List of dissertations supervised by David Hilbert
The following table contains a list of the dissertations supervised by David Hilbert in chronological order. At Hilbert, a total of 69 doctoral theses were completed in Göttingen from 1898 to 1933. Those dissertations for which Hilbert was only a second reviewer are not listed; these can also be found under " David Hilbert in the Mathematics Genealogy Project (English) ".
No. | PhD candidate | Title of the work | Date of graduation |
Publication, if necessary with associated journal publication |
---|---|---|---|---|
1. | Otto Blumenthal | About the development of an arbitrary function according to the denominators of the continued fraction for . | May 25, 1898 | 1898 |
2. | Hans von Schaper | On the theory of Hadamard's functions and their application to the problem of prime numbers. | July 26, 1898 | 1898 |
3. | Heinrich Dörrie | The quadratic reciprocity law in the quadratic number field with the class number 1. | July 29, 1898 | 1898 See: Acta Math. 1902, Vol. 26 (1), pp. 99-131 doi : 10.1007 / BF02415486 |
4th | Michael Feldblum | About elementary geometric constructions. | July 12, 1899 | 1899 |
5. | Fritz Beer | Criteria for the irrationality of functional values. | July 19, 1899 | 1899 |
6th | Legh Wilber Reid | Table of the number of classes for cubic number fields. | July 28, 1899 | 1899 See: Acta Math. 1902, Vol. 26 (1), pp. 99-131 doi : 10.1007 / BF02415486 |
7th | Anne Lucy Bosworth | Justification of a route calculation independent of the parallels axiom. | July 31, 1899 | 1899 |
8th. | Max Dehn | Legendre's theorems about the sum of angles in a triangle. | Nov 8, 1899 | 1900 Math. Ann. Vol. 53, pp. 404-439. doi : 10.1007 / BF01448980 |
9. | Karl Sigismund Hilbert | The general quadratic reciprocity law in from selected circular fields of the 2 n -th roots of unity. | Dec 1, 1899 | 1900 See: Acta Math. 1902, Vol. 26 (1), pp. 99-131 doi : 10.1007 / BF02415486 |
10. | Sophus Marxsen | About a general genus of irrational invariants and covariants for a binary form of odd order. | March 5, 1900 | 1900 |
11. | Lyubovy Sapolsky | About the theory of the relative-Abelian cubic number fields. | June 21, 1900 | 1902 |
12. | Edgar Jerome Townsend | About the concept and application of the double limit. | July 12, 1900 | 1900 |
13. | Gottfried Rückle | Quadratic reciprocity laws in algebraic number fields. | Jan. 22, 1901 | 1901 See: Acta Math. 1902, Vol. 26 (1), pp. 99-131 doi : 10.1007 / BF02415486 |
14th | Earle Raymond Hedrick | About the analytical character of the solutions to differential equations. | Feb 20, 1901 | 1901 |
15th | Felix Bernstein | Investigations from set theory. | March 2, 1901 | 1901 |
16. | Charles Albert Noble | A new method in the calculus of variations. | May 14, 1901 | 1901 |
17th | Werner Boy | About the Curvatura integra ad topology of closed surfaces. | June 19, 1901 | 1901 Math. Ann. 1903, Vol. 57 (2), pp. 151-184 doi : 10.1007 / BF01444342 |
18th | Georg Hamel | About the geometries in which the degrees are the shortest. | June 24, 1901 | 1901 Math. Ann. 1903, Vol. 57 (2), pp. 231-264 doi : 10.1007 / BF01444348 |
19th | Nadezhda Gernet | Investigation of the calculus of variations. About a new method in the calculus of variations. | July 28, 1901 | 1902 |
20th | Otto customs | Over areas with multitudes of closed lines (price writing). | July 29, 1901 | 1901 Math. Ann. 1903, Vol. 57 (1) pp. 108-133 doi : 10.1007 / BF01449019 |
21st | Johann Oswald Müller | About the minimum property of the sphere. | Feb. 24, 1902 | 1903 |
22nd | Georg Lütkemeyer | About the analytical character of the integrals of partial differential equations. | May 9, 1902 | 1902 |
