In the English language, the name of every number shares at least one letter with each number immediately before and after. For example, "one" and "two" share an o, "two" and "three" share a t, and so on. (source)

A theory put forward by Polish mathematicians Steven Banach and Alfred Tarski in the early 20^th century states that there is a way of dividing a sphere into separate parts and rearranging them so that they fill all of a larger sphere without leaving any gaps. (source)

Girolamo Cardano, a sixteenth-century Italian physician and mathematician, asserted that each face of a die will turn up exactly once in any given six rolls, despite the fact that he was a notorious gambler and should have observed quite the opposite at the gambling tables.

The longest mathematical proof produced without a computer was a 15,000 page proof, totalling about 500 articles, written by 100 mathematicians during the 1980s. It classified finite, simple groups. Cynics said that only its general contractor understood the entire proof and that he had died.