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:
“We are told that men protect us; that they are generous, even chivalric in their protection. Gentlemen, if your protectors were women, and they took all your property and your children, and paid you half as much for your work, though as well or better done than your own, would you think much of the chivalry which permitted you to sit in street-cars and picked up your pocket- handkerchief?”
—Mary B. Clay, U.S. suffragist. As quoted in History of Woman Suffrage, vol. 4, ch. 3, by Susan B. Anthony and Ida Husted Harper (1902)
“It is the true office of history to represent the events themselves, together with the counsels, and to leave the observations and conclusions thereupon to the liberty and faculty of every man’s judgement.”
—Francis Bacon (1561–1626)
“Bias, point of view, fury—are they ... so dangerous and must they be ironed out of history, the hills flattened and the contours leveled? The professors talk ... about passion and point of view in history as a Calvinist talks about sin in the bedroom.”
—Catherine Drinker Bowen (1897–1973)