In mathematics, ideas are supposedly not accepted as fact until they have been rigorously proved. However, there have been some ideas that were fairly accepted in the past but which were subsequently showed to be false. This article is meant to serve as a repository for compiling a list of such ideas. *The idea of the Pythagoreans that all numbers can be expressed as a ratio of two whole numbers. This was disproved by one of Pythagoras' own disciples, Hippasus, who showed that the square root of two is what we today call an irrational number. One story claims that he was thrown off the shi...

The Münchhausen trilemma (after Baron Münchhausen, who allegedly pulled himself and the horse on which he was sitting out of a swamp by his own hair), also called Agrippa's trilemma (after Agrippa the Skeptic), is a philosophical term coined to stress the purported impossibility to prove any truth even in the fields of logic and mathematics. It is the name of an argument in the theory of knowledge going back to the German philosopher Hans Albert, and more traditionally, in the name of Agrippa. Trilemma If we ask of any knowledge: "How do I know that it's true?", we may provide proof; y...