mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math

Reply
 
Thread Tools
Old 2018-09-22, 23:40   #1
ewmayer
2ω=0
 
ewmayer's Avatar
 
Sep 2002
República de California

5×2,351 Posts
Default Michael Atiyah claims proof of 160-year-old Riemann hypothesis

Famed mathematician claims proof of 160-year-old Riemann hypothesis | New Scientist

Michael Atiyah - no crank, he, but note the cautionary bit at end of the article:
Quote:
Atiyah is well aware of this history of failure. “Nobody believes any proof of the Riemann hypothesis, let alone a proof by someone who’s 90,” he says, but he hopes his presentation will convince his critics.

In it, he pays tribute to the work of two great 20th century mathematicians, John von Neumann and Friedrich Hirzebruch, whose developments he claims laid the foundations for his own proposed proof. “It fell into my lap, I had to pick it up,” he says.

New Scientist contacted a number of mathematicians to comment on the claimed proof, but all of them declined. Atiyah has produced a number of papers in recent years making remarkable claims which have so far failed to convince his peers.

Last fiddled with by ewmayer on 2018-09-22 at 23:45
ewmayer is offline   Reply With Quote
Old 2018-09-23, 04:35   #2
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

101010100100102 Posts
Default

Uncwilly is online now   Reply With Quote
Old 2018-09-24, 13:36   #3
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

34×7×11 Posts
Default

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 2018-09-24 at 13:36
Dr Sardonicus is offline   Reply With Quote
Old 2018-09-24, 16:12   #4
Mark Rose
 
Mark Rose's Avatar
 
"/X\(‘-‘)/X\"
Jan 2013

22·3·7·37 Posts
Default

Here is the paper: https://drive.google.com/file/d/17NB...QpfUrEKuY/view
Mark Rose is offline   Reply With Quote
Old 2018-09-24, 17:05   #5
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

5,987 Posts
Default

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?
CRGreathouse is offline   Reply With Quote
Old 2018-09-24, 19:49   #6
ccorn
 
ccorn's Avatar
 
Apr 2010

22·3·13 Posts
Default

Luboš Motl is rather disappointed:

Nice try but I am now 99% confident that Atiyah's proof of RH is wrong, hopeless:

Quote:
More importantly, while looking through the papers, I checked whether I couldn't kill the proof by the same simple argument as the argument that is enough to kill 90% of the truly hopeless attempts. The truly hopeless attempts seem to assume that you may just look at some function with a similar location of the zeros and poles and you may show that there are no nontrivial roots away from the critical axis.

Needless to say, any such attempt is wrong because the properties of the primes, the Euler and other formulae for the zeta function, or other special information about the positions of its zeroes were not used at all. There surely exist some similar functions with roots that are away from the critical axis.

And I think that Atiyah's proof sadly suffers from the same elementary problem. He claims that no functions with the symmetrically located "wrong" roots exist at all – which is clearly wrong. Just take [...]
ccorn is offline   Reply With Quote
Old 2018-09-24, 20:58   #7
CRGreathouse
 
CRGreathouse's Avatar
 
Aug 2006

5,987 Posts
Default

My assessment is similar: it sure doesn't seem like a proof.
CRGreathouse is offline   Reply With Quote
Old 2018-09-24, 22:12   #8
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

185D16 Posts
Default 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 Feit-Thompson Theorem (all groups of odd order are solvable), and a supposed proof of a conjecture about the six-sphere. 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.
Dr Sardonicus is offline   Reply With Quote
Old 2018-09-24, 22:29   #9
a1call
 
a1call's Avatar
 
"Rashid Naimi"
Oct 2015
Remote to Here/There

1001001010002 Posts
Default

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 2018-09-24 at 22:37
a1call is offline   Reply With Quote
Old 2018-09-26, 22:38   #10
jasong
 
jasong's Avatar
 
"Jason Goatcher"
Mar 2005

3·7·167 Posts
Default

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 2018-09-26 at 23:04
jasong is offline   Reply With Quote
Old 2018-09-27, 13:05   #11
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

34×7×11 Posts
Default

At least Sir Michael's paper is short. The man who first proved that the number \pi 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 mathematisch-physikalischen 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 Feit-Thompson Theorem, and the six-sphere problem.
Dr Sardonicus is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Nigerian professor claims to have solved Riemann hypothesis ixfd64 Miscellaneous Math 19 2015-11-23 14:31
Connection to the Riemann's hypothesis kurtulmehtap Math 17 2009-10-17 15:40
The Riemann Hypothesis at 150 ewmayer Math 0 2009-10-09 16:50
Riemann's hypothesis is incorrect a proof Carl Fischbach Miscellaneous Math 62 2008-11-11 14:00
Riemann Hypothesis is false????? georgekh Miscellaneous Math 3 2004-12-02 18:45

All times are UTC. The time now is 07:14.


Thu Feb 9 07:14:48 UTC 2023 up 175 days, 4:43, 1 user, load averages: 0.57, 0.73, 0.80

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