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Tables of Contents for The Hilbert Challenge
Chapter/Section Title
Page #
Page Count
The future unveiled
1
13
The shaping of a pioneer
14
46
Hilbert's student years
14
4
After Hilbert's graduation
18
5
Hilbert's breakthrough in invariant theory
23
10
How Hilbert came to Gottingen
33
2
Hilbert and number theory
35
13
Hilbert and geometry
48
8
The road to Paris
56
4
The beacons are lit
60
29
The background: mathematics in 1900
74
4
Roads not taken
78
2
Poincare's address of 1897
80
3
Poincare and electromagnetic theory
83
1
Poincare's address of 1908
84
5
The early response: 1900-1914/18
89
66
Hilbert and the viability of the Hilbert Problems
89
6
Hilbert's Problems on the foundations of mathematics
95
7
Hilbert among the philosophers
102
2
Axiomatising geometry in USA, responses to Grundlagen der Geometrie
104
5
Hilbert and Brouwer on Hilbert's Problem 5
109
4
Hilbert Problems on pure and applied mathematics
113
27
Hilbert Problems on number theory
140
1
Problems 9, 11, and 12--The comedy of errors
141
3
Hilbert's geometric Problems
144
1
Ragsdale and others on Hilbert's 16th Problem
145
6
Beiberbach on Hilbert's 18th Problem
151
4
Between the wars: foundations examined
155
33
Gottingen after the First World War; the eclipse expedition
155
7
Hilbert, Brouwer and mathematical logic
162
6
Mathematical logic after Godel
168
5
Soviet Union in the 1930s, Egorov
173
1
Gelfond's work on Hilbert Problem 7
174
1
Pontrjagin on Problem 5
175
3
The 15th Problem, on the Schubert calculus
178
1
Hilbert's 16th Problem on differential equations and the work of Dulac
179
1
Plateau problem to Douglas
180
4
Bieberbach on Hilbert, 1930
184
2
1933-45
186
2
After 1945
188
45
The Princeton Conference on Problems of Mathematics
188
2
Pure or applied mathematics
190
1
Applied mathematics after the war
191
3
Pure mathematics after the war
194
3
Nicolas Bourbaki on the international stage
197
7
Alexandre Grothendieck
204
4
Matters of taste and judgement
208
1
The Soviet case
209
5
Hilbert's 17th Problem
214
1
Hilbert Problems at the International Congresses of Mathematicians
215
3
Work on mathematical logic
218
15
Epilogue
233
54
Hilbert's lecture at the International Congress of Mathematics, Paris 1900
238
1
Editor's notes
238
2
Hilbert's lecture
240
43
References to the lecture
283
4
Appendix 1: The Hilbert Problems 1900-99
287
3
Appendix 2: Logical matters
290
4
Glossary
294
4
General references
298
12
Index
310