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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."
Would be a shame if he went out looking like a crackpot.
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.
This is going to break my favourite captcha.
No. Encryption isnt affected by a proof that its true or false
You can download it for free now -- so to speak, kinda.
Take the cheese to sickbay, the doctor should see it as soon as possible - B'Elanna Torres, "Learning Curve"
Actually many theorems on prime numbers rely on the hypothesis that Riemann's conjecture is true. A proof of it would only confirm them.
Not at all.
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.
It sounds like a joke or a less-than-serious effort.
Why would an esteemed mathematician denigrate his own forthcoming work with a self-described "simple proof"? That qualification should be raising a lot of red flags.
*many* nontrivial zeroes of the Riemann zeta function calculated with high accuracy.
Yeah, it isn't enough to know them with just a few decimal points' accuracy ;-)
Was he a "sir" before that, or was he "sired" because he proved that?
Slashdot, fix the reply notifications... You won't get away with it...
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.
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.
I tend to rant.
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.
On a long enough timeline, the survival rate for everyone drops to zero.
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.
Also, opinion is running against him presenting a viable proof, see e.g. this commentary (in German however).
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.
Oval office blow jobs must be a thing of the past?
Watched his presentation...Wasn't much more that what was in his preprint. He lays *some* groundwork for *a* solution to Reimann, but it's not comprehensive, and he doesn't grind out the legwork himself.
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
Yes, laid under the grass.
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.
Good job ignoring 80 years of change.
But at least you speak asshole like a native!
Use this one simple proof the IRS doesn't want you to know about to legally avoid owing any tax!
This one simple proof will make you a math genius overnight!
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Call me when it's not some internet scam.
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.
I tend to rant.
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.
You mean that it would take that long to run all the calculations. But you might find the solution on the very first calculation. Or on the very last.
I do not understand why you think it would. Every single prime that we presently know is prime, we obviously know their exact location, so why would knowing where new primes are make encryption broken?
Yes, in the same way quantum uncertainty *may* randomly teleport you to Mars.
Some things are unlikely enough we can just assume they will never happen.
Why would a formal proof of something that has been known for 160 years have any effect whatsoever on encryption? Stop shitposting.
See my subject: Mr. Musk's a man after my own heart (& so is this mathematician) - they're out doing useful good things of value.
* Too bad more of them don't post OR read here (& that there isn't MORE OF YOU doing the same).
APK
P.S.=> I blocked twitter off so I can't read what the man said, but I'm sure it's interesting - I do, however, wonder WHY a man of his stature in the world wouldn't use his REAL name here (especially vs. a FAKE "registered 'luser'" name)? That's HOW you get noticed & yes, it takes balls (since there are SO MANY of what I call JEALOUS "Lil' Jowie" types around here that take potshots @ those doing good things but THEY THEMSELVES are do-nothing "ne'er-do-well" zeros (& they know it))... apk
Thanks Russia.
Isn't it great that that enemy agitators can post anonymously ?
5 out of 6 people enjoy Russian Roulette & 6 out of 7 Dwarfs are not Happy
Cool story, libtard.
This would seem to have an impact on cryptography as well???
What like life forming on a tiny little rock orbiting an insignificant lonely sun somewhere in the outer spiral of the milky way?
I hope he wrote it down. At 90, the chances of him living to present the proof at all are diminishing.
SJW: a person who perceives an injustice, and while correcting it, commits a greater injustice.
Isn't it unfortunate? -- fixed it
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.
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.
I'm sure they have better thing to do than come here to read this drivel
Time for bed, said Zebedee - boing
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 ?
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.
Technically this proof will make asymmetric keys like RSA easier to solve but by a very tiny amount. The computational requirements to brute force attack will still be many multiples of the lifetime of the universe though.
Well, there's spam egg sausage and spam, that's not got much spam in it.
Good job ignoring 80 years of change.
plus ça change, plus c'est la même chose
Doubtful.
The dude wants his 15 minutes of fame, then it's back to the gutter.
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 & skipping those same overlooked primes.
It's kind of like saying "I have an 8-character password" & assuming it's equal to 64 bits of entropy (8 single-byte chars x 8 bits/byte). In reality, an attacker knows that it's likely to use only a tiny subset of values (characters that can be directly typed with a normal US keyboard), and likely that they're used in a way that vaguely resembles English words, dates, etc. So it's REALLY more like 50-55 bits at best, and more like 30-40 bits in reality.
In the same way, a "weak" key whose generation ignored a deterministic subset of potential values might "have" 4096 bits if you blindly counted the size of the largest possible values for each prime & added them up, but there might only be 2^128 actual primes within that universe of values, and only 2^48 primes a weak keygen might have actually chosen from.
