# L.E.J. Brouwer (1881-1966):

Perspectives On His Life and Work

**Time and Venue**:

24 May 2018, 9:30 am - 6 pm

Johannes Gutenberg University Mainz, Institute of Mathematics

Hilbertraum (05-432), Staudinger Weg 9, 55099 Mainz

**Morning Session: Two Lectures on Brouwer’s Life and Thought**

**9.30-10.30, 11.00-12.00**

Dirk van Dalen, **L.E.J. Brouwer, Mathematical** **Genius and indomitable** **Defender of Justice**

Dirk van Dalen,

In the course of two lectures I will offer a sketch of Brouwer’s extraordinary life in mathematics, a career filled with controversies, stunning triumphs along with setbacks and defeats. From the outset of his career, Brouwer saw himself as a philosopher, and his views were both mystical and pessimistic. His mentor in Amsterdam, D.J. Korteweg, had no patience with such speculations, so he told Brouwer to remove them from his dissertation. Out of these early ideas, however, grew a mature philosophy of mathematics, Brouwerian intuitionism, though this would only take full form in the 1920s. During the period leading up to WWI, Brouwer revolutionized the emerging field of point-set topology, first by making rigorous what others had done before, and then by introducing entirely new methods. By 1920 Brouwer was widely viewed as the leading mathematician of his generation, yet he turned down chairs in both Göttingen and Berlin in order to cultivate his own special mathematical milieu in Amsterdam-Laren-Blaricum. His visitors in Blaricum included Hermann Weyl, who was deeply attracted to Brouwer’s personality as well as his foundational views, as were many others afterward.

Weyl’s essay on the Grundlagenkrise from 1921 marks the beginning of the dramatic conflict between Brouwer and Hilbert. Brouwer had made no secret about his opposition to Hilbert’s formalist methods, which made unlimited free use of the principle of the excluded middle. Still, Hilbert simply ignored Brouwer’s critique, though he could hardly afford to do that any longer once Weyl took up the intuitionist cause. These tensions mixed together with political differences led to much bitterness by the mid-1920s. Brouwer also opposed German participation at the Bologna ICM in 1928, which Hilbert attended as head of a large delegation. Afterward, he unilaterally decided to terminate Brouwer’s position as associate editor of *Mathematische Annalen*, a decision that had devastating consequences both for the journal and for Brouwer. Although Brouwer eventually founded a new international journal, *Compositio Mathematica*, in 1934, he clearly felt betrayed by those who had supported Hilbert’s actions. After 1928, he gradually withdrew from the world of mathematics. For a variety of reasons, Brouwer was widely viewed as not sufficiently critical of the Nazis, despite the fact that he had hidden members of the resistance and Jews on his estate during the occupation of Holland. In tracing the arc of his life, one can readily see that Brouwer consistently advocated a view of mathematics as a special kind of human activity. This was the larger view that animated his mathematical work. He was a radical thinker who fought for his ideas, just as he passionately supported all kinds of other causes that he felt were both just and worthy of being defended.

**Afternoon Session: Three Lectures on Special Aspects of Brouwer’s Career**

**14.00-15.00**

Jan van Mill, Brouwer’s Contributions to Topology

Jan van Mill, Brouwer’s Contributions to Topology

Brouwer brought about several revolutions. One of them was in topology. His most well-known result in that area is probably his widely used fixed-point theorem. The easiest proof of it is due to Sperner and is of a combinatorial nature. The fixed-point theorem is also a consequence of Brouwer’s result on the topological invariance of degree. Brouwer was also the founder of dimension theory. The dimension of a topological space measures its topological complexity. In this lecture we will briefly discuss these fundamental results. In the early days of dimension theory there was a lot of confusion. We will try to elucidate the causes of the confusion, which still persist today.

**15.30-16.30**

Teun Koetsier, Wittgenstein and Brouwer’s 1928 Lecture in Vienna: The Spirit of Schopenhauer

Teun Koetsier, Wittgenstein and Brouwer’s 1928 Lecture in Vienna: The Spirit of Schopenhauer

On March 10, 1928, the mathematician L.E.J. Brouwer lectured in Vienna. The title of his lecture on the philosophical background of his views on the foundations of mathematics was *Mathematik, Wissenschaft und Sprache*. Herbert Feigl wrote later that he managed after much resistance to coax Ludwig Wittgenstein to attend the lecture. Wittgenstein came and something remarkable happened. After the lecture, Feigl and Friedrich Waismann spent several hours with Wittgenstein in a café and Feigl wrote later: *“a great event took place. Suddenly and very volubly Wittgenstein began talking philosophy – at great length. Perhaps this was the turning point, for ever since that time, 1929, when he moved to Cambridge University, Wittgenstein was a philosopher again, and began to exert a tremendous influence”. *In my talk I will speculate about what Wittgenstein heard and how it affected him on that particular Saturday in 1928.

**17.00-18.00**

David Rowe, Brouwer’s Career as Author and Editor for *Mathematische Annalen*, 1910-1928

David Rowe, Brouwer’s Career as Author and Editor for

*Mathematische Annalen*, 1910-1928

Soon after he first met Hilbert in 1909, Brouwer began publishing his monumental papers on topology in the Göttingen-dominated journal *Mathematische Annalen. *Its managing editor was Hilbert’s first doctoral student, Otto Blumenthal, who oversaw most of Brouwer’s work during the period 1911-1914. At the end of that period, Blumenthal strongly supported Brouwer’s appointment, along with Constantin Carathéodory, as associate editors to the board. In 1920 Brouwer became part of a much larger board of associate editors when the Annalen was taken over by the Berlin publisher Julius Springer. After Felix Klein stepped aside in 1924, he was replaced by Carathéodory as one of the four principal editors, alongside Hilbert, Blumenthal, and Einstein. The latter three were Francophiles, unlike Brouwer, who was one of the journal’s twelve associate editors, though by far the most active and prominent among them. In his biography of Brouwer, Dirk van Dalen has described the tensions that arose during the mid-1920s and various events that eventually culminated in Brouwer’s dismissal from the board in 1928. In this talk, I will focus on Brouwer’s longstanding relationship with Blumenthal, who fell out of sympathy with Brouwer and ultimately helped to carry out Hilbert’s execution order against him.

Organized by David E. Rowe, Tilman Sauer and Duco van Straten

Funded by Deutsche Forschungsgemeinschaft (SFB, TR45)