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Beside being the leader and untiring advocate of the intuitionist view of
mathematics, Brouewer lift his mark in other areas of the subject. He is regarded
as one of the founders of medern topology, and is particularly known
for his invariance theorem and his fixed-point theorem. the former asserts that
the dimensionality if a Cartesian n-dimensional number-manifold is a topological
invariant, and the latter that every continuous mappong of an n-dimensional
sphere onto itself has at least one fixed point. Brouwer was born in 1881, spent the major part of his professional life at the University of Amsterdam, and died in 1966. He was a ruthless fighter for his beliefs. As the editor of the Mathematische Annalen in charge if acceptance or rejection of submitted papers, he opened his attack on the free use of reductio ad adsurdem by refusing all papers that applied the law of the excluded middle to propositions whose truth or falsity could not be decided in a finite number of steps. The editorial board of the journal met the crisis by resigning and then reelecting themselves, minus Brouwer. The Dutch government was so indignant over this snub of their leading mathematician that they created a rival mathematics jouranl, with Brouwer in charge.
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