L E J Brouwer founded the doctrine of mathematical intuitionism, which views mathematics as the formulation of mental constructions that are governed by self-evident laws.Brouwer was an unsalaried lecturer at the University of Amsterdam (), and was professor of set theory, function theory and axiomatics there from to Hilbert wrote a warm letter of recommendation which helped Brouwer to the chair. However in Hilbert offered Brouwer a chair in Göttingen which he turned down.
Brouwer was a major contributor to the theory of topology and was considered by many to be its founder. He did almost all his work in topology between and He discovered characterisations of topological mappings of the Cartesian plane and a number of fixed point theorems.
Brouwer's doctrine differed substantially from the formalism of David Hilbert and the logicism of Bertrand Russell. His doctoral thesis in on the foundations of mathematics attacked the logical foundations of mathematics and form the beginning of the Intuitionist School.
He rejected in mathematical proofs the Principle of the Excluded Middle, which states that any mathematical statement is either true or false. In he published
Brouwer's Intuitionism, Volume 2 (Studies in the History and Philosophy of Mathematics) [1 ed.] ,
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STUDIES IN THE HISTORY AND PHILOSOPHY OF MATHEMATICS
Volume 2
NORTH-HOLLAND AMSTERDAM
- NEW YORK
- OXFORD
- TOKYO
BROUWER’S INTUITIONISM
Walter P. van Stigt Wolfson College, Oxford, UK
NORTH-HOLLAND AMSTERDAM
- NEW
YORK
- OXFORD
- TOKYO
ELSEVIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box AE Amsterdam, The Netherlands Sole Distributors for the USA and Canada:
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ISBN 0 3
Library of Congress Cataloging-in-Publication Data Stigt, Walter P. van, Brouwer's intuitionism / Walter P. van Stigt. p. cm. Includes bibliographical references (p. ) and index. ISBN 1, Brouwer, L. E. J. (Luitzen Egbertus Jan), 2. Mathemattcians--Nether lands--Biography. 3. Mathematics-Phi losophy. I. Title. QABS75 ° dc20
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La historia de la civilización la escriben aquellos hombres y mujeres quea lo largo de los siglos, gracias a sus obras, sus pensamientos, sus creaciones o su talento; han hecho queel mundo, de una forma u otra,avance.
Comprender las luces y las sombras de las personas destacadas como Luitzen Egbertus Brouwer, personas que hacen rodar y cambiar al mundo, es algo básica para que podamos poner en valor no sólo la existencia de Luitzen Egbertus Brouwer, sino la de todos aquellos y aquellas que fueron inspiradas por Luitzen Egbertus Brouwer, personas a quienes de de una u otra forma Luitzen Egbertus Brouwer influyó, y sin duda, conocer y descifrar cómo fue el hecho de vivir en el periodo histórico y la sociedad en la que vivió Luitzen Egbertus Brouwer.
Las biografías y las vidas de personas que, como Luitzen Egbertus Brouwer, atraen nuestra atención, deben valernos siempre como punto de referencia y reflexión para ofrendar un marco y un contexto a otra sociedad y otra época de la historia que no son las nuestras. Hacer un esfuerzo por comprender la biografía de Luitzen Egbertus Brouwer, el motivo por qué Luitzen Egbertus Brouwer vivió de la forma en que lo hizo y ac
Luitzen Egbertus Jan Brouwer
1. The Person
Brouwer studied at the (municipal) University of Amsterdam where his most important teachers were Diederik Korteweg and Gerrit Mannoury.
Korteweg (–) was professor of mathematics, mechanics and astronomy at the University of Amsterdam from –; the last five years as extraordinarius, so as to make place for Brouwer. Around , Korteweg was the most important and influential mathematician in the Netherlands, and he contributed much to the internationalisation of Dutch mathematics. A mathematical physicist trained by van der Waals, he had a particular interest in mechanics and thermodynamics. Among his many results, the best-known is probably the Korteweg-de Vries equation, describing the behaviour of waves in a shallow channel. Korteweg also had a strong historical interest, and was chief editor of vols. XI–XV of Christiaan Huygens’ collected works (–). Part of the correspondence with his PhD student Brouwer concerned the unification of physical theories (see van Stigt, , pp. –).
Mannoury (–) was a philosopher, mathematician, psychoanalyst, accountant, and political activist (Kirkels, ). La
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