Michael Atiyah claims proof of 160-year-old Riemann hypothesis

[GP2]

Originally Posted by Dr Sardonicus

It looks to me like Sir Michael might have done better merely suggesting possible new approaches to problems like RH, the Feit-Thompson Theorem, and the six-sphere problem.

Everything I've read about the situation suggests that he is too far gone even for that.

[ewmayer]

Originally Posted by Dr Sardonicus

At least Sir Michael's paper is short. The man who first proved that the number is transcendental did not fare well in his tourney with another famous (then) unsolved problem. This "proof," available on line, was 65 pages long.

To be fair, the latter problem has a long and distinguished -if that's the word for it - history of false proof claims, starting with the "OP", as it were. The 2 paired Wiles papers containing the first known proof are a total 129 pages, almost exactly twice the length of Lindemann's effort, so perhaps the good Herr Professor simply needed a suitable "Part 2". :)

Speaking of false claims, it saddens me to see that it appears my "not a crank" comment about Atiyah in the OP of this thread also appears to be such. It was clearly not so some decades ago, but age and time are mighty enemies, it is the lucky few among us who are blessed to still be alive and capable of useful scientific research at age 90. (My late near-namesake, evolutionary biologist Ernst Mayr was such a one; another who springs to mind is astrophysicist Hans Bethe.)

[Batalov]

Brenner was very sharp in his 80s but now I have not a had a chance to witness him for a decade. Hopefully, still is at 91!

[Dr Sardonicus]

I listened to the Heidelberg Laureate Forum lecture. One thing about the purported proof I gleaned, that I hadn't heard before, was that it involved "infinite iteration of exponentials." I don't know under what hypotheses this even makes sense, but I do know that arguing from authority (in this case, von Neumann) just doesn't cut the mustard.

Another thing, during the questions, was that Sir Michael mentioned that Arxiv had declined to publish his paper on the Riemann Hypothesis. Upon doing a cursory search, I found that Arxiv had published his paper on "The Non-Existent Complex 6-Sphere." It occurred to me that this might have something to do with their reticence about his current effort. I don't buy his statement that the refusal was on account of his age.

Impression: He no longer understands the topics he's talking about, and he doesn't realize or accept that. I'm not sure if anyone is willing to tell him, or if people have, but he is in denial.

The reluctance of the audience to ask any questions after his talk was excruciating.

[xilman]

Originally Posted by ewmayer

It is the lucky few among us who are blessed to still be alive and capable of useful scientific research at age 90. (My late near-namesake, evolutionary biologist Ernst Mayr was such a one; another who springs to mind is astrophysicist Hans Bethe.)

Gerhard Herzberg, also a Nobel Laureate. I met him at a conference when I was still a grad student.

[CRGreathouse]

Originally Posted by Dr Sardonicus

Another thing, during the questions, was that Sir Michael mentioned that Arxiv had declined to publish his paper on the Riemann Hypothesis.

That's pretty telling; their standards are low-to-"not-a-crank".

Originally Posted by Dr Sardonicus

I listened to the Heidelberg Laureate Forum lecture. One thing about the purported proof I gleaned, that I hadn't heard before, was that it involved "infinite iteration of exponentials." I don't know under what hypotheses this even makes sense, but I do know that arguing from authority (in this case, von Neumann) just doesn't cut the mustard.

I believe it makes sense -- see, e.g., Knoebel's famous Exponentials reiterated -- but then analyticity is not automatic, as I understand, and he doesn't prove that it still holds.

[Dr Sardonicus]

Originally Posted by CRGreathouse

I believe it makes sense -- see, e.g., Knoebel's famous Exponentials reiterated -- but then analyticity is not automatic, as I understand, and he doesn't prove that it still holds.

The function in question is the "infinite exponential tower"



I had noticed that, calling the result (if it exists) f(z), then z^f(z) = f(z).

A quick search turned up the condition that iteration converges for



(x being the real part of the complex variable z).

Sir Michael used the value 2 in his talk, for which the iterated exponential obviously diverges.

The region of convergence includes the right half of the critical strip, which suffices for the purpose of detecting zeroes in the critical strip but off the critical line, thanks to the functional equation, if memory serves.

Of course, this leaves unresolved the question of whether the resulting function is "weakly analytic." There's a power series in ln(z). Hmm. Analyticity requires being careful about the "branch cut." Could get tricky...

[CRGreathouse]

Originally Posted by ewmayer

it is the lucky few among us who are blessed to still be alive and capable of useful scientific research at age 90. (My late near-namesake, evolutionary biologist Ernst Mayr was such a one; another who springs to mind is astrophysicist Hans Bethe.)

My fellow OEIS trustee Richard Guy turns 102 on Sunday and he's still publishing great stuff.

[jwaltos]

I thought that professionals within this field would send out a pre-print to their colleagues for an assessment before making such an announcement.

Shannon was a genius who succumbed to Alzheimer's. The ability to recognize weaknesses in yourself and others and address them appropriately at any age requires courage.

The Poincare conjecture proof papers were posted online by Perelman. The back story regarding the alternative claimants to the Poincare proof is not a nice one.


I clicked on the bottom link at the end of Brenner's clip..nice touch Batalov.

[pbof]

I 've watched the video and his love and devotion to Math is telling even at this age!

Imho, If you are a Math hobbyist like myself, that's the moral of the story.