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."
"[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."
I hope it's real (Score:1)
Would be a shame if he went out looking like a crackpot.
Re:I hope it's real (Score:5, Interesting)
Re:I hope it's real (Score:5, Interesting)
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.
Re: I hope it's real (Score:2)
Re:I hope it's real (Score:5, Funny)
And I will respectfully get off his lawn in exchange for a single hard candy.
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"Anyone here" ... ?
Some of us still stop by and lurk.
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Not yet. Just too old to have enough patience for the stupidity - which is odd, 'cause I've found even dumber people and have set about seeing if I can motivate them to at least learn something new every day.
It's pretty futile, but it amuses me.
Re: I hope it's real (Score:2)
Re:I hope it's real (Score:5, Interesting)
Re: I hope it's real (Score:2)
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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)
Elon Musk apparently reads Slashdot: https://twitter.com/elonmusk/s... [twitter.com]
Re:Elon Musk (Score:5, Funny)
Donald Trump apparently edits Slashdot.
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Elon Musk apparently reads Slashdot: https://twitter.com/elonmusk/s... [twitter.com]
Bless his heart. He must have a strong stomach.
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Elon Musk apparently reads Slashdot: https://twitter.com/elonmusk/s... [twitter.com]
Of course he does. Great minds crowdsource and synthesize other great (and mediocre) minds.
Come on Elon... come clean, what is your handle?
Re:Elon Musk (Score:4, Funny)
"This 160 year old hypothesis might finally be proven!!!" ... yeah but... Did anyone notice Elon Fucking Musk reads Slashdot?!?!?
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Elon Musk apparently reads Slashdot
No wonder Tesla and SpaceX projects are always late, and he never looks like he's getting enough sleep...
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Lol (Score:5, Informative)
Ironic that Slashdot are now quoting stories from SoylentNews, because they get there first and have better coverage.
Re:Lol (Score:5, Funny)
Yes, like rain on a wedding day.
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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.
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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.
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Look at the number of digits in the UID.
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I was being sarcastic.
Oh, no!!! (Score:2)
That car you've always wanted?? (Score:2)
You can download it for free now -- so to speak, kinda.
Possible, but unlikely (Score:3)
This has been a marquee unsolved problem in Mathematics for over 150 years.
Any simple proof would have been found long ago.
Re:Possible, but unlikely (Score:5, Interesting)
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.
Re:Possible, but unlikely (Score:5, Insightful)
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".
Re:Possible, but unlikely (Score:5, Insightful)
Or when Astronomers say "soon" and actually mean 1 million years.
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Actually, the proof is 15-lines long and relies on a proof-by-contradiction (similar to the proof that the number of prime numbers is infinite).
You can find the video of the presentation here: https://www.youtube.com/watch?... [youtube.com]
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Exactly this.
It's like saying there's an easy fix to a bug that QA just uncovered.
To people who understand the problem, it may seem obvious and easy, yes.
It's dangerous wording however, because those who misunderstand the problem and/or technical details to it might interpret it as "It'll be fixed in 5 minutes." Causing those in the know-how to be under unreasonable pressure.
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I'm pretty sure it can be explained in 5 minutes.
Learning what's required to understand it takes about 60 years, though.
Re:Possible, but unlikely (Score:4, Funny)
One sponsored by the paper industry, I'm sure.
Re:Possible, but unlikely (Score:5, Informative)
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Unlikely != impossible (Score:3)
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.
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The guy is just being modest.
Indeed, he proved it at 20, 70 years ago, and decided to publish it only now.
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Brits question (Score:2)
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Before. It's pretty clear actually.
Disclaimer: Not British.
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"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
Caution... (Score:2)
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.
90 years old? (Score:2)
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.
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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).
the paper? (Score:2)
Here is the paper with the proof (Score:5, Informative)
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.
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And here is a (poor-quality) video of Atiyah's presentation:
https://twitter.com/HLForum/status/1044131411723264000 [twitter.com]
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And a better quality video:
https://www.heidelberg-laureate-forum.org/blog/video/lecture-monday-september-24-2018-sir-michael-francis-atiyah/ [heidelberg...-forum.org]
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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."
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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
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In the paper he claims the result of (1/alpha) is "137.035999..." - Wikipedia says 137.035999139 (2014 CODATA recommended value). So is there a new value? Or did his formula give a different outcome?
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Oh ouch. Okay, I'll take a look again. But if that's it, the paper's dead. As suspected. Too bad. Would have been nice :)
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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
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Well, since we math types just learned yesterday that physicists now have to contend with a contradiction in their most cherished thought experiment (new version of Schrodingers cat), I think we will just leave you to ponder that while we calculate how the universe works :)
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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.
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I'm afraid the real link will disappoint you.
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The paper I linked to without any "goatse guy" but just some maths.
Division I (Score:3)
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.
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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'
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executing the check and branch may take longer than the division.
Re: There goes most encryption (Score:5, Informative)
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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Yeah.... I'd love to see what the claimed proof is. It's interesting to note that there is a $1 Million prize for proving the hypothesis true, with requirement that the solution itself must create significant "progress" in the understanding of mathematicians on the subject of the problem (?), but there's no prize for bringing to light ways of constructing working counterexamples that would prove the Riemann Hypothesis as presented false by contradiction.
