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.
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 somebody madeof?
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 (actually, it's much better to indeed please post several answers because one answer per post so that others can upvote the ones they like most)easier), vote a lot and vote freely.
(should there be a tag 'not-math-related' or similar?)