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:
“No one can understand Paris and its history who does not understand that its fierceness is the balance and justification of its frivolity. It is called a city of pleasure; but it may also very specially be called a city of pain. The crown of roses is also a crown of thorns. Its people are too prone to hurt others, but quite ready also to hurt themselves. They are martyrs for religion, they are martyrs for irreligion; they are even martyrs for immorality.”
—Gilbert Keith Chesterton (1874–1936)
“The history of every country begins in the heart of a man or a woman.”
—Willa Cather (1876–1947)
“English history is all about men liking their fathers, and American history is all about men hating their fathers and trying to burn down everything they ever did.”
—Malcolm Bradbury (b. 1932)