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Has Michael Atiyah possibly cracked the Riemann hypothesis?

The eminent mathematician Sir Michael Atiyah will be giving a talk on Monday 2018-09-24 at the Heidelberg Laureates' Forum in which, so it is claimed, he will be presenting a proof of the Riemann hypothesis. Here's an announcement from the HLF twitter account, and an article in New Scientist magazine.

The Riemann hypothesis is arguably the most important open problem in mathematics. Somewhere around a century ago, David Hilbert is said to have remarked that if he were to fall asleep for a thousand years, his first question on waking would be "Has anyone proved the Riemann hypothesis?". It is one of the Clay Mathematics Institute's millennium problems, with a $1M reward available for its solution.

Michael Atiyah is a very eminent mathematician indeed. He was awarded the Fields medal in 1966 and the Abel prize in 2004. He has been President of the Royal Society and Master of Trinity College, Cambridge. He is in these respects exactly the sort of person who should be solving famous open problems.

On the other hand, he is 89 years old, when mathematicians are generally well past their prime. A couple of years ago he published a paper claiming to prove another long-standing conjecture, namely that the 6-dimensional sphere admits no complex structure, and it seems to be generally felt that this paper does not come close to doing what it claims to do. Some mathematicians are quite outspoken in suggesting that Atiyah's recent history makes it unlikely that he really has a proof of the Riemann hypothesis.

So we ask: Does Atiyah have an actual proof of the Riemann hypothesis? Or at least something near enough to one that it remains only to patch up a few small holes?

to keep this question short term, we'll look at the reaction to Atiyah's lecture, with resolution as follows:

Two weeks after the lecture, we will collect all public statement by Fields-prize-winning mathematicians that express a firm opinion that either (a) Atiyah may well have proved the Riemann hypothesis, or (b) Atiyah's proof is fairly clearly flawed. The question will resolve positive if all firm statement are of type (a), negative if they are of type (b), and ambiguous if they are mixed or there are no such statement.

Categories: Mathematics – Pure Mathematics

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