Re: There goes most encryption (Score:5, Informative)
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 [twitter.com] which includes a photo of his proof.
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But at least you speak asshole like a native!
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Really, all it'll do is making IDing primes easier which makes the front end of prime factoring just a tiny hair faster.
Re: There goes most encryption (Score:2)
Re:There goes most encryption (Score:5, Insightful)
Re:There goes most encryption (Score:5, Informative)
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Not at all.
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If the commentary is accurate, then we can kiss goodbye to a large chunk of encryption in use today. I wonder how we will adapt.
Your interpretation of the commentary is inaccurate. You can kiss yourself goodnight and know your WoW account will still be yours when you wake-up, child.
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Nope.
https://math.stackexchange.com... [stackexchange.com]
And elliptic curve cryptography has even less to with primes. Nor most of the "post-quantum" cryptography already available.
Re:There goes most encryption (Score:5, Insightful)
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.
Re:a "simple proof"? (Score:5, Interesting)
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"even without the $1m incentive to go looking"
What difference would a $0.001 reward make?
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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.
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A simple proof is similar to an elegant proof. It's direct and to the point.
If I recall correctly, the Four Color Map Theorem was proved by chasing down over a hundred special cases and proving each one with computer help. That would not qualify as elegant or simple.
Re: If Prime locations can be methodically determi (Score:2)
AFAIK, RSA key generation uses a Riemann-inspired algorithm to reduce the time it takes to generate a new key by making it faster to determine whether or not a particular large number is LIKELY to be prime (and thus, a candidate or non-candidate for use in the key).
As I understand it, early RSA keygens produced "weak" keys because their algorithm OVERLOOKED many primes & prematurely eliminated them as candidates. So, an attacker could considerably reduce the number of keys to try by identifying & sk
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As I understand it, early RSA keygens produced "weak" keys because their algorithm OVERLOOKED many primes
An early implementation generated primes by picking a random odd number, and then stepping forward by twos, testing each number for primality until it found one.
This made it much more likely to pick primes that are preceded by a large interval of composites ... which are probabilistically more likely to be the smaller of a pair of twin primes [wikipedia.org]. Likewise, it would almost never pick the larger twin.
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...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....
Re: If Prime locations can be methodically determi (Score:5, Interesting)
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.
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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.
Thank you for this. I always love reading about these things when defined in the terms you've set them out in.
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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
What about on 100,000 year 2020 GPUs that have 100000 CUDA cores per GPU = 10,000,000,000 number crunchers churning away at 10GHz = 100,000,000,000 core GHz, Versus your simple 1-core CPUs that only had 1,000,000 core GHz ?
Re: If Prime locations can be methodically determ (Score:2)
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While your example is true it doesn't hold up to, say, an archaeological team trying to extract information from an encrypted hard drive to piece together a story from our era.
You may find this silly, conceptually. But I promise you there are people who would use these decryption techniques for these very reasons; were they put in that scenario today.
Your credit card number might actually be part of that story, to prove you made transaction X, leading to the demise of humanity as we know it! :)
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In year 100,000 what is the value of the secret that was locked by encryption?
Who said anything about year 100,000 ? I was talking about the year 2020.
The rate of compute density acceleration by Moore's law is exponential. In other words Compute Available(t years) = c0 * c1^(t/c2) + c2
where t is the number of years from a given date, and c2 > 0, c0 > 1, c1 > 1, 0
Re: If Prime locations can be methodically determ (Score:2)
First of all you are assuming that Moore's law actually means the actual computing power increases by same amount of cores. None of which is actually a correlation. Moore's law deals with transistors not cores. And increasing the number of cores (and in this case CUDA cores) means increase in actual performance by the same rate.
With all that said and done, congrats you've reduced the computational time from many exponents of lifetime of the universe to fewer exponents of lifetime of the universe. And even i
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There's not a whole heck of a difference between 10^117 and say 10^116.. (you think we'll get a 10x speedup by then?)
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I thought it was already understood that in 10-20 years it would likely be a Beowulf cluster of 100,000 Raspberry Pis Version 8 with this much processing power in an On-Board GPU?
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Just like I said, jillions! :-) (ok, ln(n) ;-)
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Ok, li(n) if you want to get a little closer..
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If you have a list of keys you're interested in cracking, AND a way of iterating through the semiprimes randomly, AND each each semiprime has an equal chance of being the one used, then EVERY operation you complete increases the probability that you will have found one of the keys you were looking for. It may be less than 1% at first, but it will eventually grow in probability until you search the entire space.
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If finding a prime becomes negligibly cheap, then testing n semi-primes against that prime, vs testing one semi-prime against n primes become equally costly.
" It may be less than 1% at first,"
Way to oversell.
It will be less than
0.0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 00000000001% at first. But it will grow in probability until it's only
0.0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000
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In the *infinite* universe.
Given the chance was *finite* even if very small, it *had* to happen somewhere.
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Thanks Russia.
Isn't it great that that enemy agitators can post anonymously ?
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