Possible Proof of ABC Conjecture

submeta writes "Shinichi Mochizuki of Kyoto University has released a paper which claims to prove the decades-old ABC conjecture, which involves the relationship between prime numbers, addition, and multiplication. His solution involves thinking of numbers not as members of sets (the standard interpretation), but instead as objects which exist in 'new, conceptual universes.' As one would expect, the proof is extremely dense and difficult to understand, even for experts in the field, so it may take a while to verify. However, Mochizuki has a strong reputation, so this is likely to get attention. Proof of the conjecture could potentially lead to a revolution in number theory, including a greatly simplified proof of Fermat's Last Theorem."

Comments

Re:Rarely much smaller than?

[Garridan]

LMWTFY: http://en.wikipedia.org/wiki/Abc_conjecture#Formulations.

Re:Rarely much smaller than?

[Gilandune]

That is precisely the point of the proof, to determine under which conditions the sum of 2 integers is less than the product of the prime divisors of the 3 original numbers. I hope that is less vague :P

This has already been worked on...

[Anonymous Coward]

...and solved. I think it was the early (19)70's. A researcher named Jackson
(with the help of his brothers) came to the conclusion that it was simple as 1-2-3.
Additional verification shown that do-re-mi fit the bill as well. At the time, people
were sing all about it - I'm surprised this has come up again.

Re:Linking to Wikipedia to explain math

[exploder]

Nobody's measuring anyone's penis--the truth is a lot more boring (and reasonable) than that. Wikipedia is a fantastic first reference for working mathematicians or grad students--I'm sure nearly all math article editors are in these groups--who just want to quickly find out e.g. what the hell an "ultrafilter" is. And so the articles are written in a way that makes them most useful to the people who donate their time to produce them. It's not that any (non-douchebag) mathematician gets off on throwing around smart-sounding jargon. It's just that you can't actually do anything with "intuitive" descriptions.