there is a list of disproved mathematical ideas
does anyone know a conjecture in probability theory which was first thought to be true but was eventually disproved? (i really like this zeeman episode)
consider a disproved conjecture, however, assume it to be true. what are the consequence for a mathematical theory apart from obvious counterexamples? i know that mathmatics does not work this way, but can anyone think of a proven false conjecture which, if it was true, would have a great impact?
the last example in the wikipedia article says
A "theorem" of Jan-Erik Roos in 1961 stated that in an [AB4*] abelian category, lim1 vanishes on Mittag-Leffler sequences. This "theorem" was used by many people since then, but it was disproved by counterexample in 2002 by Amnon Neeman.
this eventually false theorem was indeed disproved. what nice results could one obtain provided that a false theorem is considered to be true?