The discussion about Goedel’s theorem made me wonder about this question: when was the last time a widely quoted mathematical result turned out to be false? I’ve seen preprints that had proofs I didn’t believe, and I know that journals occasionally print results that are wrong, but does anyone know of a result that was once widely accepted, but then turned out to be wrong?

Take these with a pinch of salt.

Salt because Lounesto is crankish? (because I never viewed him as such, although he comes acoss as self aggrandising) or that the errors aren’t all that famous?

The one that comes to mind right off the bat to me is the widely held belief way back when that continuous => differentiable, before everything was put on a firm footing.

Dirichlet’s principle.

This was quite common up until the end of the 19th century, but I don’t know of any examples since then. In the 19th century, I know there were competing results about Fourier series (which they eventually resolved by distinguishing continuous from uniformly continuous, and convergence from uniform convergence). And I think Peano made his early career by finding counterexamples to “theorems” people had “proved”. Which is why he got interested in putting things on firmer foundations.

Tongue-in-cheek, I propose the Four-Color Map Theorem, which is widely accepted as true, but is not yet proven by conventional mathematical methods. It may turn out to be false.