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David Hilbert and the Axiomatization of Physics (1898-1918)


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Table of Contents

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


From the reviews:

"This is a massive scholarly book on the work of David Hilbert on physics. In more than 400 pages the author provides us with an in-depth analysis of the fundamental contributions of this mathematician-born scientist to many branches of physics ... . the historical reconstruction, which was the main aim of the author is ... done with extreme competence and care, and it is, I think, of the highest quality." (Daniele Oriti, Mathematical Reviews, Issue 2006 i)

"The main message of the book is that physics played in Hilbert's research ... a much larger role than is commonly recognized. ... It is written in a lively but at the same time in a very careful academic style. ... Throughout the book the reader is confronted with many interesting ... facts. ... Leo Corry's book is a significant contribution to Hilbert studies and will be a major reference source ... . I enjoyed reading the book and can recommend it to everyone." (Lev Beklemishev, Studies in History and Philosophy of Modern Physics, Vol. 37, 2006)

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