This paper by Xian-Jin Li at arXiv purports to have proven the Riemann Hypothesis, arguably the most famous of the seven Millenium Problems. It’s just a preprint, of course, so it’s not final (or even peer-reviewed) yet. As commenters in the related Slashdot story mention, articles claiming the proof of the RH show up on arXiv about once per week, so I’m not getting my hopes up. Still, it would be a major breakthrough if it works out.
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