The preprint may or may not be from Atiyah (though the writing is consistent with his ramblings about physics and history), but this is an embarrassingly bad “preprint”. It contains almost no substance, and has a myriad of errors of all sorts. It really has many of the usual characteristics [1] of a crank paper, something you can find for a dime a dozen on Vixra.<p>I know Atiyah is supposed to present on the Riemann Hypothesis at the Heidelberg Laureate Forum on Monday. If the organizers saw this preprint and decided to green-light his lecture, I would consider that disrespectful (to Atiyah & the attendees) and borderline malicious, especially given the context of his other recent mathematical claims, along with his truly bizarre Abel lecture [2].<p>[1] <a href="https://www.scottaaronson.com/blog/?p=304" rel="nofollow">https://www.scottaaronson.com/blog/?p=304</a><p>[2] <a href="https://youtube.com/watch?v=fUEvTymjpds" rel="nofollow">https://youtube.com/watch?v=fUEvTymjpds</a>
The community should really let this drift away quietly out of respect for a legend, instead of inviting him to conferences. After the S^6 business I'm disappointed by the organisers in Heidelberg.
I’m guessing this is related to this? <a href="https://www.newscientist.com/article/2180406-famed-mathematician-claims-proof-of-160-year-old-riemann-hypothesis/" rel="nofollow">https://www.newscientist.com/article/2180406-famed-mathemati...</a><p>Edit: it seems the internet is saying, yes he is a fields medalist, but hold with the champagne for a minute until this is peer reviewed at least<p><a href="https://mathoverflow.net/questions/311062/sir-michael-atiyahs-conference-on-the-riemann-hypothesis" rel="nofollow">https://mathoverflow.net/questions/311062/sir-michael-atiyah...</a>
Atiyah obviously has a mental health problem. His purported proof of the Riemann Hypothesis should not be taken seriously. Other recent fiascos include his ludicrous claim of a 12 page proof of the Feit-Thompson Theorem, his asserted proof that there is no complex structure on the 6-sphere, and his talk at the ICM. Folks, these are not minor flubs. There is no resemblance to serious mathematics.<p>His past achievements are rightly celebrated. Most mathematicians recognize the situation and are respectfully trying to minimize the fuss.
The claimed proof on one slide in his presentation:
<a href="https://twitter.com/hrnn9107/status/1044143799683944448" rel="nofollow">https://twitter.com/hrnn9107/status/1044143799683944448</a><p>Edit: And his write-up:
<a href="https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view" rel="nofollow">https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfU...</a>
At the end, he basically says it isn't done, nor a formal proof of RH over Q. Secondly, he thinks RH is undecidable in the Godel sense, and I completely agree.<p>I studied the RH for my Senior Thesis and Godel completeness makes tons of sense here.<p>In terms of the proof, Proof by contraction has always felt like it yields short proofs. The beauty is the in the assumption and the tools afterwards.<p>In fact, the more I read the proof, the more beautiful I find the construction to be. Everything falls out. Thats why its so short.<p>This Todd Function I've never heard of so I need to do some reading.<p>Seems pretty legit to me but, you need alot of understanding here.<p>Source: I have a masters in Math and have studied the RH in depth during those studies.
The poor man lost his wife earlier this year and this is not the first time mathematics has seen grand claims coming from someone near the end of their career grappling with extreme grief. I hope we can quietly let this slide without humiliating the legend.
Here is an unofficial lifestream of the talk Atiyah gave at the Heidelberg laureate forum:<p><a href="https://www.pscp.tv/w/1zqJVLeqXYDKB" rel="nofollow">https://www.pscp.tv/w/1zqJVLeqXYDKB</a>
If this really is Atiyah's claimed proof, it is very sad and embarrassing indeed. I think it is in poor taste to discuss this as if it were a serious attempt at a proof.
For those that are unaware this is one of the Millenium problems set by the Clay mathematical institute. Its proof carries a million dollar prize along with it. If it holds up, this would be the second out of 7 to have been solved. An explanation of the problem can be found on the Numberphile youtube channel[0]<p>0: <a href="https://www.youtube.com/watch?v=d6c6uIyieoo" rel="nofollow">https://www.youtube.com/watch?v=d6c6uIyieoo</a>
PDF version of the paper.<p><a href="https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY/view" rel="nofollow">https://drive.google.com/file/d/17NBICP6OcUSucrXKNWvzLmrQpfU...</a>