What was Sir Michael Atiyah's legacy?

[George Jones]

Another great has gone.

https://royalsociety.org/news/2019/...dent-of-the-royal-society-sir-michael-atiyah/

 

[fresh_42]

I wished he would have avoided last years controverse. His (excellent) books will survive!

 

[nuuskur]

Rest in peace Sir Atiyah!

 

[jedishrfu]

One wonders if his last talk on the Riemann Hypothesis proof was a Fermat moment.

One that will forever be remembered for what could have been.

Has there been any further discussion on it?

I remember there was a piece missing that Sir Michael said would be published.

I found this on Quora but it seems nothing came of it:

https://www.quora.com/Now-that-he-s...ann-Hypothesis-likely-to-stand-up-to-scrutiny

Apparently, the proof hinged on the mysterious Todd function which no one knew how he had/if he had constructed it.

More on his other groundbreaking mathematical work:

https://en.wikipedia.org/wiki/Michael_Atiyah

 

[Auto-Didact]

Atiyah has directly shaped mathematical physics for the rest of time. Just last night I was watching an interview of his (posted by @romsofia here).

Requiescat in pace, dear Sir

One wonders if his last talk on the Riemann Hypothesis proof was a Fermat moment.

I believe the world is all the richer for his works last September, if they are viewed as they should be viewed: a conjecture by a giant, possibly who realizes that cognitive decline has begun, instead of a proper proof.

We do not know how long ago he started nor worked on the matter, before he wasn't able to work as good as he used to do. It was abundantly clear that the man wasn't at peak performance anymore; there is no shame in this, certainly not at his age.

One only needs to recall how other intellectual giants (e.g. among others Edward Witten, Robbert Dijkgraaf (both students of Atiyah who clearly should not need any introduction whatsoever here) and Roger Penrose, (a colleague of Atiyah since their time in college together under Todd (undergrad) and Hodge (graduate)) speak about Michael's towering intellect until this very day.

There is the possibility Atiyah's manuscripts and notes will become available online; depending on their contents we will either learn much more or be able to put the matter to rest.

It would indeed be a tremendous irony if it turns out that in the course of history his conjecture does turn out to carry weight, but like Fermat would need 3 centuries or more for mathematics to advance before it could be properly dissected and understood.

Apparently, the proof hinged on the mysterious Todd function which no one knew how he had/if he had constructed it.

Replicating the function is difficult, no doubt see e.g. the point @mitchell porter makes:

Here we should face again the fact that no participant in the Internet discussions around Atiyah's claims has understood his two papers in anything like a comprehensive way. People just focus on some little part that they think they understand. For example, it's only now that I really noticed the actual formula for "ж"! ... equation 8.11, a double limit of a sum of "Bernoulli numbers of higher order". And when I check the reddit attempt to reproduce Atiyah's calculation, 8.11 is all but ignored.

But it certainly is not an insurmountable problem using 8.11 and I'm sure it has privately been achieved by others as well; however, having said that, running the resulting function on a computer seems to be problematic to say the very least.

 

[mathwonk]

I doubt his proof of RH works but I am very happy he presented it. What joie de vivre! In the last two days I have read of the passing of three greats whom I had the pleasure and privilege to actually meet and exchange (or overhear) a few words with, Atiyah, Eli Stein, and Peter Swinnerton-Dyer. As to the RH stuff by Atiyah, remember one cannot make any progress without the courage to attempt something hard, and be willing to be wrong. His K theory book was one of the less than half my books that made the cut for my big move a few years back, and is still on my shelf for retirement reading. I recall his remark that Fourier series or transforms are one of the major ideas in mathematics, and it is another one I have never mastered.

 

[Auto-Didact]

One of the better obituaries, written by one of Atiyah's friends

 

[aheight]

I have be moved by one of his quotes for some time now: (paraphrased): "I do not go looking for a mathematical problem to solve, rather I just wade in the mathematical waters and let the tides move me."

That is how the RH will be proven one day I suspect.

 

[jedishrfu]

Nature has posted a moving obituary of Michael’s life and accomplishments.

https://www.nature.com/articles/d41586-019-00358-9