiom 3 (Axiom of the physical nature of the coefficients q, K, D): The characteristic
magnitudes of radiation for any given wavelength (speed of light q, emission
coefficient K, absorption coefficient D) are uniquely determined by the physical
conditions of matter in the region where the matter is found, and by them alone.
Axiom 4 (Axiom of the physical nature of the radiation density): In a state of thermal
equilibrium of radiation, the density of the radiant energy for each wavelength for
which matter is not diathermic, is uniquely determined by the physical conditions of
matter in the region where the matter is found, and by them alone.

465

466

AXIOMS OF RADIATION THEORY

Axiom 5 (Axiom of the existence of certain diversities in matter): There exist
substances whose absorptions coefficient D and refraction capacity are such that the
quotient D/q2 falls short of the wavelength O by a function which is arbitrarily
prescribed in advance.

3. THIRD VERSION (HILBERT 1914):
Axiom A (Axiom of the compensation of the total energy): Every optical system
admits a state of radiation equilibrium. In this state, the total amount of energy
emitted by all colors from any given volume element equals its total absorbed
energy.
Axiom B (Axiom of the compensation of energy for each individual color): Every
optical system admits a state of radiation equilibrium. In this state, there is no
exchange of radiant energy corresponding to different colors at any given region of
matter. Moreover, the radiation corresponding to each color is itself in a state of
independent equilibrium.
Axiom C (Axiom of the physical nature of the radiation density): In the —always
possible— state of equilibrium, the density of the radiation energy of every
wavelength is uniquely determined by the physical conditions of matter in the region
where the matter is found, and by them alone.
Axiom D (Axiom of the existence of certain differences among substances): There
are substances for which the values of D (absorption coefficient) and q (velocity of
propagation of light) are such that the quotient D/q2 equals the value of any
arbitrarily function of O prescribed in advance.

REFERENCES

COMMONLY USED ABBREVIATIONS
AHES
AIHS
AJP
AM
AMP
AMS
AP
ASN
BSL
BSPS
CPAE
CRN
DHN

DMV
DSB
EHN
EMV
ES
GdG
GDNA
GMG
GN
GTR

Archive for History of Exact Sciences
Archives int. d’histoire des sciences
American Journal of Physics
Annals of Mathematics
Archiv für Mathematik und Physik
American Mathematical Society
Annalen der Physik
Nachlass Arnold Sommerfeld, Deutsches Museum, Munich.
The Bulletin of Symbolic Logic
Boston Studies in the Philosophy of Science
The Collected Papers of Albert Einstein (Princeton, Princeton
University Press).
Nachlass Runge – Du Bois Reymond, Staatsbibliothek Berlin,
Preußischer Kulturbesitz
Nachlass David Hilbert – Niedersächsische Staats- und
Universitätsbibliothek Göttingen, Abteilung Handschriften und Seltene
Drucke, Nachlass Hilbert (Cod. Ms. D. Hilbert).
Deutschen Mathematiker-Vereiningung
Dictionary of Scientific Biography
Nachlass Erich Hückel, Staatsbibliothek Berlin, Preußischer
Kulturbesitz
Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer
Anwendungen
Einstein Studies
Grundlagen der Geometrie
Gesellschaft Deutscher Naturforscher und Ärzte
Göttingen Mathematische Gesellschaft
Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu
Göttingen, Mathematische-Physikalische Klasse
General Theory of Relavitity

467

468
GWG
HGA
HLN
HM
HPL
HSPS
ICM
JDMV
JRAM
JRE
JSHS
JSL
JSN
LCP
MA
MBN
MPIWG
MZ
PAWS
PB
PiP
PZ
SHPMP
SHPS
SiC
SN
STR
SUB Göttingen
Trans. AMS
VDPG
VGDNA
ZMP
ZP

REFERENCES
Königlichen Gesellschaft der Wissenschaften zu Göttingen
David Hilbert – Gesammelte Abhandlungen
Manuscript/Typescript of Hilbert Lecture Notes. Bibliothek des
Mathematisches Insititut, Universität Göttingen
Historia Mathematica
History and Philosophy of Logic
Historical Studies in the Physical Sciences
International Congress of Mathematicians
Jahresbericht der Deutschen Mathematiker-Vereiningung
Journal für die reine und angewandte Mathematik
Jahrbuch der Radioaktivität und Elektronik
Japanese Studies in the History of Science
Journal of Symbolic Logic
Nachlass Johannes Stark – Staatsbibliothek Berlin, Preußischer
Kulturbesitz.
Collected Papers of Hendrik Anton Lorentz
Mathematische Annalen
Nachlass Max Born, Staatsbibliothek Berlin, Preußischer Kulturbesitz
Max Planck Institut für Wissenschaftgeschichte, Berlin
Mathematische Zeitschrift
Königlich Preussische Akademie der Wissenchaften (Berlin)
Sitzungsberichte
Physikalische Blätter
Physics in Perspective
Physikalische Zeitschrift
Studies in History and Philosophy of Modern Physics
Studies in History and Philosophy of Science
Science in Context
Science Networks
Special Theory of Relativity
Niedersächsische Staats- und Universitätsbibliothek, Göttingen.
Transactions of the AMS
Verhandlungen der Deutsche Physikalische Gesellschaft
Verhandlungen GDNA
Zeitschrift für Mathematik und Physik
Zeitschrift für Physik

REFERENCES

469

PUBLISHED AND UNPUBLISHED SOURCES
Abraham, M.
1902
“Dynamik des Elektrons”, GN (1902), 20-41.
1903
“Prinzipien der Dynamik des Elektrons”, AP 10, 105-179.
1912
“Zur Theorie der Gravitation”, PZ 13, 1-14.
1915
“Neuere Gravitationstheorien”, JRE 11, 470-520.
Abrams, L.S.
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INDEX

Anschauung, 36, 62, 69, 83-84, 117, 118,
124, 399, 423-425
anthropomorphism, 9, 379, 393, 399, 423
Apelt, Ernst Friedrich (1812-1859), 36
Appell, Paul (1855-1930), 92
applied mathematics, 47, 69, 73-78, 321
Arabatzis, Theodor, 131
Archimedean axiom, 41, 86, 97, 123, 141
Archiv der Mathematik und Physik, 74
arithmetic, 7, 22-27, 35-43, 51-52, 66, 94106, 113-115, 121-125, 183, 229, 255,
281, 370, 396-397, 424-428, 446
consistency, 97, 101-104, 121-122,
426
foundations, 36, 75, 102, 104, 120123, 296, 318, 369, 396, 409, 413,
427, 434, 438, 446, 449
Aronhold, Siegfried (1819-1884), 17
Ascoli, Giulio (1843-1896), 228
astronomy, 81, 123, 130, 149-151, 166168, 175, 186, 447
atomic theory, 50, 65, 246, 412-415
atomistic conceptions/atomistic
hypothesis, 46-49, 55, 62-63, 69, 80,
92, 106, 148, 151, 169, 198, 219, 231,
234, 267-268, 282, 284, 377, 445
Aufruf an die Kulturwelt, 325, 448
Ausdehnungslehre, 36
axiom of completeness (Vollständigkeitsaxiom), 97, 100, 121

A
Aachen, 136
Abraham, Max (1875-1922), 8, 49, 133136, 174, 215-219, 273, 297, 299, 305,
306-308, 328, 419, 454-455, 459
Abrams, Len, 381
absolute differential calculus, 292, 295
absorption capacity (coefficient), 239,
242, 247-250, 255, 259-261, 417, 445,
465-466
Ackermann, Wilhelm (186-1962), 438
action and reaction principle, 305
action at a distance, 69, 150, 296, 377,
387
adiabatic process, 156, 161
aerodynamics, 73
Alexandrov, Pavel (1896-1982), 109
algebraic invariants, 3, 17, 19, 25, 89,
112, 359, 437, 446
algebraic number fields, 3, 20-21, 85, 89,
96, 227, 438
Althoff, Friedrich (1839-1922), 72
Ambronn, Leopold Friedrich Anton
(1854-1930), 81
Ampère, André Marie (1775-1836), 70
Annalen der Physik, 229, 304, 310, 363,
374, 449

497

498

INDEX

axiom of parallels, 29
axiom systems
completeness, 95-100, 111, 114, 164,
165, 181, 274, 426, 438
consistency, 56, 96-100, 104, 111-114,
122-124, 165-166, 176, 181, 183,
397, 415
ordinal independence, 44
relative consistency, 111
simplicity, 57, 59, 66, 95, 98, 114, 164
independence, 43-44, 56-58, 87, 95-104,
111-115, 121-126, 140, 164-165, 176,
181, 183, 216-217, 260, 264, 267, 276,
325, 376, 384, 397, 402, 413, 416,
424-425, 430, 436,
axiomatic approach, 3, 6, 20, 24-25, 38,
50, 59, 65, 83-85, 88, 93-98, 101, 104,
119, 142, 151, 157, 174-176, 179, 221,
262, 289, 372, 374, 396, 426, 431
axiomatic method, 3, 7, 11, 20, 54, 88,
90, 110, 118, 121-126, 157, 162, 177178, 198, 230, 239, 262, 266-278, 334,
344, 350-351, 357, 373-374, 397, 403,
418, 442

