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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."
Um, no. Symmetric encryption algorithms have nothing to do with prime numbers, and the asymmetric ones that do (like RSA) aren't going to be any easier to solve just because someone proved the Riemann hypothesis. The RSA problem is prime factorisation, which is something completely different.
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To predict the prime numbers, you need *many* nontrivial zeroes of the Riemann zeta function calculated with high accuracy. How many are we talking about I have no real idea, but the one million zeroes published by Andrew Odlyzko aren't sufficient very far.
Ironic that Slashdot are now quoting stories from SoylentNews, because they get there first and have better coverage.
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.
Actually many theorems on prime numbers rely on the hypothesis that Riemann's conjecture is true. A proof of it would only confirm them.
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.
Live today, because you never know what tomorrow brings
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.
Schroedinger's Brexit: The UK is both in and out of the EU at the same time!
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".
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
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.
Or when Astronomers say "soon" and actually mean 1 million years.
Take the cheese to sickbay, the doctor should see it as soon as possible - B'Elanna Torres, "Learning Curve"
One sponsored by the paper industry, I'm sure.
We used to have a Bill of Rights. Now, with the rights gone, all we have left is the bill.
Here is the paper with the alleged proof:
https://drive.google.com/open?id=17NBICP6OcUSucrXKNWvzLmrQpfUrEKuY
I never took proper mathematics at university so cannot begin to claim to understand any of it, but maybe someone else can.
I think it's probably the fittingly named "Enormous Theorem" on Symmetry that took dozens of mathemeticians decades to complete. That runs to over 15,000 pages just for the calculations, and even the "guide" runs to a further 1,200 pages.
UNIX? They're not even circumcised! Savages!
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
EC is not post-quantum, and the problem of solving Elliptic Equations can be turned into a factoring problem
The results of the Riemann hypothesis are already Conjectures in number theory - The Theorem being True or False is a Binary condition ---- So if the Riemann theorem being true had ANY breakthrough affect at all, then people trying to crack codes could already have TRIED the assumption that the hypothesis was true (or at least good enough) to test their cracking procedures that would only work if the supposed Hypothesis to be true.
Knowing the Truth or Falseness of 1 bit (The Riemann Hypothesis) doesn't suddenly make cracking easier --- If the value of the Truth was 1, then tests carried out depending on methods developed from the RH would already have been shown to be useful.
He has now given his talk, and presented his "proof". The overwhelming consensus of qualified mathematicians is that it proves nothing.
Here is a summary of the talk which includes a photo of his proof.