This isn't a topic I'm familiar with, just something I've read on Quanta, but according to [this article](https://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/), Richard Kershner of Johns Hopkins [claimed to have a complete classification of convex pentagon tilings](https://www.jhuapl.edu/techdigest/views/pdfs/V08_N6_1969/V8_N6_1969_Kershner.pdf) in 1968, though he notably said that "The proof that the list in Theorems 1 and 2 is complete is extremely laborious and will be given elsewhere" and that "a complete proof would require a rather large book".

However, after Martin Gardner talked about this claim in his column in *Scientific American* in 1975, it got to Marjorie Rice, a California housewife with a high school math education, who found four additional families, and Richard James, a computer programmer, who found another. Eventually, Michael Rao proved that there were exactly 15. You can read more about Rice in [this article by the same author](https://www.quantamagazine.org/marjorie-rices-secret-pentagons-20170711/).

Admittedly, this is an instance of a single professional mathematician making a false claim without giving a proof, which mathematicians consider poor form, and a nonprofessional correcting him, rather than the general mathematics community being wrong.