B
Baade, Walter (1893-1960), 322, 353
Babbage, Charles (1791-1871), 35
Baird, D., 55
Baltic Sea, 326
Bandomir, C.A., 178
Bär, Richard (1892-1940), 369, 440, 451,
458
Barbour, Julian, 51, 53, 145, 290
Bargmann, Valentin (1908-1989), 224
Barkan, Diana, 81, 244
Basel, 51, 472, 478, 480--484, 489-494
Baule, Bernhard (1891-1976), 265, 274,
317, 451, 457-458
Bauschinger, Julius (1860-1934), 168
Becquerel rays, 133
Becquerel, Jean (1878-1953), 133, 437
Behmann, Heinrich (1891-1970), 319,
369, 370, 427, 438
Behrens, Wilhelm, 263, 451, 456
Belna, J.P., 111
Bergia, Silvio, 364

Berlin, v, vi, viii, 2, 8, 13-15, 30, 34, 47,
72-73, 76, 81, 102, 119, 133, 168, 215,
289, 296-297, 320, 326-330, 345-346,
348, 351-353, 364-369, 413, 414, 428,
447-449, 454
Berlin Academy, 8, 15, 289, 296, 330,
345, 351, 364, 428, 449, 454
Bernays, Paul (1888-1977), 295, 296,
370, 427, 436, 449, 451, 458
Bernstein, Felix (1878-1956), 121, 319,
321, 326, 369, 456
Bertrand’s principle, 146-147
Besso, Michele (1873-1955), 225, 295,
328, 347, 363, 364, 459
Bianchi identities, 341
Bibliotheca Mathematica, 73
Bierhalter, G., 154
binary quadratic forms, 17
Birkhoff, Garrett (1911-1996), 420
black-body radiation, 242-246
Blackmore, J.T., 50, 55
Blaschke, Wilhelm (1885-1962), 385
Blasius, Paul Heinrich (1883-1970), 130
Blum, P., 109, 149
Blumenthal, Otto (1876-1944), 3, 18, 20,
21-24, 85, 89, 345
body alpha, 52
Bohlmann, Georg (1869-1928), 107, 164166, 171, 176
Böhm, Friedrich (1885-1965), 323, 456
Bohr Festspiele, 412
Bohr, Harald (1887-1951), 409
Bohr, Nilels (1885-1962), 412-413, 442
Boi, L., 45
Boltzmann distribution, 48, 238
Boltzmann equation, 2, 171, 229, 237,
238, 441
Boltzmann, Ludwig (1844-1906), 2, 4650, 60-65, 76, 77, 80, 92, 106-107,
129, 140, 141, 148-153, 168-171, 179180, 229, 235-251, 276-277, 441-447
Bolyai, Janos (1802-1860), 26-30, 227,
447
Bolza, Hans, 265, 458
Bonn, 14, 15, 30, 86, 129, 160, 445
Boole, George (1815-1864), 17
Boolean algebra, 116
Boos, W., 112
Borga, M., 44
Boring, E.G., 175

INDEX
Born, Max (1882-1970), viii, 4, 130, 134,
161-163, 183-189, 214-219, 225, 227,
238, 241, 246-248, 253, 263-271, 282,
287, 291, 309-326, 333, 335, 341-354,
366-368, 376, 377, 411-421, 440, 447463
Born-Wiener operator method, 415
Bortkiewicz, Ladislaus von (1868-1931),
164
Bosworth, Anne Lucy (1868-?), 120
Bougoslawski, S., 263
Brendel, Martin (1862-1939), 81
Breslau, 214, 215, 241, 252, 434
Brest-Litovsk, 322
Brigaglia, Aldo, 36, 122
Brill, Alexander von (1842-1935), 21, 30,
150, 278
Broggi, Ugo (1880-1965), 166
Brotherus, Hjalmar V. (1885-1962), 248
Brouwer, Luitzen E.J. (1881-1960), 396,
434
Browder, Felix E., 109
Brownian motion, 241
Brush, Stephen G., 2, 46, 47, 237, 265
Brussels, 161, 244, 447, 456
Bucherer, Alfred H. (1863-1927), 153
Budde, Emil (1842-1921), 92, 129
Burali-Forti, Cesare, 45
Burkhardt, Heinrich (1861-1914), 74

C
Cambridge, 75, 130, 161, 214
Caneva, Keneth, 36, 45
Cantor, Georg (1845-1918), 18, 23, 35,
37, 42, 68, 100, 101, 104, 166, 446,
459
Cantor’s continuum hypothesis, 104
capillarity theory, 12, 129, 186, 454
Carathéodory, Constantin (1873-1950),
160-163, 183, 252-257, 262, 321, 440,
448, 455-459, 462
Cario, Günther (1897-1984), 411
Carnot processes, 163
Castelnuovo, Guido (1865-1952), 75
Cattani, Carlo, 8, 297, 307
Cauchy problem, 338, 340, 362, 385
causality principle, 68, 294-296, 304,
331, 338, 340, 346, 360, 362, 377, 378,
385-386, 400-403, 435-436, 464
Cayley, Arthur (1821-1895), 17, 20, 32

499
Celestial Mechanics (Laplace), 173
Cercignani , Carlo, 2, 46
Chapman, Sidney (1888-1970), 265
Chasles, Michel (1793-1880), 30
Chicago, 19, 20, 115, 323, 447
Christiansen, M., 91
Christoffel symbol, 340
Christoffel, Elwin Bruno (1829-1900),
29, 292
civilian war prisoner, 322, 409
Clausius, Rudolf (1822-1888), 154, 161
Clifford, William Kingdon (1845-1879),
28, 29, 33
Cohn, Emil (1854-1944), 197
Compton, Karl Taylor (1887-1954), 411
Condon, Edward U. (1902-1974), 411
conductivity, 79, 196, 272
conservation laws, 204, 355, 391
conservation of mass principle, 199
continuity equation, 152, 239
contraction hypothesis, 132, 194, 211
Contro, Walter, 40, 41, 45
coordinate conditions, 295, 337, 339, 348,
352-361, 386, 405, 436
coordinate systems, 202, 273, 294, 346,
346, 385-386
coordinate transformations, 292, 309,
380-381
rotating, 294, 345
Corry, Leo, 6, 12, 21, 25, 30, 36, 37, 95,
116, 117, 118, 142, 189, 307, 322, 330,
352, 409, 420, 442
cosmology, 29, 322, 364, 388, 449
Coulomb’s law, 62, 300
Courant, Richard (1888-1972), 409, 411,
413, 414, 420, 440
covariance/invariance
Galilean, 132, 173, 174
general, 2, 7, 214, 225, 292-294, 296,
309, 316, 328, 329, 332-361, 381386, 391-394, 401, 403, 423, 433,
436, 448
limited, 307, 345, 357
Lorentz, 132, 191, 194, 196, 198, 200,
204, 205, 217, 218, 220, 222-223,
226, 235, 271, 289-292, 300-303,
333, 377, 433
Cremona, Luigi (1830-1903), 30
Crilly, Anthony, 17
cross-ratio, 32, 33, 41
Crowe, Michael, 138, 153

500

INDEX

crystal physics, 232, 234, 322
Cyclotomic fields, 19
Czuber, Emanuel (1851-1925), 21, 164167, 171

D
d’Alembert principle, 93, 146
Darboux, Gaston (1842-1917), 30, 91,
138, 140
Darrigol, Olivier, vi, 49, 71, 134, 136,
197
De Finetti, Bruno (1906-1985), 166
De Sitter, Willem (1872-1934), 364
Debye, Peter (1884-1966), 271, 317, 318,
321, 366, 411, 448, 453, 456-457
Dedekind, Richard (1831-1916), 12, 13,
21-23, 36-43, 85, 99, 100, 101, 166,
379, 380, 421, 445-446, 459-461
Dedekind's theory of cuts, 39, 99
Dehn, Max (1878-1952), 41, 120
density
charge, 189, 300
current, 189
electricity, 196, 216
energy, 302
mass, 152, 199, 290
optical, 147
radiation, 258, 261, 465, 466
Desargues, Girard (1591-1661), 30
Desargues’s theorem, 30, 32, 42, 89, 96,
97, 98
Despeyrous, Th., 91
Deutschen Mathematiker-Vereiningung,
21-22, 42, 64, 66, 72, 74, 85, 86, 99,
112, 132, 167, 189, 446
Dickson, Leonard Eugene (1847-1952),
116
dielectric constant, 196
Dieudonné, Jean (1906-1992), 6, 17, 77,
118, 228
differentiability conditions, 28, 105
differential equations, 12, 15, 19, 35, 59,
109, 151-152, 162-163, 169-170, 185186, 189, 199, 228-229, 235-236, 280,
336-338, 375, 385, 410, 427, 434, 454
Encyklopädie article, 76
dilute gases, 241, 317, 319
Dirac, Paul A.M. (1902-1984), 412- 415
Dirichlet principle, 22, 109, 127, 445

