20180922, 23:40  #1  
∂^{2}ω=0
Sep 2002
República de California
5×2,351 Posts 
Michael Atiyah claims proof of 160yearold Riemann hypothesis
Famed mathematician claims proof of 160yearold Riemann hypothesis  New Scientist
Michael Atiyah  no crank, he, but note the cautionary bit at end of the article: Quote:
Last fiddled with by ewmayer on 20180922 at 23:45 

20180923, 04:35  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10101010010010_{2} Posts 

20180924, 13:36  #3 
Feb 2017
Nowhere
3^{4}×7×11 Posts 
That popcorn is just the thing.
The video of Atiyah's Heidelberg Laureate Forum lecture (49 minutes) is now on line. RH has become increasingly tantalizing, as its analogues in other contexts (e.g. function fields over finite fields, or the Weil conjectures) have actually been proven. I didn't have popcorn handy, so skipped through the talk, and didn't get the impression he was talking much about the actual proof. His answer to the first question indicated he had used an indirect argument. Last fiddled with by Dr Sardonicus on 20180924 at 13:36 
20180924, 16:12  #4 
"/X\(‘‘)/X\"
Jan 2013
2^{2}·3·7·37 Posts 
Here is the paper: https://drive.google.com/file/d/17NB...QpfUrEKuY/view

20180924, 17:05  #5 
Aug 2006
5,987 Posts 
You'll also need this:
https://drive.google.com/file/d/1WPs...mTQE0Ww4a/view though I can't make heads or tails of it. Does the limit in (8.11)  the definition of Ж  even exist? 
20180924, 19:49  #6  
Apr 2010
2^{2}·3·13 Posts 
Luboš Motl is rather disappointed:
Nice try but I am now 99% confident that Atiyah's proof of RH is wrong, hopeless: Quote:


20180924, 20:58  #7 
Aug 2006
5,987 Posts 
My assessment is similar: it sure doesn't seem like a proof.

20180924, 22:12  #8 
Feb 2017
Nowhere
185D_{16} Posts 
Does New Scientist know what a mathematical proof is?
I was discomfited by what I read about his recent claims about a short proof of the FeitThompson Theorem (all groups of odd order are solvable), and a supposed proof of a conjecture about the sixsphere. Not least, by the phrase "failed to convince his peers."
Noooooooooo! That's not it. This is supposed to be mathematical proof, not a matter of "convincing" people. If an error is found in the argument, the proof is not valid. It's dead, Jim. 
20180924, 22:29  #9 
"Rashid Naimi"
Oct 2015
Remote to Here/There
100100101000_{2} Posts 
This discussion is well, well above my head.
But generally speaking, I think that Mathematics is not as B & W as it used to be before the advent of the Wikis/Wikipedia. Unfortunately now it is more of a democratic process rather than a matter of logic and proof. If it is referenced in a Wikipedia article then it is gospel material. Last fiddled with by a1call on 20180924 at 22:37 
20180926, 22:38  #10 
"Jason Goatcher"
Mar 2005
3·7·167 Posts 
Quick question, then a comment.
Is this that thing about prime numbers resembling crystal patterns? And the comment: I haven't examined the math, because I am certain I wouldn't understand it, but how wrong is this dude? The way I see it, a proof is supposed to be right 100% of the time, that's part of the definition. That being said, even if he's found a pattern that doesn't always hold up, that's extremely interesting, even if there's something missing from the underlying theory. Sorry, sometimes people talk to me to get out of mental ruts, so I just thought I'd put in my 2 cents. Last fiddled with by jasong on 20180926 at 23:04 
20180927, 13:05  #11 
Feb 2017
Nowhere
3^{4}×7×11 Posts 
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.
Ferdinand Lindemann (1907): Über das sogenannte letzte Fermatsche Theorem – Sitzungsberichte der mathematischphysikalischen Klasse der Bayerischen Akademie der Wissenschaften München – 1907: 287  352. It looks to me like Sir Michael might have done better merely suggesting possible new approaches to problems like RH, the FeitThompson Theorem, and the sixsphere problem. 
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