Lej brouwer biography of barack biden

Dutch mathematician and philosopher who lived from to In classical mathematics, he founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem. He also gave the first correct definition of dimension. In philosophy, his brainchild is intuitionism, a revisionist foundation of mathematics.

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Intuitionism views mathematics as a free activity of the mind, independent of any language or Platonic realm of objects, and therefore bases mathematics on a philosophy of mind. The implications are twofold. First, it leads to a form of constructive mathematics, in which large parts of classical mathematics are rejected. Second, the reliance on a philosophy of mind introduces features that are absent from classical mathematics as well as from other forms of constructive mathematics: unlike those, intuitionistic mathematics is not a proper part of classical mathematics.

Brouwer studied at the municipal University of Amsterdam where his most important teachers were Diederik Korteweg of the Korteweg-de Vries equation and, especially philosophically, Gerrit Mannoury. Brouwer's classes were also attended by Max Euwe, the later world chess champion, who published a game-theoretical paper on chess from the intuitionistic point of view Euwe, , and who would much later deliver Brouwer's funeral speech.

Among Brouwer's assistants were Heyting, Hans Freudenthal, Karl Menger, and Witold Hurewicz, the latter two of whom were not intuitionistically inclined. The most influential supporter of Brouwer's intuitionism outside the Netherlands at the time was, for a number of years, Hermann Weyl.