Dirichlet, Gustav Lejeune (1805-1859),
22, 37, 109, 127, 447
DiSalle, Robert, 51, 53
divergence, 211, 338-339, 355, 360, 390
covariant, 355
Dolezalek, Friedrich (1873-1920), 81
Doppler effect, 79-80
Dorier, J.L., 141
Droste, Johannes (1886-1963), 364
Du Bois-Reymond, Emil (1818-1896),
102
Dugac, Paul, 85
Duhamel, Jean-Marie C. (1797-1872),
129
Duhem, Pierre (1861-1916), 47
Dühring , Eugene (1833–1921), 92

E
Earman, John, 189, 290, 295, 330, 430
Eckert, Michael, 232
Eddington, Arthur S. (1882-1944), 394,
437
Edwards, Harold, 21
Edwards, M.R., 284
Ehrenfest, Paul (1880-1993), 47, 76, 77,
150, 179, 183, 220, 243, 246, 265,
291-295, 348, 364, 440, 448, 455- 459
Ehrenfest-Afanaseva, Tatyana (18761964), 47, 76, 77, 150, 179, 265, 440,
448
Einstein, Albert (1879-1956), v, vii, 2, 7,
8, 81, 132, 136, 149, 168, 182, 186195, 205-206, 211-226, 235-236, 243,
249, 271, 284-297, 300, 302-317, 320462
Einstein's 1915 Prussian Academy
communications, 375
first, 348, 351, 353
fourth, 328, 354, 356, 358, 363
fourth, 360
second, 349, 355
third, 352, 363, 375
Einstein 1915 visit to Göttingen, 320,
333, 405
Eisenstaedt, Jean, 364, 381
elasticity, 93, 214, 234, 287, 301, 311,
390
electric current, 196

INDEX
electricity, 12, 45, 56, 64, 88, 114, 125,
133, 134, 135, 189, 191, 194, 198, 208,
216, 217, 219, 246, 272, 301, 388, 446
electrodynamic potentials, 387
electrodynamics, 7, 15, 49, 54-55, 79-81,
107, 128-136, 149, 152-153, 172, 178200, 205, 210-225, 239, 246-248, 272281, 300, 304-305, 311-316, 324, 333337, 342-345, 350, 356-357, 362, 367,
375-376, 387, 390-391, 397, 401, 432434, 440, 444-447, 464
of moving bodies, 136, 149, 186-190,
194-198, 210, 213, 446
electrolysis, 317
electromagnetic field, 136, 216, 283, 310,
337
electromagnetic mass, 310
electromagnetic oscillations, 228, 280,
316, 317
electromagnetic potentials, 335, 341, 374,
377
electromagnetic reductionism, 231
electromagnetic view of nature, 49, 132134, 182, 191, 195, 206, 213, 219, 299,
311-315, 377
electromagnetism, 153, 198, 236, 242,
267, 278, 299, 337, 351, 378, 391, 430
electron
deformable, 132
high-speed, 133
rigid, 133, 216, 218
electron theory, 49, 79-81, 130-137, 149,
174, 187, 193, 198, 213, 216, 219, 228,
241, 244, 271-272, 277, 281, 300, 309,
312, 314, 317, 368, 377, 447, 463
conduction electrons, 216, 283
magnetization electrons, 216, 283
polarization electrons, 216, 283
electro-technology, 130
Ellison, W. and F., 22
emission capacity (coefficient), 239, 242,
247, 248, 255, 445, 465
Encyklopädie der mathematischen
Wissenschaften mit Einschluss ihrer
Anwendungen, 54, 66, 67, 74-77, 92,
107, 129, 135, 144, 153, 164, 168, 174,
179, 183, 197, 249, 252, 326, 436,
446-449
French version, 76
enduring core, 400, 402

501
energy, 302, 465-466
absorbed and emmited, 242
conservation principle, 46
current vector, 302
density, 282, 304
elements, 243
equal energy elements, 243
equilibrium, 253
kinetic, 146, 147, 172, 276, 277
magnetic, 133
momentum, 315
potential, 46, 149, 151, 173, 234
quanta, 244
radiant, 261, 294
self-energy, 217, 218, 300, 310
total energy density, 250
energy conservation principle, 45, 62, 93,
145-147, 156, 194, 199, 200, 214, 220,
264, 276, 293, 294, 301-302, 305-306,
311-315, 338-340, 356, 359-360, 369,
377, 384-388, 407, 435, 449
Enriques, Federigo (1871-1946), 34, 42,
75, 122
Enskog, David (1884-1947), 265, 436
entropy, 46-48, 154-161, 163, 168-169,
178, 239, 242-243, 257, 268, 270, 397,
445
Entwurf Theory (Einstein-Grossmann),
289-297, 306-307, 311, 323-333, 337,
346-349, 354, 371, 448
equation of state, 268, 270, 271
equilibrium, 48, 142, 144, 146, 155, 161,
216, 251, 253, 255, 257, 259, 262, 264,
269, 313, 465-466
chemical, 241
thermal, 154-155, 242-243, 250, 254257, 465
equivalence principle, 205, 289, 290, 291,
294, 307, 323, 373, 447
ergodic hypothesis, 241
Erlangen, 66, 222, 321, 436
Erlanger Programm, 33-35, 44, 75, 445
ether, 45, 56, 70, 130- 136, 189-191, 195,
198, 208, 216-217, 233, 273, 299-304,
311, 371
Euclid’s Elements, 37, 39
Euler equations, 129, 152, 153, 454
evangelist church, 299
Ewald, Paul P. (1888-1985), 232, 241,
249, 253, 317, 321, 440, 448, 456, 458,
460, 462

502

INDEX

Ewald, William, 26, 28, 39, 40, 398

F
Fachwerk von Begriffen, 123, 124, 393,
396, 425
Fano, Gino (1871-1952), 34, 44, 75, 77,
86
faster-than-light motion, 136
Fechner, Gustav (1801-1887), 175
Fermat’s theorem, 102, 231
Fisch, Menachem, 35
Fokker, Adriaan (1887-1968), 364
Fölsing, Albrecht, vi, 54, 55, 325, 328
Föppl, A., 129, 454, 456
Fortschritte der Physik, 252
Fowler, Ralph H. (1889-1944), 163
Franck, James (1882-1964), 411
Franco-Prussian war, 31
Frankfurt, 215, 485
Frederiks, Vsevolodk F. (1885-1943),
322, 408, 440
Fredholm, Ivar (1866-1927), 228
Frege, Gottlob (1846-1925), 86, 107,
111-114, 121, 143, 165, 446, 460
Frei, Gunther, 11, 18, 20, 72, 85, 86
Frenkel, V., 322
Fresnel, Augustine J. (1788-1827), 52,
265
Freudenthal, Hans (1905-1990), 30, 98
Freundlich, Erwin Finlay (1885-1964),
306, 307, 346, 354, 459
Friedmann, Alexander (1888-1925), 322
Friedmann, Michael, 430
Frobenius, Georg Ferdinand (1849-1917),
76, 297
Fuchs, Lazarus (1833-1902), 76, 447

G
Gabriel, G., 112-114, 121, 143, 165
Galison, Peter L., 187, 189, 191
Galois theory, 15
Gans, Richard (1880-1954), 153
Gauss, Carl Friederich (1777-1855), 11,
17, 21-27, 68, 81, 87, 88, 107, 126,
134, 145-148, 167-168, 279, 292, 324,
378-379, 387, 427, 446
Disquisitiones Arithmeticae, 23
error theorem, 167

square law, 168
three mountain peaks experiment, 87,
126, 279, 378-379, 387, 427
Gaussian coordinates, 386, 403
Gaussian integers, 21
Gauss-Weber Festschrift, 81, 107, 134
genetic approach, 99-100, 123-124, 424,
425
geodesics, 292, 384
geometry
analysis situs, 83, 116
analytic, 32, 39, 42, 48, 83-86, 98, 109,
182, 265
consistency, 96, 104
continuity assumptions, 32, 38-43, 8589, 94-101, 105, 426
differential, 29, 292, 324, 378, 380,
385
Euclidean, 26-43, 58, 86-98, 104, 113,
125, 139, 148, 209, 278-279, 290291, 296, 306, 378-388, 396, 423427, 454
foundations, 1, 3, 6, 7, 11, 19- 25, 2829, 36-44, 50, 58, 65, 84, 85-86, 90,
93, 105-106, 115, 120-123, 277,
292, 413, 417, 423, 428, 437-438
hyperbolic, 28, 33, 202
metrization, 42, 87, 98
non-Archimedean, 44, 87, 99,125, 446
non-Euclidean, 23-33, 40, 85-86, 96,
125, 190, 195, 387, 391, 445, 495
parallel postulate, 32, 87, 88, 96, 112,
427
projective, 25, 29-36, 40-44, 58, 83,
84-89, 95, 97, 111, 116, 446
pseudo-geometry, 387
Riemannian, 30, 404
spherical, 12, 28, 33, 299, 381
unification, 30-31
variable curvature spaces, 28, 33
geophysics, 81
Gesellschaft Deutscher Naturforscher
und Ärzte, 64, 128, 132, 189, 206, 249,
271, 306, 310, 446-448
Giannetto, E., 187
Gibbs, Josiah Willard (1839-1903), 138,
153, 161, 168
Gispert, Helène, vi, 76, 78
Gleason, Andrew, 106
Glymour, Clark, 189, 290, 330, 432
Gnedenko, J., 1

