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 myth of independence from the mother is abandoned in mid- life as women learn new routes around the mother—both the mother without and the mother within. A mid-life daughter may reengage with a mother or put new controls on care and set limits to love. But whatever she does, her child’s history is never finished.”
—Terri Apter (20th century)
“The foregoing generations beheld God and nature face to face; we, through their eyes. Why should not we also enjoy an original relation to the universe? Why should not we have a poetry and philosophy of insight and not of tradition, and a religion by revelation to us, and not the history of theirs?”
—Ralph Waldo Emerson (1803–1882)
“... the history of the race, from infancy through its stages of barbarism, heathenism, civilization, and Christianity, is a process of suffering, as the lower principles of humanity are gradually subjected to the higher.”
—Catherine E. Beecher (1800–1878)