The second decennium opened with Brouwer’s spectacular breakthrough in topology. In quick succession he wrote a number of epoch-making papers. The first of these settled an old conjecture of Cantor: the invariance of dimension. It led to a large number of letters concerning an alleged but faulty proof of Lebesgue. Although Lebesgue did not claim priority in his “letter to the editor” (Blumenthal), Lebesgue’s claim and communication was sufficiently patronizing to annoy Brouwer. In 1912 Brouwer applied his teorem of invariance of domain to salvage Klein’s continuity method for proving uniformization. This led to some unpleasant correspondence with Paul Koebe, who strongly disapproved of Brouwer’s excursion into, what he considered, his territory. Somewhat later Brouwer joined Schoenflies in the editing of the famous Bericht. This generated a rather ‘frank’ exchange between them, with regular clashes. Both men appealed to Hilbert.

The war had isolated Brouwer from Göttingen. Perhaps this was the reason for his return to the foundations of mathematics. This topic, being less central in the mathematical community, hardly yielded any correspondence. The flow of letters recommenced after the war; the topics were of a mixed nature: topological (partly connected with his editorial work for the Mathematishe Annalen), significs (The Dutch group addressing philosophical, psycho-linguistic issues), politics (concerning the post-war international research council and the boycott of German scientists).


Riemann Surface Fundamental Domain Closed Manifold Canonical System Automorphic Function 
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© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Dirk van Dalen
    • 1
  1. 1.Utrecht UniversityUtrechtThe Netherlands

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