Dalen L.E.J. Brouwer - Topologist, Intuitionist, Philosopher

How Mathematics Is Rooted in Life
1. Auflage 2012
ISBN: 978-1-4471-4616-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 875 Seiten

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.

Autoren/Hrsg.

Dalen, Dirk Van

Inhaltsverzeichnis

1;L.E.J. Brouwer - Topologist, Intuitionist, Philosopher;3
1.1;Preface;6
1.2;Contents;8
2;Chapter 1: Child and Student;12
2.1;1.1 School Years;15
2.2;1.2 Student in Amsterdam;22
2.3;1.3 The Religious Credo;27
2.4;1.4 Friendship: Adama van Scheltema;31
3;Chapter 2: Mathematics and Mysticism;49
3.1;2.1 Teachers and Study;49
3.2;2.2 First Research, Four-Dimensional Geometry;54
3.3;2.3 Marriage;59
3.4;2.4 Bolland's Philosophy Course;64
3.5;2.5 Among the Artists and Vegetarians;67
3.6;2.6 The Delft Lectures;72
3.7;2.7 Family Life in Blaricum;84
4;Chapter 3: The Dissertation;87
4.1;3.1 Preparations and Hesitations;87
4.2;3.2 Under Korteweg's Supervision;93
4.3;3.3 On the Role of Logic;105
4.4;3.4 Mathematics and the World;109
4.5;3.5 Observations on Set Theory and Formalism;111
4.6;3.6 The Public Defence;125
5;Chapter 4: Cantor-Schoen?ies Topology;128
5.1;4.1 The Geometry of Continuous Change;128
5.2;4.2 Lie Groups;131
5.3;4.3 Publishing in the Mathematische Annalen;136
5.4;4.4 Fixed Points on Spheres and the Translation Theorem;139
5.5;4.5 Vector Fields on Surfaces;142
5.6;4.6 Analysis Situs and Schoen?ies;146
6;Chapter 5: The New Topology;158
6.1;5.1 Invariance of dimension;158
6.2;5.2 The Fixed Point Theorem and Other Surprises;178
6.3;5.3 The Karlsruhe Meeting and the Continuity Method;184
7;Chapter 6: Making a Career;202
7.1;6.1 Financial Worries;202
7.2;6.2 First International Contacts;208
7.3;6.3 Climbing the Ladder;209
7.4;6.4 The Shortcomings of Schoen?ies' Bericht;213
7.5;6.5 Privaat Docent;218
7.6;6.6 Korteweg's Campaign for Brouwer;223
7.7;6.7 Schoen?ies Again;234
8;Chapter 7: The War Years;239
8.1;7.1 Sets and Sequences-Law or Choice?;240
8.2;7.2 The International Academy for Philosophy;249
8.3;7.3 Family Life;256
8.4;7.4 An Offer from Leiden;258
8.5;7.5 Van Eeden and the International Academy;261
8.6;7.6 Faculty Politics;273
8.7;7.7 The Flemish Cause;277
8.8;7.8 Air Photography and National Defence;279
9;Chapter 8: Mathematics After the War;286
9.1;8.1 How to Appoint Professors;290
9.2;8.2 The Return to Topology;292
9.3;8.3 The Offers from Göttingen and Berlin;297
9.4;8.4 The Academy-How Denjoy Was Elected;301
9.5;8.5 Negotiations with Hermann Weyl;304
9.6;8.6 Intuitionism and the Begründungs-Papers;309
9.7;8.7 And Brouwer-That Is the Revolution;315
9.8;8.8 Intuitionism, the Nauheim Conference;323
9.9;8.9 The Failure of the Institute for Philosophy;327
10;Chapter 9: Politics and Mathematics;333
10.1;9.1 The Conseil and the Boycott of Germany;333
10.2;9.2 The Nauheim Conference and Intuitionism;339
10.3;9.3 The Denjoy Con?ict;342
10.4;9.4 Weitzenböck's Appointment in Amsterdam;355
10.5;9.5 Kohnstamm and the Philosophy of Science Curriculum;357
10.6;9.6 The New Chronicle;360
11;Chapter 10: The Breakthrough;363
11.1;10.1 The Signi?c Circle;363
11.2;10.2 Intuitionism-Principles for Choice Sequences;371
11.3;10.3 Intuitionism in the Mathematische Annalen;382
11.4;10.4 Beyond Brouwerian Counterexamples;388
11.5;10.5 Fraenkel's Role in Intuitionism;391
11.6;10.6 Heyting's First Contributions;397
12;Chapter 11: The Fathers of Dimension;401
12.1;11.1 The Two Russians;401
12.2;11.2 The De?nition of Dimension;404
12.3;11.3 The Viennese Connection;427
12.4;11.4 The Scienti?c Legacy of Urysohn;430
13;Chapter 12: Progress, Recognition, and Frictions;441
13.1;12.1 The First Skirmishes in the Foundational Con?ict;441
13.2;12.2 Consolidation and Entrenchment;453
13.3;12.3 The Riemann Volume;464
13.4;12.4 International Relations;469
13.5;12.5 The Dutch Topological School;474
14;Chapter 13: From Berlin to Vienna;497
14.1;13.1 More Intuitionism;497
14.2;13.2 Feelings of Crisis and German Science;499
14.3;13.3 The Berlin Lectures;503
14.4;13.4 The Vienna Lectures;520
14.5;13.5 Other Activities;528
15;Chapter 14: The Three Battles;532
15.1;14.1 The Grundlagenstreit;532
15.2;14.2 The Bologna Conference;546
15.3;14.3 The War of the Frogs and the Mice;557
15.4;14.4 The Endings of the Grundlagenstreit;593
15.5;14.5 The Menger Con?ict;600
16;Chapter 15: The Thirties;607
16.1;15.1 Freudenthal Arrives;608
16.2;15.2 Intuitionistic Logic;611
16.3;15.3 The Sodalitas Affair;612
16.4;15.4 Göttingen Under the Nazi's;623
16.5;15.5 Bieberbach's Conversion;626
16.6;15.6 Compositio Mathematica;634
16.7;15.7 Göttingen Reconsidered?;640
16.8;15.8 Dutch Affairs;645
17;Chapter 16: War and Occupation;667
17.1;16.1 Occupied Holland;667
17.2;16.2 Weitzenböck's Choice;670
17.3;16.3 Freudenthal Dismissed;671
17.4;16.4 University-Resistance or Survival;675
17.5;16.5 Freudenthal's Fortunes;679
17.6;16.6 The Declaration of Loyalty;687
17.7;16.7 The Brouwer Family in Wartime;698
17.8;16.8 Weitzenböck in Uniform;702
18;Chapter 17: Postwar Events;705
18.1;17.1 Purging the University;705
18.2;17.2 Faculty Politics;727
18.3;17.3 Back to Research;741
18.4;17.4 The Loss of Compositio Mathematica;760
18.5;17.5 Rearguard Actions;771
19;Chapter 18: The Restless Emeritus;786
19.1;18.1 The Traveller;786
19.2;18.2 The Pharmacy;812
19.3;18.3 The Last Years;820
19.4;18.4 Epilogue;830
20;References;836
21;Index;853