Luitzen Egbertus Jan Brouwer

Luitzen Egbertus Jan Brouwer (1881 - 1966) was a Mathématicien Dutch.

Biography

Born on February 27th, 1881 in Overschie (Rotterdam), died on December 2nd, 1966 with Blaricum. It supports its doctorate on June 16th, 1904, with the university of Amsterdam, where it obtains a pulpit in 1912. Jan Brouwer became foreign member of the Royal Society the May 27th 1948.

Work

Brouwer is especially known for its work in Topologie, inter alia the theorem of the point fixes which bears its name. Its theoretical contribution with formal logic was not therefore negligible. In its famous conference of Vienna in 1930 on " the structure of the Continuous " (Paris, 1992), it locates its thought in the prolongation of those of Kant and Schopenhauer. Taking again the Euclidean theories, the set theory of Cantor and the axiomatic method, Brouwer was led to put in opposition the formalism, which regard mathematics as a language, and the old school intuitionalist, partly related to the formalism, for which the arithmetic residence a collection of synthetic judgments a priori. According to him, the formalism misses basic in what it limits to countable completed the number of elements composing the continuous one, by admitting the limited rationality of the numbers and the cuts of Dedekind. To conceive the continuous one as a total unit legitimately, it is necessary to extract a species from it from suitable representative continuations, i.e. convergent particular such as those of its elements which are equal are associated with equal elements of the continuum of total unit, thus allowing to conceive in theory a pure together n-finitaire characterized by a not limited continuation of choice of specified signs.

It was thus with Henri Poincaré, Hermann Weyl and Arend Heyting one of the principal craftsmen of the Théorie of the Mathématiques intuitionalists, according to which mathematics is intuitive and cannot be purely hypothético-deductive (in opposition to the Logicisme of Russel and Frege, with the Formalisme of Hilbert and with the platonism of Gödel).

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