4 ms·

It's kind of the opposite scenario (a mathematical result that people are widely skeptical of, but that could be correct), but this reminded me, I wonder what's

It's kind of the opposite scenario (a mathematical result that people are widely skeptical of, but that could be correct), but this reminded me, I wonder what's going on with Mochizuki's proof of the ABC conjecture.

jfengel 3y ago
The proof situation is pretty much unchanged. The proof uses a very obscure branch of mathematics, so that few people are capable of a real critique. Those few have mostly said that it's not complete, but Mochizuki and a few others disagree. It's kind of a philosophical question at this point about what actually comprises a valid proof, if other mathematicians can't make use of it. So the conjecture is still mostly considered unproven. That could change at any point but there have been no real advances in some time.
- vbezhenar 3y ago
  Make proof using computer system, obviously.
  - alimw 3y ago
    Mochizuki is unenthusiastic. [1] Section 1.12 of https://www.kurims.kyoto-u.ac.jp/~motizuki/Essential%20Logical%20Structure%20of%20Inter-universal%20Teichmuller%20Theory.pdf https://www.kurims.kyoto-u.ac.jp/~motizuki/Essential%20Logic....
- eddiewithzato 3y ago
  everything relies on consensus anyway
- preommr 3y ago
  > very obscure branch of mathematics This is an understatement. He developed a completely different branch of mathematics through papers that spanned hundreds of pages with very dense and very different ideas from mainstream mathematics. If it was just slightly obscure, maybe all but half a dozen mathematicians in the world might be able to understand his work. As it stands, at it's best, his proof is so opaque that even the brightest (Scholze) can only kind of understand it. At it's worst, they've rightfully identified it as flawed and that even Mochizuki himself doesn't understand that it's wrong.
bsder 3y ago
> what's going on with Mochizuki's proof of the ABC conjecture. The assumption at this point is that it's broken. The onus is on Mochizuki to either clarify the proof or use the tools of the proof on some other already established problem to show their validity.

jfengel 3y ago

The proof situation is pretty much unchanged. The proof uses a very obscure branch of mathematics, so that few people are capable of a real critique. Those few have mostly said that it's not complete, but Mochizuki and a few others disagree. It's kind of a philosophical question at this point about what actually comprises a valid proof, if other mathematicians can't make use of it. So the conjecture is still mostly considered unproven. That could change at any point but there have been no real advances in some time.

vbezhenar 3y ago
Make proof using computer system, obviously.
- alimw 3y ago
  Mochizuki is unenthusiastic. [1] Section 1.12 of https://www.kurims.kyoto-u.ac.jp/~motizuki/Essential%20Logical%20Structure%20of%20Inter-universal%20Teichmuller%20Theory.pdf https://www.kurims.kyoto-u.ac.jp/~motizuki/Essential%20Logic....
eddiewithzato 3y ago
everything relies on consensus anyway
preommr 3y ago
> very obscure branch of mathematics This is an understatement. He developed a completely different branch of mathematics through papers that spanned hundreds of pages with very dense and very different ideas from mainstream mathematics. If it was just slightly obscure, maybe all but half a dozen mathematicians in the world might be able to understand his work. As it stands, at it's best, his proof is so opaque that even the brightest (Scholze) can only kind of understand it. At it's worst, they've rightfully identified it as flawed and that even Mochizuki himself doesn't understand that it's wrong.

bsder 3y ago

> what's going on with Mochizuki's proof of the ABC conjecture. The assumption at this point is that it's broken. The onus is on Mochizuki to either clarify the proof or use the tools of the proof on some other already established problem to show their validity.