L. E. J. Brouwer

L. E. J. Brouwer
Born
Luitzen Egbertus Jan Brouwer

(1881-02-27)27 February 1881
Overschie, Netherlands
Died2 December 1966(1966-12-02) (aged 85)
Blaricum, Netherlands
NationalityDutch
Alma materUniversity of Amsterdam
Known forBrouwer–Hilbert controversy
Brouwer fixed-point theorem
Brouwer–Heyting–Kolmogorov interpretation
Jordan-Brouwer separation theorem
Kleene–Brouwer order
Phragmen–Brouwer theorem
Tietze-Urysohn-Brouwer extension theorem
Simplicial approximation theorem
Bar induction
Degree of a continuous mapping
Indecomposability
Indecomposable continuum
Invariance of domain
Spread
Proving hairy ball theorem
Intuitionism
RelativesHendrik Albertus Brouwer (brother)[3]
AwardsForeign Member of the Royal Society[1]
Scientific career
FieldsMathematics
InstitutionsUniversity of Amsterdam
ThesisOver de grondslagen der wiskunde (1907)
Doctoral advisorDiederik Korteweg[2]
Doctoral studentsArend Heyting[2]
Brouwer (right) at the International Mathematical Congress, Zurich 1932

Luitzen Egbertus Jan "Bertus" Brouwer[a] (27 February 1881 – 2 December 1966) was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis.[2][4][5] Regarded as one of the greatest mathematicians of the 20th century, he is known as one of the founders of modern topology, particularly for establishing his fixed-point theorem and the topological invariance of dimension.[6][7][8]

Brouwer also became a major figure in the philosophy of intuitionism, a constructivist school of mathematics which argues that math is a cognitive construct rather than a type of objective truth. This position led to the Brouwer–Hilbert controversy, in which Brouwer sparred with his formalist colleague David Hilbert. Brouwer's ideas were subsequently taken up by his student Arend Heyting and Hilbert's former student Hermann Weyl. In addition to his mathematical work, Brouwer also published the short philosophical tract Life, Art, and Mysticism (1905).

  1. ^ Kreisel, G.; Newman, M. H. A. (1969). "Luitzen Egbertus Jan Brouwer 1881–1966". Biographical Memoirs of Fellows of the Royal Society. 15: 39–68. doi:10.1098/rsbm.1969.0002. hdl:10077/30385.
  2. ^ a b c L. E. J. Brouwer at the Mathematics Genealogy Project
  3. ^ van DALEN, Dirk (1978). "Brouwer: The Genesis of his Intuitionism". Dialectica. 32 (3/4): 291–303. ISSN 0012-2017. JSTOR 42970321.
  4. ^ O'Connor, John J.; Robertson, Edmund F., "L. E. J. Brouwer", MacTutor History of Mathematics Archive, University of St Andrews
  5. ^ Atten, Mark van. "Luitzen Egbertus Jan Brouwer". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
  6. ^ Gillies, Donald. (2012) Philosophical Theories of Probability. Routledge. Milton Park. ISBN 9781134672455. p. 53.
  7. ^ Van Atten, Mark (2016), "Brouwer, L.E.J.", Routledge Encyclopedia of Philosophy
  8. ^ Luitzen Egbertus Jan Brouwer entry in Stanford Encyclopedia of Philosophy


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