Dutch mathematician and philosopher whose chief interests were twofold. One was a philosophical standpoint about mathematics in which he permitted only methods of reasoning that led, by direct construction, from step to step. He called this view “intuitionism,” and it was essentially pure right-brain assimilation. The second interest lay in topology, where he not only proved various important theorems, but also exposed the naivety of the ordinary conception of dimension.
“Bertus” Brouwer, the eldest son of a school teacher, was an exceptionally bright child. At age 9 (expected 12) he left the elementary school to study at the HBS (1890-95), followed by Gymnasium A and B (1897). At age 16 (expected age 18) he studied Mathematics at the University of Amsterdam (UvA). He graduated June 1904. He dissertated “cum laude” under Diederik Johannes Korteweg 19 February 1907 (at 3 PM) in Amsterdam. His doctoral thesis with the title “Over de Grondslagen der Wiskunde (About the foundations of mathematics) dealt with major philosophical questions:
Are time and 3-dimensional space given to us “a priori” as Kant believed? No, said Brouwer, only time is beforehand given to us. But we can think of many more dimensions than our eyes can see. He earlier had described the mathematics of rotation in four dimensions.
The intuitive logician Brouwer also opposed to the views of the logistic Bertrand Russell and the formalist David Hilbert. According to the by Plato influenced Brouwer Mathematical acts of reason were original spiritual acts of human creations. They spontaneously arose by intuition from the invisible depths within us. He also distanced from the formal axiomatic method (Wiki definition): “The axiomatic method involves replacing a coherent body of propositions (i.e. a mathematical theory) by a simpler collection of propositions (i.e. axioms). According to Brouwer this would lead us nowhere, as would later proof the genial mathematician Kurt Gödel in his famous “The Incompleteness Theorem” (1931). In the fifties the retired Brouwer visited Gödel at Princeton.
Brouwer wrestled with the dual logical sentence: “something is true or not true”, a formal statement. In his dissertation he acknowledged the logical impossibility of an existing third possibility (tertium non datur): But later in live, when he realised that “intuition” is also a source of knowledge, he realised that there also can be an not so logical (formally seen) third solution. Nor this, nor the opposing that, but maybe an both integrating third child, could be the right way to go.
On 12 October 1909 he became private lecturer at the UvA with the lecture “Het wezen der meetkunde”. Between 1909 and 1913 he was very productive and laid the foundations of modern topology. Some contributions were the topological invariance of dimension, the Fixpoint Theorem (Every continuous map of an n-dimensional ball to itself has a fixed point) and the first correct definition of dimension. On 19 June 1912 he was appointed as private professor of mathematics in Amsterdam (UvA) and held the inaugural speeech “Intuitionisme en formalisme” 14 October 1912. On 23 July 1913 he succeeded Korteweg as professor of mathematics.
In the twenties Brouwer took a sharp position in the “Grundlagenstreit” in the leading German scientific paper “Mathematische Annalen” between formalists like Hermann Weyl and David Hilbert and intuitionists like Einstein and Brouwer. Hibert’s formalism was fiercely defended by Hermann Weyl, who in 1928 managed to set Brouwer out of the editorial board of of the Annalen, despite of protests of Albert Einstein. Brouwer was very upset by it and never reached his former creativity.
Brouwer published his scientific work only in German and Dutch, so his influence in the English and French speaking world was low. He set early up good relations with Hilbert in Göttingen, and held lectures in Wien (1928), that were attended by Kurt Gödel and Ludwig Wittgenstein. He received an honorary doctorate in Oslo (April 1929). After he ended his career at the UvA (17 Sept 1951), he held lectures in South Africa and the U.S.
His translated writings were published in two volumes of Collected works: “Philosophy and foundations of mathematics” (1975) and “Geometry, analysis, topology and mechanic” (1976).
Brouwer died on 2 December 1966 in Blaricum. He was struck by a vehicle while crossing the road in front of his house. During his funeral in private circles master chess player and friend Max Euwe held the memorial speech. The computer scientist Max Euwe wrote in 1929 “Mengentheoretische Betrachtungen über das Schachspiel” based on the ideas of Brouwer.
Personal
On 31 Augustus 1904 Brouwer married the divorced Lize the Holl (5 Augustus 1870, Epe – 11 October 1959, Naarden), who had a daughter Louise Peijpers (26 March 1893, Nieuwer-Amstel – 18 April 1988, Amsterdam). His stepdaughter was 11 years younger than him and his wife was almost 10 years elder than him. They moved to a small house at the Torenlaan in Blaricum designed by his friend the architect Ru Mauve (a son of Anton Mauve). This “Hut” became his home/castle till his dead. Lize studied Pharmaceutics in Amsterdam (1900-) and became a pharmacist in Nieuwer-Amstel. Bertus did the bookkeeping.
Bertus Brouwer was pragmatic in social affairs. During the German occupation he advised his students to sign the hated “Loyaliteitsverklaring” to Nazi Germany, with the motivation that in this way the Nazi’s would not keep an eye on you when you actually did exactly the reverse (Matthew 22:15-22). But after the war his wise advice was misunderstood by rational thinking (or or) formalists and he was denied the teaching of logics and mathematics at the University for some months. Brouwer, who unlike his “better thinking Judges” actually helped Jews during wartime, risking his own life, was very offended by this one-dimensional thinking and considered to emigrate away from his narrow minded country.
He ended his Life, Art, and Mysticism essay with:
99/18/9
No, the world can never be reformed so as to bring good to man. Social conditions will remain wretched and life for every individual will remain a misery, only aggravated by hope for advancement and a better future. Only complete surrender and total resignation would end this misery.
Look at this world, full of wretched people who imagine that they have possessions, worried that they might lose them and ever toiling in the hope of acquiring more. Look at all these people, striving after luxury and wealth, those whose riches are secured, whose stocks and shares are safely deposited and who now nurture an insatiable appetite for knowledge, power, health, glory, and pleasure.
Only he who recognizes that he has nothing, that he cannot possess anything,that security is unattainable, only he who completely resigns himself and sacrifices all, who gives everything, who does not know anything, who does not want anything and does not want to know anything, who abandons and neglects all, he will receive all: the world of freedom is opened to him, the world of painless contemplation and of nothing.

Link to Wikipedia biography