INDEX
Goenner, Hubert, 364
Goethe, Johann Wolfgang von (17491832), 176, 409
Goldberg, Stanley, 133
Goodstein, Judith, 297
Gordan, Paul (1837-1912), 17-20, 30,
227, 326
Gordan’s basis theorem, 17
Göttingen Mathematische Gesellschaft
(GMG), 20, 73, 120, 128-130, 179,
186, 187, 189, 193, 214-217, 222, 237,
271, 310- 311, 316, 319, 323, 324,
330-331, 352, 356, 369, 388-390, 447,
454
Göttingen Nachrichten, 366, 390, 400,
434, 467
Göttinger Vereinigung zur Förderung der
Angewandten Physik, 74
Grand Prix des Sciences Mathématiques,
13
Grassmann, Hermann Gunther (18091877), 35-36, 42-44, 86, 177, 459
Grattan-Guinness, Ivor, 101, 109, 111
gravitation, 63, 84, 132-133, 153, 172,
187-205, 220, 225, 235, 273, 283-289,
289, 293, 302-404, 434, 437, 442, 447,
448
Euler-Lagrange equations, 340
Euler-Lagrange equations, 375
geometrical interpretation, 292
Mie’s theory, 300-306
Minkowski’s theory, 200-204, 212
Newtonian, 149, 200, 289, 293
Newtonian limit, 355
Nordström’s theory, 307
gravitational field, 152, 289, 290, 292,
293, 294, 304, 307, 342, 346, 356, 357,
362, 364, 375, 381, 382, 384, 430, 433,
435, 437, 441, 442, 448, 449
non-static, 407
static, 293
gravitational field equations, 8, 168, 289302, 320-329, 333, 337, 340, 342, 345,
346-362, 373-380, 383, 387, 402-404,
421, 427, 435, 436, 442, 448
first exact solution, 363
Schwarzschild solution, 380- 385, 435
trace term, 355, 358-359, 406
gravitational light rays bending, 290, 306,
307
gravitational mass, 289, 305-306, 383

503
gravitational potentials, 225, 290, 292,
305, 306-307, 335-342, 351, 357, 380,
386
gravitational red shift, 290, 306, 384, 394
Gray, Jeremy, vi, 45, 102-106
Greffe, J.L., 71
Greifswald, 299, 371
Grelling , Kurt (1886-1942), 121, 319,
326
Grommer, Jakob (1879-1933), 322, 364,
408, 436
Grossmann, Marcel (1878-1936), 289295, 311, 323-324, 348, 352, 359, 374,
448, 456
Grotrian, Walter (1890-1954), 411
group theory, 25, 29-34, 41, 73, 94, 95,
96, 98, 115-116, 126, 164, 206-210,
222, 223, 319, 391, 392
groups
continuous geometrical, 77
invariance, 291, 293, 333
transformations, 29, 32, 33, 348
Grundlagen der Geometrie (Hilbert), 11,
23, 25, 29, 32, 35, 63, 66, 69, 81-107,
114-120, 124-127, 164-166, 179-183,
257, 421, 423, 424-426, 447
Guth, E., 329, 432
GWG, see König. Ges. Wiss. Gött.

H
Halle, 42, 51, 85, 299, 370, 446
Hamel, Georg (1877-1954), 120, 138,
140, 142, 178, 183, 440
Hamilton principle, 57, 68, 93, 147, 173,
199, 218, 244, 312, 335, 373, 387, 427,
434, 436
Hamiltonian function, 147, 173, 218-219,
295, 297, 302, 312, 334-340, 346, 371374, 383, 387, 391, 403, 427, 434-435
Hardy, Godfrey H. (1877-1947), 227, 409
Harman, P.M., 45
Harvard, 420
Hashagen, Ulf, vi, 74-76
Hasse, Helmut (1898-1979), 22-23
Hausdorff, Felix (1868-1942), 117
Hawkins, Tom, vi, 29-35, 77
Heaviside, Oliver (1850-1925), 138

504
Hecke, Erich (1887-1947), 241, 265, 344,
440, 451, 456, 460, 462
Heidelberg, 12, 121, 122, 153, 299, 318,
447
Heilbron, John, 45, 47, 195, 393
Heisenberg, Werner (1901-1976), 411,
413-417, 440, 449
Hellinger, Ernst (1883-1950), 77, 215,
228, 326, 450-451
Helm, Georg Ferdinand (1881-1923), 49
Helmholtz, Hermann von (1821-1894),
15, 25-29, 42, 53, 105, 128, 129, 154,
176, 270
Helmholtz-Lie space problem, 29, 105
Hentschel, Klaus, 212, 309, 323
Herglotz, Gustav (1881-1953), 130, 136,
215, 311, 411, 447, 453-457, 463
Hermite, Charles (1822-1901), 12
Hershel, John (1792-1871), 35
Hertz, Heinrich (1857-1894), 54- 71, 8696, 106-107, 113, 136, 140-144, 147150, 153-154, 179-181, 221, 235, 273,
277-278, 299, 321, 326, 424-446, 454457
Hertz, Paul (1881-1940), 136, 241, 321,
326, 345, 346, 448
Hesse, Otto (1811-1874), 17
Hessenberg, Gerhard (1874-1925), 89
Hiebert, Erwin N., vi, 47, 50, 154
Hilbert, David (1862-1943)
1900 list of problems, 1, 3, 6, 83, 91,
92, 104, 109-111, 120, 129, 421,
426
courses on mechanics, 83, 91, 93, 129,
172, 185, 228, 234-235, 367
sixth problem, 1, 3, 6, 104, 106-110,
119, 137, 164, 178, 220, 239
theory of infinite determinants, 25
unified theory, 7, 8, 284-287, 295, 307,
309, 316, 329, 330-362, 374, 382,
391, 404-407, 415, 422
1924 version, 340, 357, 359, 392,
399, 402-404, 408
Axiom of Space and Time, 339340, 360, 402
energy concept, 338, 342-344, 351,
356, 360, 389, 422
first communication, 352
first printed version, 343, 353, 355,
361, 402-405

INDEX
Proofs version, 330, 334-345, 357361, 371, 383, 386, 400-404, 489
Proofs version, missing lines, 340
second communication, 8, 329, 340,
350, 356, 360, 366, 368, 376,
377, 379, 381, 383-388, 397,
423, 426, 431, 434-436, 449
Theorem I, 336-338, 350, 358, 386,
391, 392, 403, 422
Hirosige, Tetu, 133, 197
Hochkirchen, Thomas, 110, 164, 166
Höhnl. H., 299, 301
Holton, Gerald, 212
homogeneous bodies, 154, 248, 268
Hon, Giora, 133
Hopf, Ludwig (1884-1939), 284
Hopmann, J., 168
Howard, Don, 321, 324, 326
Hückel, Erich (1896-1980), viii, 413, 451,
458
Hund, Friederich (1896-1997), 411
Huntington, Edward V. (1847-1952), 95,
115, 116
Hurwitz, Adolf (1859-1919), 13, 15, 21,
88, 227, 460
Husserl, Edmund (1859-1938), 110, 121,
323, 447
hydrodynamics, 15-16, 47, 75, 79, 90, 93,
129, 153, 239, 287, 448, 451-453, 463
hydrogen atom, 354

I
ideal oscillator, 242
Immanuel Kant (1724-1804), 12, 57, 6970, 94, 117, 299, 429-431
incompressible fluids, 150
inertia
of a charge flow, 219
principle, 70
relativity of, 364
transverse, 133
inertia (principle of), 208, 290, 323, 430
Carl Neumann’s criticism, 51, 52, 53,
54
Hertz’s discussion, 59
Hilbert’s discussion, 143
Minkowski’s discussion, 191
inertial fields, 292
inertial mass, 218, 289, 303-306, 384
inertial motion, 143, 204

