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:
“I think that Richard Nixon will go down in history as a true folk hero, who struck a vital blow to the whole diseased concept of the revered image and gave the American virtue of irreverence and skepticism back to the people.”
—William Burroughs (b. 1914)
“Philosophy of science without history of science is empty; history of science without philosophy of science is blind.”
—Imre Lakatos (1922–1974)
“The history of the genesis or the old mythology repeats itself in the experience of every child. He too is a demon or god thrown into a particular chaos, where he strives ever to lead things from disorder into order.”
—Ralph Waldo Emerson (1803–1882)