The Hilbert challenge:
Few problems in mathematics have had the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this cent...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2000
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | Few problems in mathematics have had the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this century. A hundred years later, this book takes a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this book, the authors consider what makes this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. |
| Physical Description: | XII, 315 S. Ill., graph. Darst. |
| ISBN: | 0198506511 |
Staff View
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| 520 | 3 | |a Few problems in mathematics have had the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this century. A hundred years later, this book takes a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this book, the authors consider what makes this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. | |
| 600 | 1 | 4 | |a Hilbert, David |
| 600 | 1 | 4 | |a Hilbert, David <1862-1943> |
| 600 | 1 | 4 | |a Hilbert, David <1862-1943> - Influence |
| 600 | 1 | 4 | |a Hilbert, David, 1862-1943 -- Influence |
| 600 | 1 | 4 | |a Hilbert, David, 1862-1943 |
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| 650 | 4 | |a Mathematics -- History -- 20th century | |
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Record in the Search Index
| _version_ | 1804129268685340672 |
|---|---|
| adam_text | Contents
1 The future unveiled ]
2 The shaping of a pioneer 14
Hilbert s student years 14
After Hilbert s graduation 18
Hilbert s breakthrough in invariant theory 23
How Hilbert came to Gottingen 33
Hilbert and number theory 35
Hilbert and geometry 48
The road to Paris 56
3 The beacons are lit 60
The background: mathematics in 1900 74
Roads not taken 78
Poincare s address of 1897 80
Poincare and electromagnetic theory 83
Poincare s address of 1908 84
4 The early response: 1900 1914/18 89
Hilbert and the viability of the Hilbert Problems 89
Hilbert s Problems on the foundations of mathematics 95
Hilbert among the philosophers 102
Axiomatising geometry in USA, responses to Grundlagen der
Geometrie 104
Hilbert and Brouwer on Hilbert s Problem 5 109
Hilbert Problems on pure and applied mathematics 113
Hilbert Problems on number theory 140
Problems 9, 11, and 12—The comedy of errors 141
Hilbert s geometric Problems 144
Ragsdale and others on Hilbert s 16th Problem 145
Beiberbach on Hilbert s 18th Problem 151
XII CONTENTS
5 Between the wars: foundations examined 155
Gottingen after the First World War; the eclipse expedition 155
Hilbert, Brouwer and mathematical logic 162
Mathematical logic after Godel 168
Soviet Union in the 1930s, Egorov 173
Gelfond s work on Hilbert Problem 7 174
Pontrjagin on Problem 5 175
The 15th Problem, on the Schubert calculus 178
Hilbert s 16th Problem on differential equations and the work
ofDulac 179
Plateau problem to Douglas 180
Bieberbach on Hilbert, 1930 184
1933 45 186
6 After 1945 188
The Princeton Conference on Problems of Mathematics 188
Pure or applied mathematics 190
Applied mathematics after the war 191
Pure mathematics after the war 194
Nicolas Bourbaki on the international stage 197
Alexandre Grothendieck 204
Matters of taste and judgement 208
The Soviet case 209
Hilbert s 17th Problem 214
Hilbert Problems at the International Congresses of
Mathematicians 215
Work on mathematical logic 218
7 Epilogue 233
Hilbert s lecture at the International Congress of Mathematics,
Paris 1900 238
Editor s notes 238
Hilbert s lecture 240
References to the lecture 283
Appendix 1: The Hilbert Problems 1900 99 287
Appendix 2: Logical matters 290
Glossary 294
General references 298
Index 3JO
|
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| spelling | Gray, Jeremy J. 1947- Verfasser (DE-588)122175549 aut The Hilbert challenge Jeremy J. Gray 1. publ. Oxford [u.a.] Oxford Univ. Press 2000 XII, 315 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Few problems in mathematics have had the status of those posed by David Hilbert in 1900. Mathematicians have made their reputations by solving some of them like Fermat's last theorem, but several remain unsolved including the Riemann Hypotheses, which has eluded all the great minds of this century. A hundred years later, this book takes a fresh look at the problems, the man who set them, and the reasons for their lasting impact on the mathematics of the twentieth century. In this book, the authors consider what makes this the pre-eminent collection of problems in mathematics, what they tell us about what drives mathematicians, and the nature of reputation, influence and power in the world of modern mathematics. Hilbert, David Hilbert, David <1862-1943> Hilbert, David <1862-1943> - Influence Hilbert, David, 1862-1943 -- Influence Hilbert, David, 1862-1943 Geschichte 1900-2000 Geschichte 1900-2000 gnd rswk-swf Hypothesen gtt Mathématiciens - Allemagne - Biographies Mathématiques - Philosophie - Histoire - 20e siècle Wiskunde gtt Geschichte Mathematik Philosophie Mathematics -- Philosophy -- History -- 20th century Mathematics -- History -- 20th century Mathematicians -- Germany -- Biography Hilbertsche Probleme (DE-588)4159859-3 gnd rswk-swf Deutschland (DE-588)4006804-3 Biografie gnd-content Hilbertsche Probleme (DE-588)4159859-3 s Geschichte 1900-2000 z DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009856048&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gray, Jeremy J. 1947- The Hilbert challenge Hilbert, David Hilbert, David <1862-1943> Hilbert, David <1862-1943> - Influence Hilbert, David, 1862-1943 -- Influence Hilbert, David, 1862-1943 Hypothesen gtt Mathématiciens - Allemagne - Biographies Mathématiques - Philosophie - Histoire - 20e siècle Wiskunde gtt Geschichte Mathematik Philosophie Mathematics -- Philosophy -- History -- 20th century Mathematics -- History -- 20th century Mathematicians -- Germany -- Biography Hilbertsche Probleme (DE-588)4159859-3 gnd |
| subject_GND | (DE-588)4159859-3 (DE-588)4006804-3 |
| title | The Hilbert challenge |
| title_auth | The Hilbert challenge |
| title_exact_search | The Hilbert challenge |
| title_full | The Hilbert challenge Jeremy J. Gray |
| title_fullStr | The Hilbert challenge Jeremy J. Gray |
| title_full_unstemmed | The Hilbert challenge Jeremy J. Gray |
| title_short | The Hilbert challenge |
| title_sort | the hilbert challenge |
| topic | Hilbert, David Hilbert, David <1862-1943> Hilbert, David <1862-1943> - Influence Hilbert, David, 1862-1943 -- Influence Hilbert, David, 1862-1943 Hypothesen gtt Mathématiciens - Allemagne - Biographies Mathématiques - Philosophie - Histoire - 20e siècle Wiskunde gtt Geschichte Mathematik Philosophie Mathematics -- Philosophy -- History -- 20th century Mathematics -- History -- 20th century Mathematicians -- Germany -- Biography Hilbertsche Probleme (DE-588)4159859-3 gnd |
| topic_facet | Hilbert, David Hilbert, David <1862-1943> Hilbert, David <1862-1943> - Influence Hilbert, David, 1862-1943 -- Influence Hilbert, David, 1862-1943 Hypothesen Mathématiciens - Allemagne - Biographies Mathématiques - Philosophie - Histoire - 20e siècle Wiskunde Geschichte Mathematik Philosophie Mathematics -- Philosophy -- History -- 20th century Mathematics -- History -- 20th century Mathematicians -- Germany -- Biography Hilbertsche Probleme Deutschland Biografie |
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