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Famed Mathematician Claims Proof of 160-Year-Old Riemann Hypothesis (soylentnews.org)
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."
"[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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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.
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.
UNIX? They're not even circumcised! Savages!
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.
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It *is* raising red flags, because mathemeticians are skeptical that such a well known and long standing conjecture such as Riemann could have a relatively simple proof that hasn't already been found, even without the $1m incentive to go looking. Like Fermat, I don't think we're talking about a "relatively simple proof" that will fit in the margin of a book here, but it is certainly possible that he's managed to find some new approach in the works of von Neumann, Hirzebruch, and Dirac that is still simpler than - say - Andrew Wiles' proof of Fermat's Last Theorem, let alone Shinichi Mochizuki’s claimed proof of the ABC Conjecture.
UNIX? They're not even circumcised! Savages!
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.
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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."
Correct - let me put it in numbers better than "jillions".
Starting with sqrt(semi-prime) and going downwards (one of the primes must be necessarily lower-or-equal than that, the other greater-or-equal) , testing only divisibility of the number by the primes, without first finding whether a number is a prime through factorization, you're still left with ~10^151 "is x a factor of the semi-prime?"" tests - instead of ~10^155 numbers to go through "is x a prime, and if so, is x a factor of the semi-prime?".
It's a massive reduction of computational complexity but still useless in the grand scheme of things, because 10^151 is such a ridiculously huge number. If the operation of finding the next prime and checking if the semi-prime is divisible took a single CPU cycle of a 10GHz processor in a cluster of 100,000 such processors, it would still take about 10^117 times the age of the universe.
45 5F E1 04 22 CA 29 C4 93 3F 95 05 2B 79 2A B2
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