Atiyah and the Riemann Hypothesis: What are the next steps?
The eagerly awaited talk yesterday morning by Sir Michael Atiyah about what he says is a proof of the famous Riemann Hypothesis was very enjoyable. Feel free to read up on it in my blow-by-blow sequence of live tweets, which begins with Atyah’s first slide – click to read the rest of it on Twitter:
— Markus Pössel (@mpoessel) September 24, 2018
(If you would like to learn more about what the Riemann Hypothesis actually is, here is a great HLF blog article by Katie Steckles.)
But listening to a diverting lecture is one thing. Reasonable certainty that one of the most famous open problems in mathematics has been solved is a completely different kettle of fish.
So let me briefly recapitulate what the next steps will be. Given that the Riemann hypothesis, of which Atiyah has claimed to have presented a proof in today’s lecture, is so famous – it is one of the seven Millenium problems posed by the Clay Mathematics Institute in 2000, and (part of) one of Hilbert’s problems collected by the German mathematician David Hilbert in 1900 – there is bound to be excitement after today’s presentation. So it’s important to remember that we are at the beginning of a longer process.
I am not aware that Hilbert left us any specific criteria for when he would regard one of his problems to have been solved. The Clay Institute has been much more explicit.
So far, we have Atiyah’s lecture, as well as what appears to be a write-up, and also this earlier write-up that contains some of the needed definitions (thanks to, respectively, Thilo Kueppers and Angel Lopez for pointing me to these). His findings now have to be discussed and evaluated within the mathematical community.