INDEX
inertial properties of matter, 49, 213
infinite matrices, 414
infinitesimal element, 27, 201
Ingrao, Bruna, 75
insurance mathematics, 107, 164, 171173, 177, 323
integral equations, 2, 3, 21, 25, 77, 109,
127, 171, 228-230, 238-239, 246-261,
265, 267, 285, 317, 377, 414, 417, 438,
447
intensity magnitudes, 301-303
International Congress of Mathematicians
(ICM), 1, 20, 101, 121-122, 153, 166,
228, 244, 325, 446, 447
intuitionism, 396, 434
invariant theory, 15, 17, 20, 93, 321, 339,
389
isothermal, 157-158
Israel, Giorgio, 35, 75

J
Jacobi principle, 12, 91, 93
Jacobi, Carl Gustav (1804-1851), 12
Jahrbuch der Radioaktivität und
Elektronik, 211, 308
Jahresbericht der Deutschen
Mathematiker-Vereiningung, 20, 21,
22, 64, 75, 86, 109, 128, 129, 130, 179,
186, 193, 214, 215, 237, 253, 254, 257,
259, 261, 262, 271, 296, 310, 311, 319,
323, 324, 330, 331, 352, 356, 368, 369,
388, 390, 445, 453
Janssen, Michel, vi, 132, 287, 291, 293,
294, 295, 346
Jeans, James (1877-1946), 243-244
Johann Georg Rosenhain (1816-1887), 12
Jordan, Camille (1838-1921), 30
Jordan, Pascual (1902-1980), 411, 414418, 437, 440
Jungnickel, Christa, 13, 45, 48, 49, 51,
54, 61, 79, 92, 132, 134, 232, 234, 297,
317, 321

K
Kahle, R., 104, 121
Karachalios, Andreas, 411
Kármán, Theodor von (1881-1963), 241,
265, 455, 456

505
Kassel, 129, 453
Kast, W., 299
Katzir, Shaul, vi, 187, 232
Kaufmann, Walter (1871-1947), 49, 130,
133-134, 196, 211-212, 299
Kennedy, H., 43-44
Kepler’s law, 204, 213, 382
Kerszberg, Pierre, 364
Khinchin, Aleksandr Y. (1894-1959),
227
Killing , Wilhelm (1847-1923), 29, 33,
34, 42
kinetic theory, 2, 3, 7, 12, 46-49, 64, 76,
107, 168-171, 179, 214, 226, 229-250,
265, 267-274, 284, 301, 310, 317, 320,
382, 397, 417, 445-448
equipartition theorem, 48, 252
H-curve, 48
Stossanzahlansatz, 179
Umkehreinwand, 47
Wiederkehreinwand, 47, 179
Wiederkehreinwand, 179
Kirchhoff, Gustav (1824-188), 51, 55, 64,
91, 129, 239, 242, 247-264, 445
Kirchhoff’s laws, 239-264, 445
Klein, Felix (1849-1925), 4, 11, 12-14,
18-47, 54, 58, 66, 72-97, 119, 130,
193, 214-224, 263, 266, 321-326, 338,
359, 365, 366, 369, 376, 388-392, 399,
407-409, 419, 431, 435-450
Klein, Martin, 46, 150, 152, 179, 266
Kneser, Adolf (1862-1930), 76
Kneser, Hellmuth (1898-1973), 413, 416
Koebe, Paul (1882-1945), 251
Kohl, G., 306
Kohlschütter, Arnold (1883-1969), 130
Kolmogorov, Andrei N. (1903-1987), 166
Köln, 199, 206, 223, 447
Königlichen Gesellschaft der
Wissenschaften zu Göttingen (GWG),
127, 138, 193, 249, 263, 320, 329-330,
334, 354, 357, 361, 366, 384, 390, 417,
447-449, 457
Königsberg, 4, 12-20, 51, 58, 61, 73, 7883, 89, 90, 129, 166, 180, 227, 416,
429, 447-453
Köthe, G., 77
Kox, Anne J., 364
Kragh, Helge, 13, 134, 243, 414
Krakow, 271
Kratzer, Adolf (1893-1983), 451, 458

506

INDEX

Kremer, R.L., 176
Kretschmann, Erich (1887-1973), 365
Kronecker, Leopold (1823-1891), 18, 2124, 72, 102-104, 123, 379, 417
Kuhn, Thomas .S., 46-48, 79, 154, 168,
242-247
Kummer, Edward E. (1810-1893), 21-24

L
Lacki, J., 412, 413
Ladenburg, Rudolf (1882-1952), 248,
253, 263-264
Laemmel, Rudolf (1879-1962), 166
Lagrange, Joshep-Louis (1736-1813), 17,
70, 91, 128, 129, 277-278, 312, 315,
324, 336, 340, 375
Lagrangian equations, 109, 145-147, 277,
278, 312, 377, 390, 391
Lagrangian function, 133, 152, 174, 235,
278, 312-316, 335, 342-346, 358
Lamb, Horace (1849-1934), 75, 153
Lanczos, Cornelius, 145, 335
Landau, Edmund (1877-1938), 215, 409,
447
Landé, Alfred (1888-1975), 232, 321,
368, 440, 458
Lange, Louise, 323
Lange, Ludwig, 53, 145
Laplacian operator, 152, 290
Larmor, Joseph (1857-1942), 69, 130,
132, 143-144
Laub, Jakob (1882 – 1962), 224
Laue, Max von (1879-1960), 130, 224,
225, 243, 278, 359, 381, 440, 454
Laugwitz, Detlef, 28
Le Sage, Georges L. (1724-1803), 283
least action principle, 68, 133
least squares principle, 145, 167
Leibniz, Gottfried W. (1646-1716), 52
Leiden, 130, 271, 364
Leipzig, 12-13, 44, 51, 54, 74, 175, 411,
445
Leopold Infeld (1893-1968), 310
Lesezimmer, 4, 91, 129, 445
Levi-Civita, Tulio (1873-1941), 8, 292,
297, 320, 328, 365
Lewis, Gilbert .N., 136, 187, 276
Lewy, Hans (1904-1988), 420
Lexis, Wilhelm (1837-1914), 171

Lie , Sophus (1842-1899), 25-34, 86, 105,
106, 391, 445
light-cone, 212
Lindemann, Ferdinand (1852-1939), 13
line element, 27, 225
linear associative algebras, 116
Liouville's theorem, 48, 178-179
Lipschitz , Rudolf (1832-1903), 29, 37,
38, 292
Listing, Johann Benedikt (1808-1882), 78
Littlewood, John E. (1885-1977), 227
Lobatchevskii, Nikolai (1792-1856), 26-30
logic
foundations, 37, 47, 51-52, 57, 97,
100-111, 116-122, 125, 183, 296,
318-319, 370, 398, 426, 429, 450
symbolic, 66
longitudinal mass, 133
Lord Kelvin, 150, 161
Lorentz, Hendrik Anton (1853-1928), 49,
76, 77, 79, 129-136, 153, 174, 187235, 243, 244, 271-273, 280-289, 291293, 300-306, 312, 314, 333, 345, 346,
363-364, 375-377, 432-435, 446-447,
455-456, 460-461
Lorey, Wilhelm, 91, 92, 241, 445
Loria, Gino (1862-1954), 75
Loschmidt, Josef (1821-1895)., 47
Love, Augustus E.H. (1863-1940), 75,
153
Lübeck, 86
Lützen, Jesper, vi, 58, 60, 91, 148

M
Mach, Ernst (1838-1916), 47-51, 55, 57,
64, 68, 92, 106, 129, 145, 251, 290,
323, 446
Madelung, Erwin (1881-1972), 241, 284,
440
magnetic permeability, 196
Majer, Ulrich, vi, 54, 87, 111, 400, 428,
464
Maltese, Giulio, 218, 377
Mancosu, Paolo, vi, 319, 326, 370
Manegold, Karl-Heinz, 74
Marburg, 91, 409
Marxsen, Sophus, 20
Masani, P.R., 414

