# conjecture in probability, assume conjecture to be true

there is a list of disproved mathematical ideas

https://en.wikipedia.org/wiki/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?

The list of disproved statements on wiki is misleading!

I mention only one example which is important in the light of one of your questions. ("Consider a disproved conjecture, however, assume it to be true. What are the consequence for a mathematical theory apart from obvious counterexamples?")

Wiki says

"Euclid's parallel postulate stated that if two lines cross a third in a plane in such a way that the sum of the "interior angles" is not 180° then the two lines meet."

According to Wiki the statement above was believed to be true for 2000 years.

The quoted statement was found to be independent from the other axioms of geometry; it was not disproved. (An axiom cannot be disproved unless it turns out that it leads to a contradiction together with the rest of the axioms.)

So negating (and not disproving) the statement above had led to the invention of hyperbolic geometry, the greatest impact on mathematics ever.

Also, note that the author of the Wiki article mistakes certain mathematical statements for certain physical things.

• thanks for you answer, i understand what you mean. i just explained my question in a bit more detail. – user248188 Oct 26 '15 at 8:18