L. E. J. Brouwer
| L. E. J. Brouwer | |
|---|---|
 |
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| Born | Luitzen Egbertus Jan Brouwer 27 February 1881 Overschie |
| Died | 2 December 1966 (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 (/ˈbraʊər/; 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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