L.E.J. Brouwer – Topologist, Intuitionist, Philosopher (eBook)

How Mathematics Is Rooted in Life

Dirk Van Dalen (Autor)

eBook Download: PDF

2012 | 2013
XII, 875 Seiten
Springer London (Verlag)
978-1-4471-4616-2 (ISBN)

Infos

Dirk van Dalen's biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer's main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name 'intuitionism'. This made him one of the main protagonists in the 'foundation crisis' of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

Inhalt

L.E.J. Brouwer - Topologist, Intuitionist, Philosopher 3
Preface 6
Contents 8
Chapter 1: Child and Student 12
1.1 School Years 15
1.2 Student in Amsterdam 22
1.3 The Religious Credo 27
1.4 Friendship: Adama van Scheltema 31
Chapter 2: Mathematics and Mysticism 49
2.1 Teachers and Study 49
2.2 First Research, Four-Dimensional Geometry 54
2.3 Marriage 59
2.4 Bolland's Philosophy Course 64
2.5 Among the Artists and Vegetarians 67
2.6 The Delft Lectures 72
2.7 Family Life in Blaricum 84
Chapter 3: The Dissertation 87
3.1 Preparations and Hesitations 87
3.2 Under Korteweg's Supervision 93
3.3 On the Role of Logic 105
3.4 Mathematics and the World 109
3.5 Observations on Set Theory and Formalism 111
3.6 The Public Defence 125
Chapter 4: Cantor-Schoen?ies Topology 128
4.1 The Geometry of Continuous Change 128
4.2 Lie Groups 131
4.3 Publishing in the Mathematische Annalen 136
4.4 Fixed Points on Spheres and the Translation Theorem 139
4.5 Vector Fields on Surfaces 142
4.6 Analysis Situs and Schoen?ies 146
Chapter 5: The New Topology 158
5.1 Invariance of dimension 158
5.2 The Fixed Point Theorem and Other Surprises 178
5.3 The Karlsruhe Meeting and the Continuity Method 184
Chapter 6: Making a Career 202
6.1 Financial Worries 202
6.2 First International Contacts 208
6.3 Climbing the Ladder 209
6.4 The Shortcomings of Schoen?ies' Bericht 213
6.5 Privaat Docent 218
6.6 Korteweg's Campaign for Brouwer 223
6.7 Schoen?ies Again 234
Chapter 7: The War Years 239
7.1 Sets and Sequences-Law or Choice? 240
7.2 The International Academy for Philosophy 249
7.3 Family Life 256
7.4 An Offer from Leiden 258
7.5 Van Eeden and the International Academy 261
7.6 Faculty Politics 273
7.7 The Flemish Cause 277
7.8 Air Photography and National Defence 279
Chapter 8: Mathematics After the War 286
8.1 How to Appoint Professors 290
8.2 The Return to Topology 292
8.3 The Offers from Göttingen and Berlin 297
8.4 The Academy-How Denjoy Was Elected 301
8.5 Negotiations with Hermann Weyl 304
8.6 Intuitionism and the Begründungs-Papers 309
8.7 And Brouwer-That Is the Revolution 315
8.8 Intuitionism, the Nauheim Conference 323
8.9 The Failure of the Institute for Philosophy 327
Chapter 9: Politics and Mathematics 333
9.1 The Conseil and the Boycott of Germany 333
9.2 The Nauheim Conference and Intuitionism 339
9.3 The Denjoy Con?ict 342
9.4 Weitzenböck's Appointment in Amsterdam 355
9.5 Kohnstamm and the Philosophy of Science Curriculum 357
9.6 The New Chronicle 360
Chapter 10: The Breakthrough 363
10.1 The Signi?c Circle 363
10.2 Intuitionism-Principles for Choice Sequences 371
10.3 Intuitionism in the Mathematische Annalen 382
10.4 Beyond Brouwerian Counterexamples 388
10.5 Fraenkel's Role in Intuitionism 391
10.6 Heyting's First Contributions 397
Chapter 11: The Fathers of Dimension 401
11.1 The Two Russians 401
11.2 The De?nition of Dimension 404
11.3 The Viennese Connection 427
11.4 The Scienti?c Legacy of Urysohn 430
Chapter 12: Progress, Recognition, and Frictions 441
12.1 The First Skirmishes in the Foundational Con?ict 441
12.2 Consolidation and Entrenchment 453
12.3 The Riemann Volume 464
12.4 International Relations 469
12.5 The Dutch Topological School 474
Chapter 13: From Berlin to Vienna 497
13.1 More Intuitionism 497
13.2 Feelings of Crisis and German Science 499
13.3 The Berlin Lectures 503
13.4 The Vienna Lectures 520
13.5 Other Activities 528
Chapter 14: The Three Battles 532
14.1 The Grundlagenstreit 532
14.2 The Bologna Conference 546
14.3 The War of the Frogs and the Mice 557
14.4 The Endings of the Grundlagenstreit 593
14.5 The Menger Con?ict 600
Chapter 15: The Thirties 607
15.1 Freudenthal Arrives 608
15.2 Intuitionistic Logic 611
15.3 The Sodalitas Affair 612
15.4 Göttingen Under the Nazi's 623
15.5 Bieberbach's Conversion 626
15.6 Compositio Mathematica 634
15.7 Göttingen Reconsidered? 640
15.8 Dutch Affairs 645
Chapter 16: War and Occupation 667
16.1 Occupied Holland 667
16.2 Weitzenböck's Choice 670
16.3 Freudenthal Dismissed 671
16.4 University-Resistance or Survival 675
16.5 Freudenthal's Fortunes 679
16.6 The Declaration of Loyalty 687
16.7 The Brouwer Family in Wartime 698
16.8 Weitzenböck in Uniform 702
Chapter 17: Postwar Events 705
17.1 Purging the University 705
17.2 Faculty Politics 727
17.3 Back to Research 741
17.4 The Loss of Compositio Mathematica 760
17.5 Rearguard Actions 771
Chapter 18: The Restless Emeritus 786
18.1 The Traveller 786
18.2 The Pharmacy 812
18.3 The Last Years 820
18.4 Epilogue 830
References 836
Index 853

Produkt-Details

• Erscheint lt. Verlag: 4.12.2012
• Zusatzinfo: XII, 875 p.
• Verlagsort: London
• Sprache: englisch
• Themenwelt: Sachbuch/Ratgeber ► Natur / Technik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Naturwissenschaften ► Biologie
• Themenwelt: Sozialwissenschaften
• Themenwelt: Technik
• Schlagworte: Biography • Brouwer • Grundlagenstreit • History of Mathematics • Intuitionism • Topology
• ISBN-10: 1-4471-4616-6 / 1447146166
• ISBN-13: 978-1-4471-4616-2 / 9781447146162