History
The Brouwer fixed point theorem was one of the early achievements of algebraic topology, and is the basis of more general fixed point theorems which are important in functional analysis. The case n = 3 first was proved by Piers Bohl in 1904 (published in Journal für die reine und angewandte Mathematik). It was later proved by L. E. J. Brouwer in 1909. Jacques Hadamard proved the general case in 1910, and Brouwer found a different proof in the same year. Since these early proofs were all non-constructive indirect proofs, they ran contrary to Brouwer's intuitionist ideals. Methods to construct (approximations to) fixed points guaranteed by Brouwer's theorem are now known, however; see for example (Karamadian 1977) and (Istrăţescu 1981).
Read more about this topic: Brouwer Fixed-point Theorem
Famous quotes containing the word history:
“The history of all hitherto existing society is the history of class struggles.”
—Karl Marx (1818–1883)
“All things are moral. That soul, which within us is a sentiment, outside of us is a law. We feel its inspiration; out there in history we can see its fatal strength.”
—Ralph Waldo Emerson (1803–1882)
“The only history is a mere question of one’s struggle inside oneself. But that is the joy of it. One need neither discover Americas nor conquer nations, and yet one has as great a work as Columbus or Alexander, to do.”
—D.H. (David Herbert)