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L. E. J. Brouwer

L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer.jpeg
Born Luitzen Egbertus Jan Brouwer
(1881-02-27)27 February 1881
Overschie
Died 2 December 1966(1966-12-02) (aged 85)
Blaricum
Nationality Dutch
Fields Mathematics
Institutions University of Amsterdam
Alma mater University of Amsterdam
Doctoral advisor Diederik Korteweg
Doctoral students Maurits Belinfante
Johanna Geldof
Bernardus Haalmeijer
Arend Heyting
Frans Loonstra
Barend Loor
Wilfrid Wilson
Known for Brouwer–Hilbert controversy
Phragmen–Brouwer theorem
Brouwer fixed-point theorem
Proving Hairy ball theorem
Influences Immanuel Kant
Arthur Schopenhauer
Influenced Hermann Weyl
Michael Dummett
Notable awards Foreign Member of the Royal Society

Luitzen Egbertus Jan Brouwer ForMemRS (/ˈbrər/; Dutch: [ˈlœy̯tsə(n) ɛɣˈbɛrtəs jɑn ˈbrʌu̯ər]; 27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis. He was the founder of the mathematical philosophy of intuitionism.

Early in his career, Brouwer proved a number of theorems that were in the emerging field of topology. The main results were his fixed point theorem, the topological invariance of degree, and the topological invariance of dimension. The most popular of the three among mathematicians is the first one called the Brouwer Fixed Point Theorem. It is a simple corollary to the second, about the topological invariance of degree, and this one is the most popular among algebraic topologists. The third is perhaps the hardest.

Brouwer also proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, of the treatment of general continuous mappings. In 1912, at age 31, he was elected a member of the Royal Netherlands Academy of Arts and Sciences.


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