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Mathematics After the War

In: L.E.J. Brouwer – Topologist, Intuitionist, Philosopher

Author

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  • Dirk van Dalen

    (Utrecht University, Department of Philosophy)

Abstract

The post war years brought Brouwer back to topology and to intuitionism. Mostly ‘unfinished business’; mathematicians were catching up with Brouwer’s innovations, hence an exchange of ideas and problems. As the topology editor for the Mathematische Annalen Brouwer also got more papers to handle (e.g. Nielsen and Kerékjártó). Most of Brouwer’s efforts, however, went into his intuitionism; from 1918 on he published substantial papers to put the subject on a firm footing. The first paper in the series introduced choice sequences and a constructive, but not finitistic, notion of set, now known as spread; furthermore the continuity principle—which was immediately applied to prove that the set of all number theoretic functions is not denumerable. Brouwer got offers from Göttingen and Berlin, he remained however in Amsterdam on favorable conditions. One of those was that he could offer a position to Hermann Weyl, who in turn used the offer to improve his conditions in Zürich. The first international conference Brouwer attended after the war was the one in Nauheim, where he gave his first talk on intuitionistic mathematics, ‘Does every real number have a decimal expansion?’.

Suggested Citation

  • Dirk van Dalen, 2013. "Mathematics After the War," Springer Books, in: L.E.J. Brouwer – Topologist, Intuitionist, Philosopher, edition 127, chapter 0, pages 279-325, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4471-4616-2_8
    DOI: 10.1007/978-1-4471-4616-2_8
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