When an amateur mathematician from Indiana managed to solve one of mathematics' great problems—squaring the circle—he decided to copyright his proof, but allow his home state to use it for free. Sadly, things didn't quite go to plan.
It turned out that his proof incorrectly assumed that pi was exactly 3.2—but a bill had already been passed by the house of representatives approving the algebra by the time a mathematician noticed the mistake. Fortunately, said mathematician stepped in by the time it reached the Senate. This video explains how the US narrowly avoided pi becoming 3.2. [YouTube]