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.
I’ heard that the idea of using muliplication of points on elliptic curves to prove the abc conjecture is not new, but given in an arxiv paper, before this paper. What is your opinion on this?