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Math

Famed Mathematician Claims Proof of 160-Year-Old Riemann Hypothesis (soylentnews.org) 193

Slashdot reader OneHundredAndTen writes: Sir Michael Atiyah claims to have proved the Riemann hypothesis. This is not some internet crank, but one the towering figures of mathematics in the second half of the 20th century. The thing is, he's almost 90 years old. According to New Scientist, Atiyah is set to present his "simple proof" of the Riemann hypothesis on Monday at the Heidelberg Laureate Forum in Germany. Atiyah has received two awards often referred to as the Nobel prizes of mathematics, the Fields medal and the Abel Prize; he also served as president of the London Mathematical Society, the Royal Society and the Royal Society of Edinburgh.

"[T]he hypothesis is intimately connected to the distribution of prime numbers, those indivisible by any whole number other than themselves and one," reports New Scientist. "If the hypothesis is proven to be correct, mathematicians would be armed with a map to the location of all such prime numbers, a breakthrough with far-reaching repercussions in the field."
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Famed Mathematician Claims Proof of 160-Year-Old Riemann Hypothesis

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  • by Anonymous Coward

    Would be a shame if he went out looking like a crackpot.

    • Re:I hope it's real (Score:5, Interesting)

      by aleksander suur ( 4765615 ) on Monday September 24, 2018 @02:57AM (#57366424)
      If the proof is a dud or just some nonsense, it get's written off as an unfortunate case of dementia, doesn't invalidate lifetime of excellent work. If it checks out however, well solving a millennium problem at age 90 is just a cherry on top.
      • Re:I hope it's real (Score:5, Interesting)

        by Kjella ( 173770 ) on Monday September 24, 2018 @03:48AM (#57366498) Homepage

        If the proof is a dud or just some nonsense, it get's written off as an unfortunate case of dementia, doesn't invalidate lifetime of excellent work. If it checks out however, well solving a millennium problem at age 90 is just a cherry on top.

        And the middle ground is still the most likely, that it'll be a plausible proof but somehow gets poked holes in. That's what happens to most people who think they've solved the big conjectures no matter their credentials. But if it stands up to scrutiny he'll rise from famed to legend.

        • I too think this is more likely. Take the case of Andrew Wiles who thought he had proved Fermat's Last Theorem until it was checked and there was a flaw in his proof. It took him and Richard Taylor a year to fix it.
      • by h33t l4x0r ( 4107715 ) on Monday September 24, 2018 @05:20AM (#57366598)
        Still I'm sure he's forgotten more math than anyone here will ever know.
        And I will respectfully get off his lawn in exchange for a single hard candy.
        • by KGIII ( 973947 )

          "Anyone here" ... ?

          Some of us still stop by and lurk.

        • Sorry, those candies are permanently fused together the bowl. You wanted one, now you have a peppermint and butterscotch cluster.
    • Re:I hope it's real (Score:5, Interesting)

      by Zocalo ( 252965 ) on Monday September 24, 2018 @03:45AM (#57366492) Homepage
      I doubt that will happen. A lot of his recent mathematical claims have apparently been met with skepticism, so it's hardly surprising that this one is being treated the same, and I doubt it will change how people view his legacy. He's confident enough to go up in front of his peers and present it though, and even if he is over-looking some flaw in the proof it might still help others - or be resolved, as was the case with Andrew Wiles’ proof of Fermat’s last theorem. He's also claiming it's a "relatively simple proof" (echos of Fermat there!), so unlike Shinichi Mochizuki’s claimed but inpeneterable proof of the ABC Conjecture at least we should know for sure pretty quickly, although that is also ringing alarm bells; long standing mathematical problems don't generally have relatively simple proofs.
      • From what I remember about Wiles' proof, it's like 200+ pages long and uses a lot different areas and techniques of math. Because of this, peole doubt that if Fermat has a proof, it certainly wasn't the same one Wiles published.
      • by harrkev ( 623093 )

        This proof is not big deal. I proved the Riemann hypothesis once. But the proof was too big to fit in the margin of the book that I was reading at the time.

  • Elon Musk (Score:5, Interesting)

    by darkain ( 749283 ) on Monday September 24, 2018 @02:23AM (#57366370) Homepage

    Elon Musk apparently reads Slashdot: https://twitter.com/elonmusk/s... [twitter.com]

  • Lol (Score:5, Informative)

    by ledow ( 319597 ) on Monday September 24, 2018 @02:42AM (#57366392) Homepage

    Ironic that Slashdot are now quoting stories from SoylentNews, because they get there first and have better coverage.

    • Re:Lol (Score:5, Funny)

      by Megol ( 3135005 ) on Monday September 24, 2018 @03:17AM (#57366442)

      Yes, like rain on a wedding day.

    • Re: (Score:2, Informative)

      by Anonymous Coward

      Slashdot's owners not listening to users during the beta fiasco spawned SoylentNews.

      "Get woke, go broke" [urbandictionary.com] of the new Slashdot owners has maintained and even allowed Soylent to grow.

    • by AmiMoJo ( 196126 )

      You must be new around here. Slashdot has a long, proud tradition of posting "news" a week or two after it breaks.

      The editors seem to hold some stories back for a while, to fill in quiet periods. Also people submit old stories that they haven't seen here just to be part of the debate.

  • This is going to break my favourite captcha [devilsworkshop.org].
  • You can download it for free now -- so to speak, kinda.

