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 greatest horrors in the history of mankind are not due to the ambition of the Napoleons or the vengeance of the Agamemnons, but to the doctrinaire philosophers. The theories of the sentimentalist Rousseau inspired the integrity of the passionless Robespierre. The cold-blooded calculations of Karl Marx led to the judicial and business-like operations of the Cheka.”
—Aleister Crowley (1875–1947)
“Every literary critic believes he will outwit history and have the last word.”
—Mason Cooley (b. 1927)
“Tell me of the height of the mountains of the moon, or of the diameter of space, and I may believe you, but of the secret history of the Almighty, and I shall pronounce thee mad.”
—Henry David Thoreau (1817–1862)