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Luitzen Egbertus Jan Brouwer, usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, a graduate of the University of Amsterdam, 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 breakthroughs in the emerging field of topology. The most celebrated result was his proof of the topological invariance of dimension. Among his further results, the Brouwer fixed point theorem is also well known. 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.
Brouwer in effect founded the mathematical philosophy of intuitionism as an opponent to the thenprevailing formalism of David Hilbert and his collaborators Paul Bernays, Wilhelm Ackermann, John von Neumann and others (cf. Kleene (1952), p. 46–59). As a variety of constructive mathematics, intuitionism is essentially a philosophy of the foundations of mathematics.[5] It is sometimes and rather simplistically characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning.



Luitzen Egbertus Jan Brouwer, usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, a graduate of the University of Amsterdam, 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 breakthroughs in the emerging field of topology. The most celebrated result was his proof of the topological invariance of dimension. Among his further results, the Brouwer fixed point theorem is also well known. 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.
Brouwer in effect founded the mathematical philosophy of intuitionism as an opponent to the thenprevailing formalism of David Hilbert and his collaborators Paul Bernays, Wilhelm Ackermann, John von Neumann and others (cf. Kleene (1952), p. 46–59). As a variety of constructive mathematics, intuitionism is essentially a philosophy of the foundations of mathematics.[5] It is sometimes and rather simplistically characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning.
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