Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
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Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
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Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#2I think this would count as esoteric if you ignore the drama portion of it. Just to get to the point of understanding what they're talking about would probably take months of dedicated uninterrupted work. Neat. I have no idea where to even start.
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#3I think this would count as esoteric if you ignore the drama portion of it. Just to get to the point of understanding what they're talking about would probably take months of dedicated uninterrupted work. Neat. I have no idea where to even start. https://en.wikipedia.org/wiki/Anabelian_geometry
I don't profess to understand the mathematics behind these papers but i have been following the debate for a couple years now. It is weird for such eminent mathematicians to not be able to reach a conclusion as to whether mochizukis arguments are true or false. I think this is the first time a really eminent mathematician like scholze has put in his two cents that the proof might not be right. At least it looks like work is being done at a serious level to prove or disprove these papers.
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#4I think this would count as esoteric if you ignore the drama portion of it. Just to get to the point of understanding what they're talking about would probably take months of dedicated uninterrupted work. Neat. I have no idea where to even start. https://en.wikipedia.org/wiki/Anabelian_geometry
I think what makes these number theory arguments so interesting to me is how simple the theorems are, but how impenetrable the proofs are. For example, Fermat's last theorem is so easy to understand, but there's no chance in hell I'll ever understand Wiles' paper proving it.
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#5https://galoisrepresentations.wordpress.com/2017/12/17/the-a...
Terence Tao and Peter Scholze (and others) join the discussion in the comments section.
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#6> When he told colleagues the nature of Scholze and Stix’s objections, he wrote, his descriptions “were met with a remarkably unanimous response of utter astonishment and even disbelief (at times accompanied by bouts of laughter!) that such manifestly erroneous misunderstandings could have occurred.”
Is this normal in advanced Math or is this guy kind of a jerk?
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#7> When he told colleagues the nature of Scholze and Stix’s objections, he wrote, his descriptions “were met with a remarkably unanimous response of utter astonishment and even disbelief (at times accompanied by bouts of laughter!) that such manifestly erroneous misunderstandings could have occurred.” Is this normal in advanced Math or is this guy kind of a jerk?
He is being a jerk. Also, not responding to the actual argument, as far as I can tell (which is technical, but quite clear). There are some other damning statements in the rebuttal, too--for example, they say that all the new machinery developed for anabelian geometry lies unused in the case to which Corollary 3.12 applies (meaning most of the effort mathematicians have been spending in order to try to understand Mochizuki's new mathematics has been wasted). They also mention other incidental complexities that serve to obfuscate the argument but don't seem to buy anything (for example, not choosing a specific isomorphism at one point in the proof, but instead asking the reader to consider all isomorphisms with particular properties, for reasons he has been unable to justify). Someone in his position should be aiming to clean up his proofs to be as straightforward as possible, not making them deliberately harder to verify.
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#8> When he told colleagues the nature of Scholze and Stix’s objections, he wrote, his descriptions “were met with a remarkably unanimous response of utter astonishment and even disbelief (at times accompanied by bouts of laughter!) that such manifestly erroneous misunderstandings could have occurred.” Is this normal in advanced Math or is this guy kind of a jerk?
New Law: Any Internet discussion will be reduced to jerk/non-jerk within 30 minutes.
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#9I wonder if language is a factor in this at all? I know mathematics is written entirely in English but most likely discussions still happen in local languages. Could part of the proof be lost in translation?
Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
#10> When he told colleagues the nature of Scholze and Stix’s objections, he wrote, his descriptions “were met with a remarkably unanimous response of utter astonishment and even disbelief (at times accompanied by bouts of laughter!) that such manifestly erroneous misunderstandings could have occurred.” Is this normal in advanced Math or is this guy kind of a jerk?
Well, let's lay aside the fact that there clearly are plenty of jerks in academia. The entire article seems to layout a sort of string of unusual and problematic situations. Whether it's people who hit upon the problem conjecture and chose not to speak out for fear of causing trouble, or the journal publishing the proof being edited by the author, or the large number of 'delegates' who seem to be pushing the proof without being able to explain the proof, it seems this is a mix of problems that are arising from an unhealthy situation.