## Possible Proof of ABC Conjecture 102 102

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."*
## Re:Rarely much smaller than? (Score:5, Informative)

## Re:Rarely much smaller than? (Score:5, Informative)

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

## Re:Rarely much smaller than? (Score:4, Informative)

"Rarely much smaller than"? What kind of mathematical statement is that? Are we to assume that most of the time, d is somewhat smaller than c? Are there conditions where d is larger than c? How are you supposed to get anything done with vague statements like "rarely much smaller than"?

There exists mathematical statements which sounds rather "unmathematical" at first, as an example, "almost everywhere" has a precise meaning in measure theory.

http://en.wikipedia.org/wiki/Almost_everywhere

## See Peter Woit / Not Even Wrong (Score:5, Informative)

Peter had a pretty good first glance reaction to the paper: http://www.math.columbia.edu/~woit/wordpress/?p=5104 [columbia.edu]

I haven't seen any good discussions of the actual math content of the paper yet though.

## Re:Linking to Wikipedia to explain math (Score:4, Informative)

Which makes it even more non-sensical to post it here, on slashdot, a general-interest geek site, where only very few are working mathemeticians or grad students.

A page like this: http://abcathome.com/conjecture.php [abcathome.com] would have been more apropos. No reaching for the jargon, and an actual mini-tutorial on what an ABC triple is and what the conjecture is.

--

BMO

## Good discussions on math content (Score:4, Informative)

See http://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture for a discussion on the mathematical content by experts.