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Riemann hypothesis, the fine structure constant, and the Todd function (johndcook.com)
37 points by tacon 20 days ago | hide | past | web | favorite | 7 comments



I'm a mathematician, but I work on things that are not even remotely related to the Riemann hypothesis. I could not possibly weigh in on the validity of the proof. My colleagues who know this area better are extremely skeptical, in part due to their opinions of Atiyah's work over the last decade. Mathematically, the point of skepticism seems to be the existence of the Todd function with the properties that Atiyah requires in his proof. See [1] for an informed opinion.

Atiyah is one of the most influential living mathematicians. His prior contributions give him a prominent platform from which to announce this result, which has quickly generated a media firestorm. To me, the worst part is that the work doesn't stand alone---a proof is a proof when it is understood by a community of experts. Until it has been carefully evaluated, no one should be criticizing him due to his age or past failures, nor should they be celebrating his achievement.

1. https://motls.blogspot.com/2018/09/nice-try-but-i-am-now-99-...


> As far as I know, none of the critics have a Fields Medal or Abel Prize in their closet.

Few years ago when Atiyah was publishing his 12 page proof of Feit-Thompson theorem Serre (both Fields Medal and Abel price) said this:

"I hope Atiyah's "proof" will not be published; I have seen it : it is hopelessly wrong." https://plus.google.com/+TimothyGowers0/posts/Troy62f3AS6

Those who have the level of understanding needed to understand and critique his work don't seem to think that he just makes normal mistakes anymore. The word proof was in quotes. Let them be the critics and let's not make news about this.


Rumor has it that his most recent proof also received private criticism and he rejected it. But the experts are being discreet. They're not jumping on twitter. Instead you had unqualified people who hadn't seen the papers or the talk saying that it had to be wrong.


that seems very strange that the limit of a purely mathematical function would yield the fine structure constant based on anything other than a coincidence, especially considering we can only measure the fine structure constant to only so many significant figures based on the accuracy of our experiments

however if it indeed is the case that the value of ratios of speed of light, planks constant, electron charge and electric permittivity of the vacuum are related to prime numbers would be indescribable

edit - this appears to be closer to the paper https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE...


So my reading of the article is that Atiyah has claimed that he has a proof of the Riemann hypothesis as a corollary to another theorem that is not yet published?


This is the clearest, most balanced thing I've yet read on the subject.

We wait to see what the manuscript on the Todd function says.


Michael Atiyah is taking a big risk. I’ve seen lots of criticism of Atiyah online. As far as I know, none of the critics have a Fields Medal or Abel Prize in their closet.

I don't see how it's a big risk. the worst that can happen is it's wrong. I'm pretty sure he put a lot of thought to it.




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