As you already know, a brand new biography on Brouwer has just seen the
light through the eyes and pen of Professor Dirk van Dalen. To my request
he has kindly listed below the chapter titles, and has added a small
resume of the contents. Below I append his message for the benefit of
all interested readers.
Regards to all,
Julio Gonzalez Cabillon
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Author: Dirk van Dalen, Utrecht University
Title: Mystic, Geometer, and Intuitionist: The Life of L.E.J. Brouwer
Volume 1 (1999) The Dawning Revolution. 448 pages.
Publisher: Oxford University Press
ISBN: 0-19-850297-4
Contents:
1. Child and Student
2. Mathematics and Mysticism
3. The Dissertation
4. Cantor-Schoenflies Topology
5. The New Topology
6. Making a Career
7. The War Years
8. Mathematics After the War
9. Politics and Mathematics
10. The Breakthrough
11. Bibliography of Brouwer's Writings
Contents of Volume 2
References
Index
L.E.J. Brouwer 1881 - 1966.
The biography deals with Brouwer's life up to and including his great
intuitionistic results, culminating in the famous theorem: all real
functions on [0,1] are uniformly continuous.
Brouwer's youth and student years are reported in some detail. The mystic
period and the intense activity of preparing the dissertation are covered
in detail. Indeed the germs of his later philosophy can be traced back to
his mystic views. The dissertation held the "first intuitionistic
program", in addition to work on Lie groups and geometry.
The topological work in the first period (1909-1913) is split into two
parts: the first part deals with 'elementary point-set topology' in the
style of Cantor and Schoenflies. Results from this part are, among others,
the fixed point theorem for a sphere, the theory of vectorfields on
spheres, indecomposable continua, the translation theorem. After 1909
the second period starts, the one based on simplicial approximation, the
mapping degree, etc. The best known results from that period are Brouwer's
fixed point theorem for n-dimensional balls and the invariance of
dimension-theorem, the invariance of domain-theorem. A by-product from
that period is the proof of the Continuity Method of Felix Klein. His
work brought him into unpleasant clashes with Lebesgue and Koebe.
The period closed with a general definition of dimension, including the
proof of the pudding: Rn has dimension n.
After this topological period the First World War interrupted Brouwer's
international contacts. During that period he returned to foundational
research, he also joined a psycho-linguistic philosophy project, the
Signific Circle.
In 1918 Brouwer returned to topology, while at the same time vigorously
developing intuitionism. His novel introduction of 'choice sequences'
revolutionized his mathematics and opened up the second and final
intuitionistic program. Hermann Weyl's contributions to intuitionism are
also discussed.
The life and actions of Brouwer form an integral part of the book. This
includes description of the artist communities Laren and Blaricum, where he
lived. Science affairs and international contacts (e.g. with Goettingen)
are given their proper place.
Prof. Dr. D. van Dalen
Department of Philosophy
P.O. Box 80.126
3508 TC Utrecht The Netherlands
tel. 030-2531834, fax 030-2532816
030-6663857(home)
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