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If you're not a mathematician, you may not know that the ABC-conjecture is a vast generalization of Fermat's Last Theorem. (See for details. Now there is a serious claim to have proved it. It will be fabulously exciting if it pans out, though experience suggests that that's quite a big if. It raises interesting questions about mathematical credit: if it is correct, then will Mochizuki become as big a star as Wiles? He wouldn't be the first to prove FLT, but he would have a completely different method, and would dispose of a large number of other conjectures at the same time (which have been shown to follow from ABC). My guess is that he would become a megastar -- for example, I think the proof would be widely reported in the mainstream media. 
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Strictly speaking, the implication of FLT from ABC only works for sufficiently large exponents.  

As for whether the conjecture will appeal to the public as much as FLT, I'm skeptical; from experience, any mathematical statement that contains at least one epsilon in it is quite hard for anyone not having some exposure to analysis to really appreciate.  But the name of the conjecture will probably be intriguing to the public, at least (and the headlines write themselves...).
Thanks for the info. Sir. Was Really intrigued by the name of the theorem. And the scientific american article from where i was directed to this post made for interesting reading.
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