Slashdot Mirror
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.
Elon Musk apparently reads Slashdot: https://twitter.com/elonmusk/s...
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.
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.
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!
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.
dunno the source https://drive.google.com/file/...
-- mg
...And even if the proof is were constructive, why would knowing prime locations allow for you to factor semi-primes (the product of two primes)?
You might know where the primes are but theres still jillions to check when you're talking about 1024bit numbers....
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.
Calling a proof "simple" is not an insult to a mathematician: it is a compliment.
You think he is denigrating his work while he is really bragging in a way that is so over your head that you think it is beneath you.
Ask me how I know you aren't a mathematician.
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.
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
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.
(-1: Post disagrees with my already-settled worldview) is not a valid mod option.
Nope.
https://math.stackexchange.com...
And elliptic curve cryptography has even less to with primes. Nor most of the "post-quantum" cryptography already available.
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.