INDEX
Mathematische Annalen, 18, 34, 54, 73,
102, 163, 215-216, 229, 331, 340, 357,
359, 399-403, 445, 449
Mathematische Zeitschrift, 410, 449
matrix calculus, 190, 414
matrix mechanics, 414-417
Maxwell equations, 191, 193, 216, 273,
282-284, 299-304, 312, 341, 351, 362,
432
Maxwell, James Clerk (1831-1879), 46,
48, 54, 55, 64, 114, 131, 134, 153, 169,
170, 191, 193, 195, 216, 237-240, 248,
264, 273, 282-284, 296-304, 310-312,
314, 341, 344, 351, 362, 394, 430, 432,
433, 445, 446, 453, 454
Maxwell’s electromagnetic theory, 54,
55, 64, 114, 134, 248, 264, 300, 310,
394, 430
Mazzoni, L., 364
McCormmach, Russell, 13, 45, 48, 49,
51, 54, 61, 79, 92, 132, 134, 232, 234,
284, 297, 317, 321
mechanical models, 49, 50, 65
mechanical world view of nature, 50
mechanics
analytical, 93, 129, 311
applied, 263
axiomatic approach, 93
Boltzmann’s presentation, 63, 148
celestial, 411
classical, 92, 173, 174, 191, 198, 208,
218, 235, 278, 281, 290, 390, 391
fluid, 130
foundations, 54-58, 69-71, 86, 100,
147, 148, 277, 405, 424
Hertz’s presentation, 55-59, 64, 69,
144
Hilbert’s presentation, 147
history, 368
Lagrangian, 312
lectures, 73
Newtonian, 51, 132, 199, 204, 206,
209, 217, 272, 276, 297
non-Galilean, 144
non-Lagrangian, 276
non-Newtonian, 276
of a mass-point, 92
of continua, 127, 128, 129, 149, 150,
151, 185, 228, 234, 236
of continua (Euler’s approach), 150

507
of continua (Lagrange’s approach),
150
principles, 67-71, 142, 145, 148, 178,
199, 447
rational, 70, 75, 251
relativistic, 280, 287
statics, 142, 397
statistical, 76, 179, 183, 228, 266, 268,
270, 284, 287, 323, 417, 448
Medicus, Hermann, 329
Mehra, Jagdish, 189, 265, 399, 411, 412,
413, 415, 419, 432
Mehrtens, Herbert, 112, 118
Mercury
anomalous perihelion motion, 291,
294, 346, 352-355, 384, 407, 448
Mertens, Franz (1840-1927), 17
Methoden der mathematischen Physik
(Hilbert-Courant), 410-411, 440
Michelson-Morley experiment, 187, 191,
210, 212, 279, 323, 430
Mie effect, 299
Mie, Gustav (1868-1957), vi, viii, 7, 182,
234, 251, 271-273, 280-285, 287, 298319, 324, 333-382, 404-407, 421, 433436, 447-448, 456-462
Mie’s electromagnetic theory of matter,
234, 298-319, 333-382, 405, 421, 435436, 447, 448, 456
Born’s version, 311, 315, 316, 335,
341, 344, 448
Milan, 297
Miller, Arthur I., 88, 133, 189, 191, 197,
218
minimal constraint principle, 68, 93, 145,
148
Minkowski metric, 380, 427
Minkowski, Hermann (1864-1909), viii,
ix, 7, 13-15, 20-23, 73, 86-87, 101,
105, 110-111, 119, 128-136, 149, 152,
175, 182-228, 231, 235-236, 239, 242,
247, 250, 265, 268, 271, 278, 289-305,
309, 313, 318, 324, 333-34, 345, 361,
367, 380, 388, 402, 405, 411, 421, 427,
433, 436, 440-447, 453-456, 461-464
Minkowskian limit, 382
Möbius, August Ferdinand (1790-1868),
30, 32, 36
Molk, Jules (1857-1914), 76
Montgomery, D., 106

508

INDEX

Moore, Eliakim H. (1862-1932), 95, 115,
116, 447
Moore, G.H., 45, 47, 97, 100, 121, 141
Müller, Conrad, 215, 368
Müller, Georg Elias (1850-1934), 178
Munich, 64, 74, 99, 232, 271, 317, 323,
326, 411, 446
Münster, 249, 251, 253, 257, 261, 262,
271, 310, 448
Murray, D., 178

N
Nabl, J., 77, 447
Nagel, Ernst, 40
natural numbers, 37-39, 43, 169
n-body problem, 102, 281
n-electron problem, 273, 281, 282
Nelson, Leonard (1882-1927), 121, 319,
323
Nernst, Walter (1864-1941), 81, 129, 160,
241, 249, 252, 271, 317, 446, 448,
453-456, 464
Netto, Eugene (1848-1919), 75-76, 446
Neumann, Carl G. (1832-1925), 8, 51-53,
70, 73, 84, 143, 145, 179, 445
Neumann, Franz Ernst (1798-1895), 12,
51, 79, 166
Newtonian physics, 51, 57, 62, 63, 131,
132, 145-151, 162, 176, 200, 235-236,
272, 289-290, 295, 341, 352, 382, 393,
394, 430-431, 483, 486
n-manifold, 26
Noether, Emmy (1882-1935), 21, 38, 321,
326, 337, 356, 362, 369, 376, 388,
390-392, 403-409, 420, 441, 448-449,
456, 457
Noether, Max (1844-1921), 30
Noether’s invariance theorems, 337, 362
Noll, W., 178
non-holonomic systems, 150
Nordheim, Lothar (1899-1985), 8, 413418, 440, 449-452, 458
Nordström, Gunnar (1881-1923), 289,
306, 307, 364
Norlund, Niels E. (1885-1969), 76
North, J., 284
Norton, John D., vi, 192, 206, 222, 287,
289, 290, 291, 294, 306, 321, 324, 326,
349
nostrifizierung, 8, 99, 328, 406

number theory, 12, 13, 15, 20-25, 37, 78,
84, 86, 89, 93, 101, 104, 136, 169, 170,
222, 227, 396, 409, 429, 437, 450, 463

O
observational errors, 166
Olesko, Katheryn M., 13, 61, 79, 92, 166
Oppenheimer, Robert (1904-1967), 411
Oppolzer, Egon Ritter von (1869-1907),
175-176
optics, 12, 15, 88, 135, 147, 176, 215,
232, 246, 262, 264, 265, 322, 446
Orlando, L., 218, 377
Osterbrock, Don, vi, 322
Ostrowski, Alexandre (1892-1986), 409
Ostwald, Wilhelm (1853-1932), 47, 49,
50
Oxford, England, 13, 441
Oxford, Ohio, 323

P
Padoa, Alessandro (1868-1937), 111-112
Padova, 297
Pais, Abraham, 189, 224, 307, 322, 329,
432
Pappus’s theorem, 42, 89, 96-98
parallelogram law, 138, 140, 209, 396
Pareto, Vilfredo (1848-1923), 75
Paris, 1, 12, 13, 30, 35, 62, 65, 101, 105,
111, 122, 128, 149, 220, 445, 446
Paris Academy, 13
Parshall, Karen H., 17, 20, 31, 115
Pasch, Moritz (1843-1930), 25, 40-44, 57,
84, 85, 113, 115, 445
Pauli, Wolfgang (1900-1958), 77, 195,
306, 326, 375, 406, 411, 415, 416, 431,
436, 437, 449, 460
Peacock, George (1791-1858), 35
Peano ,Giuseppe (1858-1930), 36, 43, 44,
45, 86, 92, 111, 115, 446
Peckhaus, Volker, 47, 97, 104, 112, 121,
123, 319
perpetuum mobile, 145, 146, 154, 270
Perron, Oskar (1880-1975), 76
perturbation theory, 411
Petersen, Julius (1839-1910), 91, 129
Petrograd, 322

INDEX
phenomenology, 49, 64, 66, 79, 80, 195,
234-239, 251, 268, 273, 285
mathematical, 65
physics
continuity assumptions, 59, 68, 69,
139, 140-147, 156, 172, 177-178,
182, 214, 220, 418
foundations, 3, 6, 7, 11, 28, 49, 63, 71,
246, 267, 278, 290, 316, 331-334,
357, 366, 368, 380, 390, 396, 399,
403, 428, 432, 434, 438
Newtonian, 46, 47, 51, 131, 144-153,
173, 192, 203-205, 218, 235, 272,
276-277, 287, 290, 291, 294, 323,
380, 383, 394, 404, 405, 431
non-Archimedean, 141, 416
physics
theoretical, 237, 373
Physikalische Zeitschrift, 76, 241, 249,
250, 251, 252, 262, 271, 307, 310
Physikalische Zeitung, 76
Picard, Émile (1856-1941), 12
Pieri, Mario (1860-1913), 44, 45, 111
piezoelectricity, 232, 319, 322
plagiarism, 417
Planck, Max (1858-1947), v, 46, 47, 64,
81, 129, 130, 154, 162, 168, 178, 179,
190, 191, 195, 212, 231-233, 242-257,
261-266, 271, 278, 284, 326, 369, 393,
423, 447-448, 455-457, 461-462
Planck’s law, 447
Planck’s radiation law, 232, 244, 447
Plücker , Julius (1801-1868), 30, 33
Pohl, Robert Wichard (1884-1976), 411
Poincaré, Henri (1854-1912), 12, 29, 34,
47, 71, 102, 135, 136, 149, 164, 165,
174, 186, 187, 190, 191, 194, 205, 212,
220, 223, 224, 227, 231, 244, 246, 289,
446, 447, 455, 456, 460
Poisson equation, 152, 162, 290, 293, 362
Poncelet, Jean Victor (1788-1867), 30
postulational analysis, 111-116
potential theory, 12, 15, 51, 73, 93, 127
Prandtl , Ludwig (1875-1953), 73, 119,
130, 153, 215, 411, 447, 455, 456
pre-established harmony, 103, 186, 213,
214, 252, 394, 423, 429
pressure, 58, 152, 155, 161, 169, 267,
268, 301, 397
Principia Mathematica (Russell Withehead), 319

