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)
“The only thing worse than a liar is a liar that’s also a hypocrite!
There are only two great currents in the history of mankind: the baseness which makes conservatives and the envy which makes revolutionaries.”
—Edmond De Goncourt (1822–1896)
“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)