In other words, the historical problem RSA has had with Riemann isn't that it might be "wrong", but rather that it (or ESPECIALLY software implementations of it) might be TOO conservatively "right" (never mistaking a non-prime for a prime, but occasionally determining that an ACTUAL prime is non-prime).
At worst, if Riemann were "proven" wrong (by identifying non-primes it identifies as prime), it might mean there are a few RSA keys that are fundamentally-flawed & using non-prime numbers, but in real life now, it's more likely for an implementation of it to be flawed... the underlying theory itself has generally worked as expected. The thing is, in advanced math, "always works for me" isn't good enough... formal proof is much more rigorous & difficult.
I'm sorry but old geezers don't create breakthroughs. He is old, senile, and deluded.
Real mathematics is a young man's game. By the time someone hits 40, it's all over, mathematically speaking.
Really, all it'll do is making IDing primes easier which makes the front end of prime factoring just a tiny hair faster.
"Truth is what works" -- William James "It works!!" -- o-dark-AM comment
In year 100,000 what is the value of the secret that was locked by encryption? Congrats you can spoof my credit card now that I'm long dead. And second, aren't you assuming that new encryption techniques to locking secrets hasn't been developed in 99,882 years?
Well, there's spam egg sausage and spam, that's not got much spam in it.
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. Likewise, it would almost never pick the larger twin.
Says you UNIDENTIFIABLE anonymous nobody do-nothing "ne'er-do-well" vs. 30 reviews by registered /.ers on quality/efficacy of my work https://tech.slashdot.org/comments.pl?sid=12478398&cid=57130680/ https://tech.slashdot.org/comments.pl?sid=12478398&cid=57137806/ https://tech.slashdot.org/comments.pl?sid=12478398&cid=57137868/ https://tech.slashdot.org/comments.pl?sid=12478398&cid=57137916/ https://tech.slashdot.org/comments.pl?sid=12478398&cid=57137944/
* Want more? Ask & "ye shall receive" (like 100,000++ users of my program WORLDWIDE...)
DO THEY DO THAT FOR YOUR NON-EXISTENT WORK? No.
I'm not here to win some "highschool popularity contest" - I'm here to WIN so everyone online does vs. threats.
Your kind (lowest of the LOW do-NOTHING "ne'er-do-well" chatterboxes) does nothing but LOSE & you know it (by comparison).
APK
P.S.=> Truth is, you MUST detest yourself since you HIDE behind UNIDENTIFIABLE anonymous posts STALKING me constantly you loser... apk
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! :)
I tend to rant.
In that case it'll only take 10^112 times the lifetime of the universe. Put the kettle on, I'll be right over.
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 ?
Mathematically then it would take 1x10^111 times the age of the universe to break...
This claimed proof of the Riemann hypothesis does not seem right even on a cursory reading. The general structure of the proof is a proof by contradiction. It assumes the existence of a zero off the critical strip and then supposedly derives a contradiction. However, it does not even seem to use the hypothesis that the zero actually is off the critical strip, or even the basic properties of the zeta function.
"What lies behind us, and what lies before us are tiny matters compared to what lies within us." Ralph Waldo Emerson
Anyone attacking asymmetric encryption is simply going to assume the Riemann Hypothesis; knowing that for sure it's true is not going to do anything but change some theoretical upper bounds.
EC discrete log cannot be reduced to factoring (though it is correct that it's still not post-quantum, and for essentially the same resasons).
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
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.
Yep. So instead of assuming they have to try an estimated kajillion primes, now they'll know the exact number of kajillion primes they have to try.
Well, there's spam egg sausage and spam, that's not got much spam in it.
Assuming he's correct, does this mean that the Prime95 app is now obsolete?
Just like I said, jillions! :-) (ok, ln(n) ;-)
Ok, li(n) if you want to get a little closer..
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?)
In the *infinite* universe.
Given the chance was *finite* even if very small, it *had* to happen somewhere.
45 5F E1 04 22 CA 29 C4 93 3F 95 05 2B 79 2A B2
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 0000000000 00001% eventually.
You increase the efficiency hundredfold, you just cut 2 out of the 10^112 times the age of the universe, now you're at 10^110. You increase the efficiency tenfold every year, you'll be at "age of the universe" in 110 years.
45 5F E1 04 22 CA 29 C4 93 3F 95 05 2B 79 2A B2
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 if you could break the encryption in 2 years time, how valuable would that particular piece of information be? Congrats you've gotten a credit card that someone may not be using anymore.
Well, there's spam egg sausage and spam, that's not got much spam in it.
You missed a perfect opportunity for a Beowulf cluster joke.
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?