Today the internet has been getting excited about Sir Michael Atiyah’s claimed proof of the Riemann Hypothesis, which he presented at the Heidelberg Laureate Forum this morning. We’ve collected all the relevant links and tweets to help you make sense of what’s going down in critical-line-town.
Firstly, Aperiodical roving reporters Katie and Paul were present in the room, allowing @Aperiodical to live-tweet a blow-by-blow of the talk itself. The thread is here (click the date-time link to see the whole thread):
Our @stecks is in the room with Atiyah at #hlf2018, but can't tweet and listen. We'll try to relay what's going on.
— The Aperiodical (@aperiodical) September 24, 2018
The talk itself was live-streamed by the conference, but due to heavy traffic their streaming servers, and the backup servers they switched to, were unable to support the load. One plucky reporter streamed it on Periscope, but the actual video has now been put up on the conference’s YouTube channel:
The actual paper Atiyah’s presenting has been doing the rounds online, and there are links to a 5-page PDF outlining the proof sketch and agreeing with the content of the talk, as well as a paper on the Fine Structure Constant referenced in that one which has more detail.
Some immediate analysis in this Twitter thread by Markus Pössel, who was also in the room (click the date-time link to see the whole thread):
Atiyah has promised this to be accessible to non-mathematicians. #HLF18 pic.twitter.com/4tg384IHyB
— Markus Pössel (@mpoessel) September 24, 2018
Markus has also now written a brief post for the HLF blog about what will happen next.
New Scientist has posted a follow-up to its initial announcement, with a more cautious treatment of what has happened, including quotes from friend of the site Nicholas Jackson.
Here are a few non-rigorously-selected discussions of the mathematics from around the web (again, click the timestamp in tweets to see the full thread):
Here his paper on RH https://t.co/O67PgPt6dK
— Francesco Vaccarino (@fvaccarino) September 23, 2018
Atiyah's "proof" of RH. The argument relies on the existence of an auxiliary function T, not constructed in the paper. But some of its properties are listed — enough to conclude that there is no such function. So there's no proof. https://t.co/71a1yQR8Ni
— my office door is open (@chocolitt88) September 24, 2018
A Reddit thread attempting to collect discussion in the wake of the lecture:
Atiyah’s lecture on the Riemann Hypothesis from math
There’s also a lively Twitter discussion on the reaction to the proof, in this thread:
I see this attitude all over math Twitter that it will be embarrassing for Atiyah if his proof of the #riemannhypothesis doesn't pan out. As if aiming for a big prize and missing is a bad thing.
— John D. Cook (@JohnDCook) September 24, 2018
And finally, this MathOverflow thread What is the definition of the function T used in Atiyah’s attempted proof of the Riemann Hypothesis? provides some insight into the mysterious Todd function.
If any further developments occur, we’ll post about it as soon as we hear. The Heidelberg Laureate Forum continues for the rest of the week, and Paul and Katie will attempt to write about any other interesting maths as it happens, here and over on the HLF blog.