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 am ashamed to see what a shallow village tale our so-called History is. How many times must we say Rome, and Paris, and Constantinople! What does Rome know of rat and lizard? What are Olympiads and Consulates to these neighboring systems of being? Nay, what food or experience or succor have they for the Esquimaux seal-hunter, or the Kanaka in his canoe, for the fisherman, the stevedore, the porter?”
—Ralph Waldo Emerson (1803–1882)
“Certainly there is not the fight recorded in Concord history, at least, if in the history of America, that will bear a moment’s comparison with this, whether for the numbers engaged in it, or for the patriotism and heroism displayed.”
—Henry David Thoreau (1817–1862)
“He wrote in prison, not a History of the World, like Raleigh, but an American book which I think will live longer than that. I do not know of such words, uttered under such circumstances, and so copiously withal, in Roman or English or any history.”
—Henry David Thoreau (1817–1862)