4 ms·

Math student here. This whole process reflects very poorly on Mochizuki, IMO. The proper thing to do when claiming to have solved a major open problem is to mak

Math student here. This whole process reflects very poorly on Mochizuki, IMO. The proper thing to do when claiming to have solved a major open problem is to make yourself available to the mathematical community, for example by giving lectures on your work. Releasing a preprint on your website and expecting other mathematicians to drop what they're doing and devote years of their time to understand your obscure paper just screams of arrogance. Also, publishing your work in a journal where you are the editor isn't a good look; it gives the impression of a conflict of interest. The critique by Scholze et al is the final nail in the coffin as far as I'm concerned.

antonzabirko 7y ago
Not even all that - it's that he hasn't addressed the issues in his paper.
wolfgke 7y ago
The whole situation is in my opinion much more complicated. Here are some texts from the internet concerning this: David Michael Roberts - A Crisis of Identification: https://inference-review.com/article/a-crisis-of-identification https://inference-review.com/article/a-crisis-of-identificat... Two Quora posts: https://www.quora.com/Did-Peter-Scholze-and-Jakob-Stix-really-find-a-serious-flaw-in-Shinichi-Mochizukis-proof-of-ABC-conjecture/answer/Xiaowei-Xu-1 https://www.quora.com/Did-Peter-Scholze-and-Jakob-Stix-reall... https://www.quora.com/What-do-you-think-about-Stix-and-Scholze-coming-out-and-saying-Mochizukis-proof-of-the-abc-conjecture-is-wrong/answer/Xiaowei-Xu-1 https://www.quora.com/What-do-you-think-about-Stix-and-Schol... Also relevant: https://thehighergeometer.wordpress.com/2019/01/18/taylor-dupuy-on-mochizukis-iutt-infamous-corollary-3-12/ https://thehighergeometer.wordpress.com/2019/01/18/taylor-du...
- hyperpape 7y ago
  Thanks for this. Tao’s comment made quite an impression on me, but important for outsiders like me to remember that the facts on the ground can change as time goes on.
  - Koshkin 7y ago
    To quote, "To take an extreme example, if Mochizuki had carved his argument on slate in Linear A and then dropped it into the Mariana Trench, then there would be little doubt that asking about the veracity of the argument would be beside the point. The reality, however, is that this description is not so far from the truth."
    - chx 7y ago
      That's Frank Calegari's writing at https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/ https://www.galoisrepresentations.com/2017/12/17/the-abc-con... not Tao's. Tao left a comment there: https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/#comment-630 https://www.galoisrepresentations.com/2017/12/17/the-abc-con...
  - kzrdude 7y ago
    Where did you see his comment?
    - chx 7y ago
      https://news.ycombinator.com/item?id=15976979 https://news.ycombinator.com/item?id=15976979 in a comment: https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/#comment-630 https://www.galoisrepresentations.com/2017/12/17/the-abc-con...
  - deleted 7y ago
    [deleted]
akvadrako 7y ago
He has been doing that for years. Are you even familiar with the situation?
- nilkn 7y ago
  The real problem is that his response to Scholze and Stix didn’t manage to convince anyone who wasn’t already in his camp. At this point there is a major and clearly stated objection to the proof out in public to which no reasonable refutation has been offered.
  - wolfgke 7y ago
    > At this point there is a major and clearly stated objection to the proof out in public to which no reasonable refutation has been offered. The problem is: Scholze and Stix formulated their objections to a "simplified" version of IUTT (i.e. they did quite some identifications). Their claim is that these simplifcations do not matter for whether IUTT holds or not, but Mochizuki claims that the details that Scholze and Stix "wiped away" do matter. No side could convince the other side of their position. If you want to dive into the gory details: http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf (Scholze & Stix) http://www.kurims.kyoto-u.ac.jp/~motizuki/Rpt2018.pdf http://www.kurims.kyoto-u.ac.jp/~motizuki/Rpt2018.pdf (Mochizuki) If you love flamewars, read: Ivan Fesenko: Remarks on Aspects of Modern Pioneering Mathematical Resarch; https://www.maths.nottingham.ac.uk/plp/pmzibf/rapm.pdf https://www.maths.nottingham.ac.uk/plp/pmzibf/rapm.pdf
    - zamalek 7y ago
      He didn't give his two biggest critics the time of day. You can't fault them for sticking to their conclusion, the authority to the contrary is completely uninterested in defending their position. We'll probably never know if he actually solved it. Few have the knowledge, fewer had the patience and nobody has had rebuttal. Scholze and Stix conclusions hold exactly as much weight as Mochizuki's. They are unwilling to change their mind and recant, just as much as Mochizuki is. This whole fiasco reflects very poorly on the mathematical community in general.
bsder 7y ago
> This whole process reflects very poorly on Mochizuki, IMO. It's worse than that. At this point, the person who bridges that gap will almost certainly get his name added to the proof--that's a big incentive. The fact that nobody seems to be able to bridge that gap is a gigantic glaring flag that something is wrong.
- wolfgke 7y ago
  > It's worse than that. At this point, the person who bridges that gap will almost certainly get his name added to the proof--that's a big incentive. Taylor Dupuy together with Anton Hilado is attempting this: https://thehighergeometer.wordpress.com/2019/01/18/taylor-dupuy-on-mochizukis-iutt-infamous-corollary-3-12/ https://thehighergeometer.wordpress.com/2019/01/18/taylor-du...

