In late May, Peter Woit posted that Lucien Szpiro had announced a proof of the abc conjecture at the Goldfeld conference. In comments here, commenter Z passes along a rumor (with emphasis on rumor) that Szpiro’s proof has a significant flaw. Peter has updated his post to mention he’s hearing similar things.

Peter links to a couple of resources on the conjecture, which implies several other results (including most famously Fermat’s Last Theorem): The abc conjecture home page, and a survey article by Dorian Goldfeld.