509
mechanics, 66
Principles of Mechanics (Hertz), 221
Pringsheim, Alfred (1850-1941), 75-76
Pringsheim, Ernst (1859-1917), 75, 247266, 373, 446, 448
priority, 8, 134, 187, 280, 328, 350, 353,
362, 407, 408, 436, 449
probabilistic arguments, 170
probability calculus, 21, 47, 81, 107, 164,
166, 168, 169, 170, 171, 229, 267, 276
proper time, 199, 200, 204, 213, 385
propositional logic, 123
pseudo-geometry, 385, 387
psychophysics, 175-177, 276, 397
Purkert, Walter, vi, 117
Pycior, Elena, 35
Pyenson, Lewis, 103, 129, 130, 136, 174,
186, 187, 188, 189, 198, 324, 394, 432
Pythagoras, 393

Q
q-calculus, 414
q-numbers, 415, 417
quantity magnitudes, 301-302
quantum discontinuity, 243, 244
quantum hypothesis, 231, 268-271
quantum mechanics, 8, 214, 413-419,
440, 449
quantum theory, 49, 79, 178, 179, 232,
243, 246, 284, 300, 317, 369, 377, 393,
397, 411-418, 449
quaternions, 193

R
Rademacher, Hans (1892-1969), 227
radiation
diffuse, 283, 284
monochromatic, 259
thermal, 231, 242
radiation theory, 7, 129, 154, 226-255,
256, 261, 264-268, 273, 276, 310, 317,
329, 358, 373, 397, 403, 408, 415, 417,
421, 438, 448, 464, 465
radioactivity, 49
Ramser, L., 61
Raum und Zeit (Minkowski), ix, 143, 205,
206, 209, 217, 222, 278, 279, 313, 345,
399, 402, 442, 451, 453, 480, 485

510
Raum-Zeit-Materie (Weyl), 364, 433-435,
449
Rausenberg, Otto, 92, 129
Rayleigh-Jeans law, 243
real numbers, 35-39, 96-104, 121, 138
continuity assumptions, 96, 101
Rechenberg, H., 410, 411, 413, 415, 419
reductionism
electromagnetic, 7, 231, 285, 310, 313,
316, 333, 384
energicist, 49, 64
mechanical, 7, 46, 49, 50, 69, 221,
231, 235, 268, 285, 313
reference frame, 212, 292
accelerated, 187, 289, 293
inertial, 205, 235, 290
Reich, Karin, 29, 66, 190, 292
Reid, Constance, 3, 8, 22, 118, 185, 227,
232, 241, 325, 369, 409, 416, 420, 440,
442
Reiff, Richard (1855-1908), 149, 152
relativity
of the gravitational potential principle,
305
postulate, 152, 187, 193, 198-216, 220221, 236
principle, 7, 8, 130, 185, 186, 187,
190-223, 239, 268, 274, 278, 285,
287, 290, 300-307, 321, 364
general theory, 2, 3, 7, 8, 77, 81, 106,
141, 152-153, 168, 182, 189, 206,
214, 225, 246, 284-287, 290-297,
302, 304, 309, 311, 320-333, 341,
345, 353, 356, 361-449, 464
eclipse expedition, 365-394
gravitational field-equations, 2, 225,
403, 441
Renn, Jürgen, vi, 287, 294, 330, 331, 337,
338, 340, 341, 345, 353, 380, 386, 387,
404, 405, 437
Resnik, Michael, 112, 118
reversible processes, 47, 156
Reye, Theodor (1838-1919), 83, 84
Ricci-Curbastro, Gregorio (1853-1925),
292
Richards, Joan L., 29
Riecke, Eduard (1845-1915), 72, 78, 79,
81, 232, 297, 307, 321, 411, 445, 446
Riemann curvature scalar, 341, 353
Riemann, Bernhard (1826-1866), 22-29,
33, 36, 37, 42, 44, 70, 84, 87, 105, 251,

INDEX
292-293, 309, 324, 337, 341, 346, 352353, 359, 445
rigid body, 29, 133, 142, 150, 210, 217,
218, 219, 246, 272-273, 291, 312, 368,
376, 377, 447
free mobility of, 27, 28, 105
Rockefeller Foundation, 410
Rodriguez, Laura, 229
Röhle, S., 365
Rome, 166, 228, 244, 447
Röntgen, Wilhelm Conrad (1845-1932),
49
Rostock, 299
rotating disk, 291
Routh, Edward J. (1831-1907), 92, 129
Rowe, David E., v, 12, 17, 18, 22, 23, 24,
31, 32, 33, 35, 54, 72, 73, 74, 76, 85,
104, 112, 115, 296, 322, 341, 359, 364,
374, 375, 389, 390, 391, 421, 429, 434,
440, 441
Rüdenberg, L., 15, 20, 22, 105, 129
Rudolf Alfred Clebsch (1833-1872), 17,
20, 30, 54, 66, 73, 445
Rügen, 326, 448
Runge, Carl (1856-1914), 73, 119, 130,
142, 214-215, 321, 322, 391, 411, 447,
455-457, 461
Russell, Bertrand (1872-1970), 121, 319,
369, 370, 398, 427, 449, 460

S
Saalschütz, Louis (1835-1913), 12
Sabidussi, G., 91
Sackur, Otto (1880-1914), 241
Sánchez-Ron, José M., 364
Sarkowski, H., 410
Sauer, Tilman, vi, 287, 294, 314, 325,
326, 329, 330, 339, 340, 345, 349, 351,
355, 356, 358, 360, 366, 369, 400
Scanlan, W., 97, 116
Schell, Wilhelm (1826-1904), 91
Schellenberg, Kurt, 265
Schemmel, Matthias, 321
Scherrer, Paul (1890-1966), 317, 321,
411
Schirrmacher, Arne, xii, 79, 129, 186,
230, 232, 234, 247, 249, 250, 251, 253,
257, 317

INDEX
Schlömilch, Oscar Xavier (1823-1901),
142
Schmidt, Arnold (1902-1967), 95, 413
Schmidt, Erhard (1856-1959), 414
Schmidt, Friderich, 322
Schneider, Ivo, 166
Schoenflies. Arthur M. (1853-1928), 21,
61, 73, 89
Scholz, Erhard, vi, 28, 73, 88, 434
Schottky, Heinrich (1851-1935), 76, 297
Schrödinger equation, 415
Schrödinger, Erwin (1887-1961), 365,
414-416
Schubert, H.A. (1848-1911), 74, 75, 446
Schubring, Gert, 78
Schur, Friedrich (1856-1932), 42-43, 8790, 95, 97-99, 115, 138, 140-142, 297,
446
Schur, Issai (1875-1941), 297
Schwarz, Hermann Amandus (18431921), 47, 297
Schwarzschild, Karl (1873-1916), 72, 81,
130, 136, 174, 215, 321-326, 363, 364,
380-385, 435, 447, 454-455, 460
Schwermer, Joachim, 13-15, 61, 222
Seelig, Carl, 224
segments arithmetic (Streckenrechnung),
98
Segre, Michael, 34-36, 43, 75
set theory, 21, 45, 47, 101-102, 104, 120122, 229, 274, 321, 369, 379-398, 413,
450
axiomatization, 319
well-ordering axiom, 121, 369
Shimmack, Rudolf (1881-1912), 138
Siebert, H., 12
Sieg, Wilfried, 319, 370
Siegel, Carl Ludwig (1896-1981), 409
Siegmund-Schultze, Reinhard, 228, 410,
420
Sigurdsson, Skuli, 324, 442
Simon, Hermann Theodor (1870-1918),
130, 146, 321, 366, 372
Sinaceur, Houria, 89
Smith, Henry J.S (1826-1883), 13
sodium flames, 248
Solvay conference, 244
Sommer, Klaus, viii, 257, 326
Sommerfeld, Arnold (1868-1951), 73, 76,
129, 136, 187, 190, 205, 218, 224, 225,
232, 247, 250-251, 271, 302, 317, 320,

