Numbers have become more real. A few more discoveries like this and you'll be able to hold a 2 in your hand.
Someone will make a thread on GAF about it, and you will post in that thread.
Respect for these posts. Each one made me laugh.Triangles as we know it will never be the same. Keep this next part under your hat though.... word on the street is this may effect a couple rectangles as well. If I were you I'd put all my money into circles. You just never know.
Hah, if there's an easy way to test primes, hacking also got so much easier.
As someone who is in precalculus, I can confirm your suspicions that being able to count oneself among the "mathematical elite" is indeed awesome.
I'd like to share a quote by John von Neumann, one of the greatest mathematicians of the 20th century:
"A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful."
Mathematics is quite often developed well before any practical use is known. The field of number theory, of which this problem is from, was thought to be completely useless in the real world for a long time. That is until people realized it had major implications in cryptography, which has done things such as help break Nazi codes in World War II to powering encrypted internet communications today. Stating that a new advancement in mathematics is "theoretical wankery with no practical application" is only really showing how very clueless about the subject you are.
this sounds like theoretical wankery with no practical application but maybe I'm wrong.
and yours is a terribly useless one. If you have some arcane knowledge about this that the rest of us don't then please, share.
I honestly can't understand a word of that :lol
Mathematics is like a completely different language
I know that this is a copy/paste, but I think you should have modified the text to say something more like a^n + b^n = c^n since we don't have superscript.
this sounds like theoretical wankery with no practical application but maybe I'm wrong.
It is believed by many that artificial intelligence could rely on solutions to NP problems.
Jordan Ellenberg at Quomodocumque reports here on a potential breakthrough in number theory, a claimed proof of the abc conjecture by Shin Mochizuki.
...
Jordan is an expert of this kind of thing, and he has some of the best mathematicians in the world (Terry Tao, Brian Conrad and Noam Elkies) commenting, so his blog is the place to get the best possible idea of what is going on here. After consulting a couple experts, it looks like this is a very interesting and possibly earth-shattering moment for this field of mathematics.
That's true, but man, forget quantum computing. If this pans out, we're probably already fucked right now. lol
I would half disagree here, and say only a perfect AI that's always right would need to rely on solutions to NP problems. If you're going for human-like AI, heuristic and probabilistic algorithms are good enough, and probably better, since those algorithms are both faster and occasionally make mistakes (as humans do).
I don't fucking get it, but way to go Japanese fellow! Thanks for advancing humanity.
See shit like this is important because a dude way smarter than us may have solved a problem which may, in the future, help other dudes way smarter than us make life better for our ancestors.
That's really the best way a layman can grasp it, I guess.
Hrm, then I suppose it becomes a question of whether or not computer scientists can turn this proof into some kind of working methodology/algorithm then?The thing about a rigorous analytical proof of something like this is that it's just a confirmation. Things like the Riemann hypothesis or Fermat's Last Theorem were always assumed true and tested for astronomical amounts of numerical combinations. It was already "true" (just like the above and many other mathematical conjectures), this just proves it analytically.
I'm going to admit my ignorance here, because I haven't seriously thought about math in nearly a decade, but iirc a lot of encryption (at least 5-10 years ago) is based on the idea that it's not trivial to test whether or not large numbers or prime. So if there's a way to easily test a number, then people need to figure out new math to make things secure again.Wait... how?
i think you meant descendants?
Not unless he's hoping time travel gets invented! I mean, what if our ancestors only survived due to someone in the future traveling back to them and teaching them basic sciences like agricultural?
wouldnt an error prone (closer to human like) AI defeat the purpose?....
Not unless he's hoping time travel gets invented! I mean, what if our ancestors only survived due to someone in the future traveling back to them and teaching them basic sciences like agricultural?
Nearly all encryption techniques are built on the fact that factoring products of large prime numbers are difficult. Like, it would take longer than the universe has currently existed long, given enough digits, whereas multiplying the primes to generate said number would take about a minute or so. If we can factor large numbers quickly, well, all that stuff you thought was private is, well, no longer private. You'd be able to crack codes in milliseconds. The fact that there's no quick way to factor large numbers (of which ones made by large prime numbers are exceptionally difficult) is what keeps current encryption algorithms working.
See http://en.wikipedia.org/wiki/Integer_factorization
I was gonna post that but then it's a 500 page proof right now...
What if...
what if we evolved into the greys and made ufos and time travel and went back in time and taught ourselves?
i think you meant descendants?
Whoops, I missed this. Basically what he said. lolNearly all encryption techniques are built on the fact that factoring products of large prime numbers are difficult. Like, it would take longer than the universe has currently existed long, given enough digits, whereas multiplying the primes to generate said number would take about a minute or so. If we can factor large numbers quickly, well, all that stuff you thought was private is, well, no longer private. You'd be able to crack codes in milliseconds. The fact that there's no quick way to factor large numbers (of which ones made by large prime numbers are exceptionally difficult) is what keeps current encryption algorithms working.
See http://en.wikipedia.org/wiki/Integer_factorization
http://www.nature.com/news/proof-claimed-for-deep-connection-between-primes-1.11378
The several papers cited above that cover the proof:
Mochizuki, S. Inter-universal teichmuller theory I: construction of Hodge Theatres (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory I.pdf
Mochizuki, S. Inter-universal teichmüller theory II: HodgeArajekekiv-theoretic evalulation (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory II.pdf
Mochizuki, S. Interuniversal teichmüller theory III: canonical splittings of the log-theta-lattice (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory III.pdf
Mochizuki, S. Interuniversal teichmüller theory IV: log-volume computations and set-theoretic foundations (2012). available at http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal Teichmuller Theory IV.pdf
And the mathematician's home page: http://www.kurims.kyoto-u.ac.jp/~motizuki/papers-english.html
Just to clarify, this affects public key encryption, like SSL connections to websites, not private key encryption, like password-encrypted hard drives.Whoops, I missed this. Basically what he said. lol
It's a total game changer if testing primes is trivial.
So what are the consequences in real life?
Nearly all encryption techniques are built on the fact that factoring products of large prime numbers are difficult. Like, it would take longer than the universe has currently existed long, given enough digits, whereas multiplying the primes to generate said number would take about a minute or so. If we can factor large numbers quickly, well, all that stuff you thought was private is, well, no longer private. You'd be able to crack codes in milliseconds. The fact that there's no quick way to factor large numbers (of which ones made by large prime numbers are exceptionally difficult) is what keeps current encryption algorithms working.
See http://en.wikipedia.org/wiki/Integer_factorization