23. | Paul Kirchberger | About Tchebychef approaches. | July 17, 1902 | 1902 Math. Ann. 1903, Vol. 57 (4) pp. 509-540 doi : 10.1007 / BF01445182 |
24. | Oliver Kellogg | On the theory of integral equations and Dirichlet's principle. | Nov 24, 1902 | 1902 |
25th | Rudolf Fueter | The class field of the quadratic fields and the complex multiplication. | February 23, 1903 | 1903: |
26th | Charles Max Mason | Boundary value problems in ordinary differential equations. | April 24, 1903 | 1903 |
27. | Albert Kraft | About whole transcendent functions of infinitely high order. | June 17, 1903 | 1903 |
28. | Albert Andrae | Aid for a general theory of the linear elliptic differential equation of the 2nd order. | June 26, 1903 | 1903 |
29 | Walther Lietzmann | About the biquadratic reciprocity law in algebraic number fields. | Oct. 29, 1903 | 1904 |
30th | Erhard Schmidt | Development of arbitrary functions according to systems prescribed. | June 29, 1905 | 1905 |
31. | Wilhelmus David Allen Westfall | On the theory of integral equations. | July 19, 1905 | 1905 |
32. | Hugo Kistler | About functions of several complex variables. | July 26, 1905 | 1905 |
33. | Alexander Myller | Ordinary higher-order differential equations in relation to the integral equations. | May 2, 1906 | 1906 |
34. | David Clinton Gillespie | Applications of the theorem of independence to the solution of the differential equations of the calculus of variations. | July 25, 1906 | 1906 |
35. | Wera Lebedeff | The theory of integral equations applied to some series expansion. | Oct. 24, 1906 | 1906 |
36. | Arthur Robert Crathorne | The spatial isoperimetric problem. | Feb 21, 1907 | 1907 |
37. | Ugo Broggi | The axioms of probability. | May 8, 1907 | 1907 |
38. | Charles Haseman | Application of the theory of integral equations to some boundary value problems in function theory. | June 28, 1907 | 1907 |
39. | William Deweese Cairns | The application of the integral equations to the second variation in isoperimetric problems. | July 3, 1907 | 1907 |
40. | Robert King | Oscillation properties of the eigenfunctions of the integral equation with a definite kernel and the Jacobian criterion of the calculus of variations. | July 10, 1907 | 1907 |
41. | Ernst Hellinger | The orthogonal variants of quadratic forms of infinitely many variables. | July 17, 1907 | 1907 |
42. | Hermann Weyl | Singular integral equations with special consideration of Fourier's integral theorem. | Feb 12, 1908 | 1908 Math. Ann. 1908, Vol. 66 (3) pp. 273-324 doi : 10.1007 / BF01450690 |
43. | Andreas Speiser | On the theory of binary quadratic forms with coefficients and indeterminates in any number field. | March 3, 1909 | 1909 |
44. | Alfréd hair | On the theory of orthogonal function systems. | June 16, 1909 | 1909 Math. Ann. 1910, Vol. 69 (3) pp. 331-371 doi : 10.1007 / BF01456326 |
45. | Margarete Kahn | A general method of studying the shapes of algebraic curves. | June 30, 1909 | 1909 |
46. | Klara Löbenstein | About the proposition that a flat, algebraic curve of the 6th order with 11 mutually exclusive ovals does not exist. | June 30, 1909 | 1910 |
47. | Richard Courant | About the application of Dirichlet's principle to the problems of conformal mapping. | Feb 16, 1910 | 1910 Math. Ann. 1911, Vol. 71 (2) pp. 145-183 doi : 10.1007 / BF01456646 |
48. | Erich Hecke | On the theory of the modular functions of two variables and their application to number theory. | March 3, 1910 | 1910 See Math. Ann. Vol. 71, pp. 1-37 doi : 10.1007 / BF01456926 |
49. | Kurt Grelling | The axioms of arithmetic with special consideration of the relations to set theory. | June 8, 1910 | 1910 |