511
321, 324, 327, 345-349, 351, 356, 364,
368, 374, 41, 413, 416, 436, 447, 448,
455-462
Sommerfeld-Bohr atomic model, 416
space
absolute, 52, 178, 187
space-time manifold, 224, 347
space-times coordinates, 339
spatial intuitions (Raumanschauungen),
36
Spehl, Helmut, vi, 299
Speiser, Andreas, (1885-1970), 20, 216
Springer, Ferdinand (1881-1965), 408
Springer’s Grundlehre Yellow Series,
410, 440
St. Petersburg, 150, 164, 266
stability theory, 128, 464
Stachel, John, vi, 212, 287, 291, 292, 294,
330, 331, 337-345, 353, 380, 386, 387,
403-405, 437
Staley, Richard, vi, 189, 195, 198, 212,
216, 225, 432
Stark, Johannes (1874-1957), viii, 211,
212, 277, 308, 459-461
Steiner, Jacob (1796-1863), 30
Stern , Otto (1888-1969), 284
Stoltz, Otto (1842-1905), 30
Stölzner, Michael, 419
straightest path principle, 93, 148
Strasbourg, 72
Strobl, W., 13
structural algebra, 25, 37, 116, 321, 409,
420
structure of matter, 7, 148, 168, 216, 231,
234, 267, 283, 284, 285, 315-319, 333,
344, 350-368, 403-405, 411
Struik, Dirk (1894-2000), 421
Strutt, John William - Lord Rayleigh
(1842-1919), 243
Study, Eduard (1862-1930), 17
Swiss Mathematical Society, 396
Sylvester, James Joseph (1814-1897), 17,
20
symmetric function, 149, 228
Szanton, A., 411

T
tensor
contravariant, 335
gravitational, 293

512
metric, 291, 293, 294, 316, 333, 335,
344, 378, 385, 387, 407
Ricci, 293, 341, 348, 349, 355, 359,
375
Riemann, 293, 352, 359
second-rank, 407
stress-energy, 293, 294, 315, 316, 342,
344, 349, 355, 383, 390, 404, 435
stress-energy, 315
theology, 18, 299
theoretical physics, 13, 47, 49, 51, 78, 79,
81, 251, 280, 281, 299, 317, 411, 441,
445, 446
theory of bilinear forms, 66
theory of invariants, 12, 19, 20, 23, 91,
101, 228, 344, 361, 376
theory of matter, 8, 182, 191, 194, 226228, 237, 246, 249, 268, 271-272, 285,
287, 299-302, 308-309, 315- 319, 407,
435, 447, 448
thermochemistry, 241
thermodynamics, 15, 49, 79, 128, 129,
154-163, 171, 173, 181, 183, 212, 234,
241-249, 270, 271, 276, 397
continuity axiom, 159
relativistic, 191, 287
second law, 46, 47, 220, 239, 270, 271,
393
third law (Nernst law of heat), 241,
270, 317
Thiele, Rüdiger, 109
Thirring, Hans (1888-1976), 365
Thomson, Joseph James (1856-1940), 15,
91, 129, 130, 150, 284, 456
Tobies, Renate, 35, 54
Toepell, Michael Markus, 32, 44, 66, 83,
84-90, 93-99, 118, 323, 423
Toeplitz, Otto (1881-1940), 24, 77, 215,
227, 228, 436
Tollmien, Cordulla, 356
Tolman, Robert C., 276
Torretti, Roberto, 28, 29, 32, 40, 43, 44,
95
Traktoren, 190
transcendence of S, 13
transfinite cardinals, 100
transformations
Galilean, 132, 207, 208, 210
Lorentz, 79, 132, 174, 190-197, 208,
235, 271, 272, 280, 306, 432
Truesdell, Clifford, 178

INDEX
Tübingen, 51
Turner, R.S., 176

U
Über den Zahlbegriff (Hilbert), 104, 123,
426, 479
ultraviolet catastrophe, 243
unification
gravitation and electrodynamics, 172
mechanics and electrodynamics, 153
optics and electromagnetism, 134
unified foundations of physics, 231, 309,
331-333, 351, 397
unimodularity, 348
Urbantke, 365
USSR, 322

V
van Dalen, Dirk, 396
van der Waerden, Bartel L. (1903-1996),
420, 459
van Dyck, Walther (1856-1934), 74, 75,
76, 77, 446
variational calculus, 47, 102, 104, 109,
214, 339, 344, 361, 391
variational derivation, 152, 295, 313, 373,
374, 375, 449
variational methods, 295, 353, 404, 414,
436
variational principles, 7, 109, 128, 133,
150, 182, 295, 312-314, 326, 336, 362,
373, 404, 436, 454
Veblen, Oswald (1880-1960), 97, 116
vector, 79, 138-151, 156-157, 178, 181,
189-191, 196-205, 224, 246, 283, 292,
301, 304, 314, 339, 360, 374, 390
contravariant, 360
four-vector, 190-194, 204-205, 301,
447
six-vector, 301
vectorial notation, 153
Veronese, Giusseppe (1854-1917), 25,
44, 86-87, 93, 99, 111, 419, 444
Vienna, 47, 74, 150, 306, 307-308, 316,
323, 448, 470
virtual velocities principle, 93
Voigt, Woldemar (1850-1919), 15, 61,
72, 78-81, 92, 121, 129, 215, 232-234,

INDEX
248-249, 297, 317, 319, 321-322, 41,
445, 461
Volkert, Klaus, 12
Volkmann, Paul (1856-1938), 15, 61-63,
68, 81, 103, 106, 126, 180, 182, 446,
461, 462
Vollrath, Hans-Joachim, vi, 66
Volterra, Vito (1860-1940), 228
von Neumann, John (1903-1957), 412,
417-419, 449
von Smoluchowski, Marian (1872-1917),
249-262, 271, 369, 448, 456, 457
von Staudt , Christian (1798-1867), 30,
32, 40, 42, 43, 83-84, 97
Voss, Aurel (1845-1931), 66-71, 75, 92,
129, 132, 138, 143-144, 180, 447, 461462

W
Walter, Scott, vi, 49, 133, 189, 192, 205,
211, 212, 224, 322, 411
Waring’s problem, 227-228
Warwick, Andrew C., 75, 92, 130, 132,
364
Was sind und was sollen die Zahlen?
(Dedekind), 38, 39, 47, 85, 100, 446
wavelength, 176-177, 242-243, 252-262,
283, 463, 466
wave-mechanics, 414
Weber, Ernst Heinrich (1795-1878), 175
Weber, Heinrich (1842-1913), 12-13, 7274, 175, 446, 461, 463
Weber-Fechner law, 175-176
Weierstrass , Karl (1815-1897), 34, 35,
72, 102, 123, 379
Weyl, Hermann (1885-1955), 3, 4, 17, 20,
22, 89, 183, 215, 324, 359, 364, 373,
374, 392, 395, 431-436, 439, 442, 449,
451-463
Whittaker, Edmund (1873-1956), 75
Wiechert, Emil (1861-1928), 72, 81, 107,
130, 134, 136, 215, 321, 411, 446, 455,
463
Wien, Wilhelm (1864-1928), 49, 70, 129132, 153, 242-252, 299, 363, 369, 371,
446, 455, 460-461
Wiener, Hermann L. (1857-1939), 42, 43,
85, 87, 97, 99, 414-415, 446
Wien's formula, 243
Wightman, A.S., 1

513
Wigner, Eugene (1902-1995), 413, 458
Wilhelm Weber (1804-1891), 11, 78-79,
445-446
Wilkens, Alexander (1881-1968), 130
Wise, Norton, 301
Wolfskehl lectures, 231, 244, 271, 317,
320, 368, 371-372, 411-413, 448-449,
455-457
Wolfskehl, Paul (1856-1906), 231
Woodrow Wilson College, 323
World War I, 75, 319, 322, 370, 409
world-function, 7, 152, 302-303, 313, 315
world-lines, 201-204, 208, 300
world-parameters, 335, 339
world-points, 335
world-postulate, 152, 193, 199, 200, 206,
211-213, 223-225, 235, 402
Wüllner, Adolph (1835-1908), 12
Würzburg, 66, 369

Y
Yandell, B.H., 1
Yavetz, Ido, 138
Young, Thomas (1773-1829), 52, 119,
176, 489

Z
Zach, Richard, 370
Zahlbericht (Hilbert), 22-24, 71, 418, 446
Zahlkörpersspaziergängen, 89
Zangger, Heinrich (1874-1957), 287, 297,
324-325, 328, 355, 407, 419, 460
Zassenhaus, Hans, 15, 20-22, 105, 129
Zeeman effect, 79, 136
Zeeman, Pieter (1865-1943), 79, 130, 136
Zeitschrift für Mathematik und Physik,
73, 142
Zermelo, Ernst (1871-1953), 2, 47-48,
120-121, 215, 296, 319, 369, 398, 446447, 455
Ziegler, R., 30
Zippin, L., 106
Zsigmondy, Richard A. (1865-1927), 369
Zurich, 12-15, 129, 289, 297, 317, 318,
324, 369, 370, 406, 446, 448



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