User abhishek gupta - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T07:04:27Z http://mathoverflow.net/feeds/user/22747 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95865/examples-of-conjectures-that-were-widely-believed-to-be-true-but-later-proved-fal/106385#106385 Answer by Abhishek Gupta for Examples of conjectures that were widely believed to be true but later proved false Abhishek Gupta 2012-09-04T22:02:57Z 2012-09-04T23:17:28Z <p>In introductory functional analysis one learns that every normed linear space with a Schauder basis is separable. The converse of this was a famous question raised by Banach- does every separable Banach space have a Schauder basis? Since almost all known separable Banach spaces had been shown to possess a Schauder basis it was believed that this must be true. But in 1972 Enflo constructed a counterexample to this.</p> <p>For this achievement of his Enflo was awarded a live goose by Stanislaw Mazur.</p> <p>See <a href="http://en.wikipedia.org/wiki/Per_Enflo#Enflo.27s_solution" rel="nofollow">this</a>.</p> http://mathoverflow.net/questions/95865/examples-of-conjectures-that-were-widely-believed-to-be-true-but-later-proved-fal/101216#101216 Answer by Abhishek Gupta for Examples of conjectures that were widely believed to be true but later proved false Abhishek Gupta 2012-07-03T07:06:15Z 2012-07-03T07:06:15Z <p><a href="http://en.wikipedia.org/wiki/Polya_conjecture" rel="nofollow">Polya conjecture</a> was proved to be false in 1958.</p>