  • by swm ( 171547 ) <swmcd@world.std.com> on Monday September 24, 2018 @03:32AM (#57366470) Homepage
    A "simple" proof of the Riemann Hypothesis seems unlikely.
    This has been a marquee unsolved problem in Mathematics for over 150 years.
    Any simple proof would have been found long ago.
    • by PolygamousRanchKid ( 1290638 ) on Monday September 24, 2018 @04:37AM (#57366554)

      Any simple proof would have been found long ago.

      Well, I took a walk by outside where the Forum is being held, and asked a participant who was outside what he thought of the talk.

      He cautioned that he was a physicist, and not fully qualified in that area, but the proof seemed to make sense to him. It is a proof by contradiction, and he could understand the contradiction.

      What is interesting, is that Atiyah was not directly looking at the Riemann Hypothesis, but was studying something else . . . and just happened to stumble across this.

      I'll see if I can stumble across some more participants, and ask them later . . . this evening, after they've had a few beers.

    • by Opportunist ( 166417 ) on Monday September 24, 2018 @04:42AM (#57366562)

      If an ancient, famed mathematician talks about a "simple" proof, it usually means the paper is only the size of a phone book instead of a whole library.

      They use words differently than you or me would. It's like when astronomers talk about "nearby objects".

    • This has been a marquee unsolved problem in Mathematics for over 150 years. Any simple proof would have been found long ago.

      Just because nobody has figured out a "simple proof" after a lot of years of trying it doesn't logically follow that one cannot exist. You had it right when you said a simple proof "seems unlikely" which the evidence would suggest is true.

  • Was he a "sir" before that, or was he "sired" because he proved that?
    • Before. It's pretty clear actually.

      Disclaimer: Not British.

    • by ledow ( 319597 )

      "Atiyah was made a Knight Bachelor in 1983 and made a member of the Order of Merit in 1992."

      Didn't take much to Wiki that.

      He's certainly got a very impressive track record. However, there is a certain amount of doubt because the proof incorporates knowledge of his "particular" way of doing things, that's almost impenetrable to most mathematicians. To verify this is going to take a LONG time.

      As someone linked above, the second paper is the basis of the mathematics and joining the two together to any sembla

  • This is a famous mathematician but he's also in his late 80s and in recent years has made claims to other big open conjectures that didn't hold up to muster.

  • i'm not sure what the 90 years old comment has to do with anything.

    is it meant to be positive or negative, still even haven't worked that out.
    negative - don't get your hopes up, this guy is 90 years old and probably doesn't even remember his kids names.
    positive - you're never to old to make big contributions to science/mankind.

    • by Hodr ( 219920 )

      Probably just meant to be interesting, as there is a belief that most large contributions to mathematics are made earlier in one's life (obviously there are exceptions).

  • dunno the source https://drive.google.com/file/... [google.com]
  • by SmilingBoy ( 686281 ) on Monday September 24, 2018 @06:33AM (#57366774)

    Here is the paper with the alleged proof:

    https://drive.google.com/open?id=17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY [google.com]

    I never took proper mathematics at university so cannot begin to claim to understand any of it, but maybe someone else can.

    • And here is a (poor-quality) video of Atiyah's presentation:

      https://twitter.com/HLForum/status/1044131411723264000 [twitter.com]

    • Re: (Score:3, Interesting)

      by Anonymous Coward

      It "proves" the hypothesis for pretty much any function, not just the Riemann zeta function. Which... doesn't make sense. I mean, it just says "this holds for most any function, no need to even look at the Riemann zeta specifically, it's just an obvious corollary."

      It's like saying "pick any number. OK here's proof it's at most 4. This proves graphs can be four-colored."

    • Re: (Score:2, Informative)

      by Anonymous Coward

      Here is the paper [2] he cites everywhere that does all of the heavy lifting in the proof.

      https://drive.google.com/file/d/1WPsVhtBQmdgQl25_evlGQ1mmTQE0Ww4a/view

    • Re: (Score:2, Interesting)

      by Anonymous Coward

      I am a mathematician (PhD in cryptography to be precise) and these 5 pages to me look like written by God itself, or whatever closest to the idea of.

      I am not qualified enough to comment on the subtleties of the underlying results used as building blocks (i.e., von Neumann and Hirzenbruch's works on the T function), but if this proof goes through it might easily turn out to be the legendary math achievement of this century.

      Seriously, WTF :|

      P.S.: Captcha: topology

    • Re: (Score:3, Funny)

      by Anonymous Coward

      My favorite line from the proof is "a weakly analytic function of a weakly analytic function is weekly analytic". One wonders what it is on the other six days.

  • by Impy the Impiuos Imp ( 442658 ) on Monday September 24, 2018 @07:42AM (#57366948) Journal

    While dividing by 1 is a well-defined mathematical operation, I question if "dividing" by 1, alone among all numbers, is really dividing anything at all. "Numbers only divisible by themselves" seems a better simple description and avoids the pedantry.

    • The best description of the nature of a prime number, and the one that's never used - even though it would likely be the most helpful to high school students - is that a prime number is an integer value that cannot be arranged in a grid. Give a child thirteen draughts pieces, and see if they can find a way of arranging them in a grid pattern that isn't just a single row of counters.

      The formal mathematical statement needs the '1' though, because '1' is a number, and it does divide every other number. So you'

There's no sense in being precise when you don't even know what you're talking about. -- John von Neumann

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