Luitzen Egbertus Jan Brouwer (February 27, 1881 - December 2, 1966), usually cited as L. E. J. Brouwer, was a Dutch mathematician, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis. The Brouwer fixed point theorem is named in his honor. He proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, the treatment of general continuous mappings. February 27 is the 58th day of the year in the Gregorian Calendar. ... 1881 was a common year starting on Saturday (see link for calendar). ... December 2 is the 336th day (337th in leap years) of the year in the Gregorian calendar. ... 1966 was a common year starting on Saturday (link goes to calendar) // Events January January 1 - In a coup, Colonel Jean-Bédel Bokassa ousts president David Dacko and takes over the Central African Republic. ... A mathematician is a person whose area of study and research is mathematics. ... From Athenaeum Illustre to University In January 1632 two internationally acclaimed scientists, Caspar Barlaeus and Gerardus Vossius, held their inaugural speech in the Athenaeum Illustre - the illustrious school - which had its seat in the 14th-century Agnietenkapel. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. ... Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematics, a measure is a function that assigns a number, e. ... Complex analysis is the branch of mathematics investigating holomorphic functions, i. ... In mathematics, the Brouwer fixed point theorem states that every continuous function from the closed unit ball D n to itself has a fixed point. ... In mathematics, the simplicial approximation theorem is a foundational result for algebraic topology, guaranteeing that continuous mappings can be (by a slight deformation) approximated by ones that are piecewise of the simplest kind. ... Algebraic topology is a branch of mathematics in which tools from abstract algebra are used to study topological spaces. ... In mathematics, a simplicial complex is a topological space of a particular kind, built up of points, line segments, triangles, and their n-dimensional counterparts. ...

Brouwer adhered to an intuitionist philosophy of mathematics. This is a variety of constructive mathematics. It is sometimes and rather simplistically characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning. Brouwer in effect founded mathematical intuitionism, as an opponent of the prevailing trend towards formalism. In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as the constructive mental activity of humans. ... In the philosophy of mathematics, constructivism asserts that it is necessary to find (or construct) a mathematical object to prove that it exists. ... In logic, the law of excluded middle (tertium non datur in Latin) states that for any proposition P, it is true that (P or ~P). ... The word formalism has several meanings: A certain school in the philosophy of mathematics, stressing axiomatic proofs through theorems specifically associated with David Hilbert. ...

He was member of the Significs group, containing others with a generally neo-Kantian philosophy. It formed part of the early history of semiotic study, around Victoria, Lady Welby in particular. The original meaning of his intuitionism can probably not completely be disentangled from the intellectual milieu of that group. Neo-Kantianism means a revived or modified type of philosophy along the lines of that laid down by Immanuel Kant in the eighteenth century. ... Victoria, Lady Welby (also styled the Hon. ...

His ideas were initially exposed in Beweis des Jordanschen Satzes für N Dimensionen (1912) ("Proof of Jordan's theorem for N dimensions"). He uncovered some of the main principles, such as triple negation, of intuitionistic logic; which then was taken up by Andrei Kolmogorov and (for a period) by Hermann Weyl, with rather different attitudes. Brouwer spent much time searching for the intuitionistic theory of real numbers, which he called species. This effort would now be considered misplaced: there is no single theory. Intuitionism later became more respectable once Kurt Gödel and later Stephen Kleene had fitted it into mathematical logic; but this was certainly to cut across Brouwer's anti-formal intentions. 1912 is a leap year starting on Monday. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... Andrey Nikolaevich Kolmogorov (Андре́й Никола́евич Колмого́ров) (kahl-mah-GAW-raff) (April 25, 1903 in Tambov - October 20, 1987 in Moscow) was a Russian mathematician who made major advances in the fields of probability theory and topology. ... Hermann Weyl Hermann Weyl (November 9, 1885 - December 8, 1955) was a German mathematician. ... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... Kurt Gödel Kurt Gödel [kurt gøːdl], (April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... Stephen Cole Kleene (January 5, 1909 - January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...

He was combative from a young man. He was involved in a very public and eventually demeaning controversy in the later 1920s with David Hilbert, over editorial policy at Mathematische Annalen, at that time a leading learned journal. Politically Brouwer was pro-German. He became relatively isolated; the development of intuitionism at its source was taken up by his student Arend Heyting. David Hilbert David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician born in Wehlau, near Königsberg, Prussia (now Znamensk, near Kaliningrad, Russia) who is recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... The Mathematische Annalen is a German mathematical research journal published by Springer-Verlag. ... In academic publishing, a scientific journal is a periodical publication intended to further the progress of science, usually by reporting new research. ... Arend Heyting (May 9, 1898 – July 9, 1980) was a Dutch mathematician and logician. ...

External links

• Biography at the MacTutor archive
• Stanford Encyclopedia of Philosophy entry