Luitzen Egbertus Jan Brouwer

Luitzen Egbertus Jan Brouwer (27 February 1881 – 2 December 1966) was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory, and complex analysis. 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. Brouwer also became a major figure in the philosophy of intuitionism, a constructivist school of mathematics which argues that mathematics 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). He proved a number of theorems in topology, including his fixed point theorem, the topological invariance of degree, and the topological invariance of dimension. He also proved the simplicial approximation theorem in the foundations of algebraic topology. He founded intuitionism, a philosophy of mathematics that challenged the then-prevailing formalism of David Hilbert. It is sometimes characterized by saying that its adherents do not admit the law of excluded middle as a general axiom in mathematical reasoning. Brouwer was a member of the Significs Group, which formed part of the early history of semiotics. Arthur Schopenhauer had a formative influence on Brouwer. In later years Brouwer became relatively isolated; the development of intuitionism at its source was taken up by his student Arend Heyting. He was killed in 1966 at the age of 85, struck by a vehicle while crossing the street in front of his house.