World of Scientific Discovery on Luitzen Egbertus Jan Brouwer
Brouwer was unusually intelligent, which he demonstrated by graduating from high school at the age of fourteen. After studying Greek and Latin for two years, he was admitted, in 1897, to the University of Amsterdam, where he studied mathematics. His abilities were quickly noticed. In 1904, the Dutch Royal Academy published an important paper by Brouwer on the subject of continuous motions in four-dimensional space. Two years after receiving his doctor of science degree in 1907, Brouwer was hired as a lecturer at the university.
Early in his career, Brouwer became interested in the logical foundations of mathematics. The study of this problem took on the form of a debate between mathematicians of opposing views. Bertrand Russell and David Hilbert believed that formal logic alone could provide the basis on which mathematics is built. On the other side, mathematicians such as Henri Poincaré, with whom Brouwer agreed for the most part, adopted the view that formal logical systems, useful as they may be in describing the properties of a mathematical situation, are not capable of generating the self-consistent axioms on which mathematics is based. This debate over the very foundations of mathematics became Brouwer's main preoccupation for much of his career.
In 1912, Brouwer was promoted to Professor of Mathematics, a post he held until his retirement in 1951. Brouwer's work focused on an elaboration of his view that the roots of mathematics were based on intuitive principles and not on formal systems. This view came to be called intuitionism, a method by which fundamental mathematical functions can be described. Instead of proving or logically deriving a function, the function must be constructed. For example, if a = b and b = c, therefore a = c is a logical derivation. The intuitionist approach would be to construct the pathway to prove that a = c.
Brouwer's arguments were absorbed by the mathematical community without much interest other than polite acknowledgement of their existence. But in 1920, when Kurt Gödel stunned the mathematical world with his proof of the incompleteness of formal systems, which swept aside the approach taken by Russell and Hilbert, Brouwer's work suddenly gained significance. In addition to his work in the foundations of mathematics, Brouwer also made important contributions to the theory of topology, including a number of fixed point theorems. In recognition of his outstanding work, Brouwer was awarded the Knighthood of the Order of the Dutch Lion in 1932. He died in Blaricum, Netherlands in 1966.
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