Some mistakes in mathematics made by extremely smart and famous people can eventually lead to interesting developments and theorems, e.g. Poincare's 3d sphere charaterization or the search to prove that Euclid's parallel axiom is really ~~necessary~~ unnecessary.

But I also think there are less famous mistakes worth hearing about. So, here's a question:

What's the most interesting mathematics mistake that you know of?

This question is community wiki, meaning neither the question nor the answers receive points (which are reserved for "hard" questions). So please post as much as you like (indeed **please post one answer per post** so that others can upvote the ones easier), vote a lot and vote freely.

(should there be a tag 'not-math-related' or similar?)

EDIT: There is a similar question which has been closed as a duplicate to this one, but which also garnered some new answers. It can be found here: