It appears that someone has found a flaw in Xian-Jin Li’s proposed proof of the Riemann hypothesis according to the Not Even Wrong blog. (Hat tip: Ars Mathematica)
This doesn’t mean that all is lost. Andrew Wiles’ first attempt at proving Fermat’s Last Theorem was flawed, but he fixed it. Perhaps Li can patch his proof. If not, he may be able to salvage a proof of something valuable short of the Riemann hypothesis.
The news of Li’s proof and its refutation underscores a point I made in an earlier post about proofs of false statements. Namely, “… in mainstream areas of math, blunders are usually uncovered very quickly.” The Riemann hypothesis is very much in the mainstream, and it looks like a blunder was uncovered within 24 hours.
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Richard Elwes 07.04.08 at 07:21
This doesn’t mean that all is lost. Andrew Wiles’ first attempt at proving Fermat’s Last Theorem was flawed, but he fixed it.
But the difference is that Wiles’ proof was long, and made advances in deep number theory. Li’s is short and comparatively elementary. Anyway he’s already up to version 4 on the ArXiV, which to be honest isn’t a promising sign…