antonzabirko 7y ago

Not even all that - it's that he hasn't addressed the issues in his paper.

wolfgke 7y ago

The whole situation is in my opinion much more complicated. Here are some texts from the internet concerning this: David Michael Roberts - A Crisis of Identification: https://inference-review.com/article/a-crisis-of-identification https://inference-review.com/article/a-crisis-of-identificat... Two Quora posts: https://www.quora.com/Did-Peter-Scholze-and-Jakob-Stix-really-find-a-serious-flaw-in-Shinichi-Mochizukis-proof-of-ABC-conjecture/answer/Xiaowei-Xu-1 https://www.quora.com/Did-Peter-Scholze-and-Jakob-Stix-reall... https://www.quora.com/What-do-you-think-about-Stix-and-Scholze-coming-out-and-saying-Mochizukis-proof-of-the-abc-conjecture-is-wrong/answer/Xiaowei-Xu-1 https://www.quora.com/What-do-you-think-about-Stix-and-Schol... Also relevant: https://thehighergeometer.wordpress.com/2019/01/18/taylor-dupuy-on-mochizukis-iutt-infamous-corollary-3-12/ https://thehighergeometer.wordpress.com/2019/01/18/taylor-du...

hyperpape 7y ago
Thanks for this. Tao’s comment made quite an impression on me, but important for outsiders like me to remember that the facts on the ground can change as time goes on.
- Koshkin 7y ago
  To quote, "To take an extreme example, if Mochizuki had carved his argument on slate in Linear A and then dropped it into the Mariana Trench, then there would be little doubt that asking about the veracity of the argument would be beside the point. The reality, however, is that this description is not so far from the truth."
  - chx 7y ago
    That's Frank Calegari's writing at https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/ https://www.galoisrepresentations.com/2017/12/17/the-abc-con... not Tao's. Tao left a comment there: https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/#comment-630 https://www.galoisrepresentations.com/2017/12/17/the-abc-con...
- kzrdude 7y ago
  Where did you see his comment?
  - chx 7y ago
    https://news.ycombinator.com/item?id=15976979 https://news.ycombinator.com/item?id=15976979 in a comment: https://www.galoisrepresentations.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/#comment-630 https://www.galoisrepresentations.com/2017/12/17/the-abc-con...
- deleted 7y ago
  [deleted]

akvadrako 7y ago

He has been doing that for years. Are you even familiar with the situation?

nilkn 7y ago
The real problem is that his response to Scholze and Stix didn’t manage to convince anyone who wasn’t already in his camp. At this point there is a major and clearly stated objection to the proof out in public to which no reasonable refutation has been offered.
- wolfgke 7y ago
  > At this point there is a major and clearly stated objection to the proof out in public to which no reasonable refutation has been offered. The problem is: Scholze and Stix formulated their objections to a "simplified" version of IUTT (i.e. they did quite some identifications). Their claim is that these simplifcations do not matter for whether IUTT holds or not, but Mochizuki claims that the details that Scholze and Stix "wiped away" do matter. No side could convince the other side of their position. If you want to dive into the gory details: http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf http://www.kurims.kyoto-u.ac.jp/~motizuki/SS2018-08.pdf (Scholze & Stix) http://www.kurims.kyoto-u.ac.jp/~motizuki/Rpt2018.pdf http://www.kurims.kyoto-u.ac.jp/~motizuki/Rpt2018.pdf (Mochizuki) If you love flamewars, read: Ivan Fesenko: Remarks on Aspects of Modern Pioneering Mathematical Resarch; https://www.maths.nottingham.ac.uk/plp/pmzibf/rapm.pdf https://www.maths.nottingham.ac.uk/plp/pmzibf/rapm.pdf
  - zamalek 7y ago
    He didn't give his two biggest critics the time of day. You can't fault them for sticking to their conclusion, the authority to the contrary is completely uninterested in defending their position. We'll probably never know if he actually solved it. Few have the knowledge, fewer had the patience and nobody has had rebuttal. Scholze and Stix conclusions hold exactly as much weight as Mochizuki's. They are unwilling to change their mind and recant, just as much as Mochizuki is. This whole fiasco reflects very poorly on the mathematical community in general.

bsder 7y ago

> This whole process reflects very poorly on Mochizuki, IMO. It's worse than that. At this point, the person who bridges that gap will almost certainly get his name added to the proof--that's a big incentive. The fact that nobody seems to be able to bridge that gap is a gigantic glaring flag that something is wrong.

wolfgke 7y ago
> It's worse than that. At this point, the person who bridges that gap will almost certainly get his name added to the proof--that's a big incentive. Taylor Dupuy together with Anton Hilado is attempting this: https://thehighergeometer.wordpress.com/2019/01/18/taylor-dupuy-on-mochizukis-iutt-infamous-corollary-3-12/ https://thehighergeometer.wordpress.com/2019/01/18/taylor-du...