Mystic, Geometer, and Intuitionist The Life of L. E. J. Brouwer Volume 1: The Dawning Revolution

by Van Dalen, Dirk

• ISBN13: 9780198502975
• ISBN10: 0198502974
• Format: Hardcover
• Copyright: 1999-04-15
• Publisher: Oxford University Press

Summary

Luitzen Egbertus Jan Brouwer is a remarkable figure, both in the development of mathematics and in wider Dutch history. A mathematical genius with strong mystical and philosophical leanings, he advocated the intuitionist view of mathematics and science as a constructive mental activity. Thisdrew him into a discussion with David Hilbert, the leading advocate of the formalist school, about the nature of mathematics, a debate which made Brouwer a legend during his lifetime. He also contributed significantly to research in topology, and was a member of the socio- linguistic SignificCircle. As well as his diverse mathematical interests he had a great impact in wider Dutch society. His keen sense of justice made him a party in many conflicts, both scientific and political. He would often be involved in controversial issues, such as the campaign to undo the boycott of Germanscientists, and this made him a figure both of admiration and embarrassment in his native Holland. Although his abilities won him offers from prestigious universities such as Berlin and Gottingen, he preferred to stay in Amsterdam, so that he could pursue a life of quiet unconventionality in theartist community at Laren. This book provides a sophisticated analysis of this crucial era of mathematical research, but also gives an important insight into the wider life of one of the most fascinating characters involved. This book is available at the specially discounted price of L49.95 tocustomers in the Netherlands.

Table of Contents

Child and Student	1	(40)
School years	4	(8)
Student in Amsterdam	12	(5)
The religious credo	17	(5)
Friendship: Adama van Scheltema	22	(19)
Mathematics and Mysticism	41	(39)
Teachers and study	41	(5)
First research, four-dimensional geometry	46	(6)
Marriage	52	(4)
Bolland's philosophy course	56	(3)
Among the artists and vegetarians	59	(5)
The Delft lectures	64	(13)
Family life in Blaricum	77	(3)
The Dissertation	80	(42)
Preparations and hesitations	80	(7)
Under Korteweg's supervision	87	(12)
On the role of logic	99	(3)
Mathematics and the world	102	(3)
Observations on set theory and formalism	105	(13)
The public defense	118	(4)
Cantor-Schoenflies Topology	122	(29)
The geometry of continuous change	122	(4)
Lie groups	126	(4)
Publishing in the Mathematische Annalen	130	(3)
Fixed points on spheres and the translation theorem	133	(3)
Vector fields on surfaces	136	(4)
Analysis situs and Schoenflies	140	(11)
The new Topology	151	(46)
Invariance of dimension	151	(21)
The fixed point theorem and other surprises	172	(6)
The Karlsruhe meeting and the Continuity Method	178	(19)
Making a Career	197	(37)
Financial worries	197	(6)
First international contacts	203	(2)
Climbing the ladder	205	(3)
The shortcomings of Schoenflies' Bericht	208	(5)
Privaat Docent	213	(5)
Korteweg's campaign for Brouwer	218	(11)
Schoenflies again	229	(5)
The War years	234	(50)
Sets and sequences---law or choice?	235	(8)
The International Academy for Philosophy	243	(7)
Family life	250	(2)
An offer from Leiden	252	(3)
Significs and Jacob Israel de Haan	255	(3)
Van Eeden and the International Academy	258	(12)
Faculty politics	270	(5)
The Flemish cause	275	(1)
Air photography and National Defense	276	(8)
Mathematics after the War	284	(52)
How to appoint professors	288	(2)
The return to topology	290	(5)
Brouwer, Schouten and the Mathematische Annalen	295	(5)
The offers from Gottingen and Berlin	300	(4)
The Academy-how Denjoy was elected	304	(2)
Negotiations with Hermann Weyl	306	(6)
Intuitionism and the Begrundungs papers	312	(5)
And Brouwer---that is the revolution	317	(8)
Intuitionism, the Nauheim Conference	325	(5)
The failure of the Institute for Philosophy	330	(6)
Politics and Mathematics	336	(31)
The Conseil and the boycott of Germany	336	(5)
The Nauheim conference and Intuitionism	341	(3)
The Denjoy conflict	344	(14)
Weitzenbock's appointment in Amsterdam	358	(3)
Kohnstamm and the Philosophy of Science curriculum	361	(3)
The New Chronicle	364	(3)
The Breakthrough	367	(38)
The Signific Circle	367	(8)
Intuitionism---principles for choice sequences	375	(12)
Intuitionism in the Mathematische Annalen	387	(5)
Beyond Brouwerian counterexamples	392	(3)
Fraenkel's role in intuitionism	395	(6)
Heyting's first contributions	401	(4)
Bibliography of Brouwer's writings	405	(13)
Contents of Volume 2	418	(1)
References	419	(7)
Index	426