50. | Wallie Abraham Hurwitz | Boundary value problems in systems of linear partial differential equations of the first order. | July 13, 1910 | 1910 |
51. | Johannes Otto Mühlendyck | Classification of the regularly symmetrical surfaces of the fifth order. | December 7, 1910 | 1911 |
52. | Hugo Steinhaus | New applications of Dirichlet's principle. | May 10, 1911 | 1911 |
53. | Paul Funk | Over areas with nothing but closed geodetic lines. | May 22, 1911 | 1911 Math. Ann. 1913, Vol. 74 (2) pp. 278-300 doi : 10.1007 / BF01456044 |
54. | Ludwig Föppl | Stable arrangements of electrons in the atom | March 1, 1912 | 1912 Excerpt in: Journ. Pure Applied Math. Vol. 141 pp. 251-302. |
55. | Gerhard Janssen | About the introduction of affine and equiform geometry by definition on the basis of the axioms of connections. | Feb. 19, 1913 | 1913 |
56. | Hans Bolza | Application of the theory of integral equations to electron theory and the theory of dilute gases. | July 2, 1913 | 1913 |
57. | Jakob Grommer | Whole transcendent functions with all real zeros. | July 16, 1913 | 1914 Journ. Pure Applied Math. Vol. 144 pp. 114–166. |
58. | Bernhard Baule | Theoretical treatment of the phenomena in dilute gases. | Feb. 18, 1914 | 1914 Ann. Phys. F. 4 vol. 44 doi : 10.1002 / andp.19143490908 |
59. | Kurt Schellenberg | Application of the integral equations to the theory of electrolysis. | June 24, 1914 | 1915 Abridged in: Ann. Phys. F. 4 vol. 47. doi : 10.1002 / andp.19153520904 |
60. | Georg Prange | The Hamilton-Jacobian theory for double integrals (with an overview of the theory for simple integrals). | Dec 21, 1914 | 1915 |
61. | Heinrich Behmann | The antinomy of the transfinite number and its resolution by the theory of Russell and Whitehead. | June 5, 1918 | 1922 |
62. | Willi Windau | About fourth order linear differential equations with singularities and the associated representations of arbitrary functions. | July 7, 1920 | 1921 Math. Ann. 1921 vol. 83 pp. 256-279 doi : 10.1007 / BF01458384 |
63. | Hellmuth Kneser | Investigations on quantum theory. | March 2, 1921 | 1921 Math. Ann. 1921 vol. 84 pp. 277-302 doi : 10.1007 / BF01459411 |
64. | Walther Rosemann | The structure of planar geometry without the axiom of symmetry. | December 11, 1922 | 1923 Math. Ann. 1923, Vol. 90 (1) pp. 108-128 doi : 10.1007 / BF01456245 |
65. | Wilhelm Ackermann | Justification of the "tertium non datur" using Hilbert's theory of consistency. | Aug 4, 1924 | 1925 Math. Ann. 1925 Vol. 93 pp. 1–36 doi : 10.1007 / BF01449946 |
66. | Gabriel Sudan | About the ordered sets. | July 20, 1925 | 1925 Buletinul de Stințe Matematice pure și aplicate. Anul 28. |
67. | Haskell Brooks Curry | Basics of combinatorial logic. | June 24, 1929 | 1930 American Journ. of Math. 1930 Vol. 52 pp. 509-536 doi : 10.2307 / 2370619 JSTOR 2370619 , pp. 789-834 doi : 10.2307 / 2370716 |
68. | Arnold Schmidt | The derivation of the reflection from the plane movement. | July 20, 1932 | 1934 Math. Ann. 1934 vol. 109 pp. 538-571 doi : 10.1007 / BF01449154 |
69. | Kurt Schütte | Investigations into the decision problem of mathematical logic. | May 10, 1933 | 1934 Math. Ann. Vol. 109 pp. 572-603 doi : 10.1007 / BF01449155 |
Web links and source
- List of doctoral theses prepared by Hilbert. In: David Hilbert - Gesammelte Abhandlungen, Volume III: Analysis, Fundamentals of Mathematics, Physics, Various, Life History. Springer-Verlag Berlin, Heidelberg, pp. 431-433. ISBN 978-3-662-23645-1 . doi : 10.1007 / 978-3-662-25726-5
- David Hilbert in the Mathematics Genealogy Project (English)
References and comments
- ↑ The list of publications does not claim to be complete.