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Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

quantamagazine.org

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Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#31

Post by Moodles »

doitLP wrote: post #25
Moodles wrote: post #12

I have a MSc in mathematics so I am by no means an expert in mathematics proofs but I get the gist of it. To me a proof is literally a logical argument that you can follow to "believe" that a theorem is true. I do worry how many people actually understand or verify mathematics proofs. How many people have actually read and verified Perelman's or Wiles' proofs (I'm only singling them out because they're famous, not be…

> We seem to think that once a proof is published in a reputable journal then it is definitely true, but really we should only think "a small number of qualified people have read it and think it is fine" This same could be said of many other professions, medicine and psychology to start. It seems a related manifestation of the Gells-Mann Amnesia.

Yup, not picking on mathematics at all :-)

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#32

Post by a-nikolaev »

jim777 wrote: post #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?

Math academic community is actually very healthy overall, in my experience.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#33

Post by spydum »

I do have to wonder, if the proof is so complex, and yet doesn't offer insights to any other proof or theories.. does it matter?

Older threads for reference:

    https://news.ycombinator.com/item?id=15971802
    https://news.ycombinator.com/item?id=4502856
    https://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjecture

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#34

Post by contravariant »

zokier wrote: post #13

So what would this imply over the larger body of Mochizukis work? As far as I have understood the situation, the abc proof is more of a sideproduct of him developing this completely new system(?) for maths rather than the main thrust of the works. Is it all falling down like house of cards, or is there still workable and useful bits there?

Somewhere in this comment section someone quoted the following line by Terrence Tao:

>It seems bizarre to me that there would be an entire self-contained theory whose only external application is to prove the abc conjecture after 300+ pages of set up, with no smaller fragment of this setup having any non-trivial external consequence whatsoever.

so it's not so much that the main result is called into question but there are some useful and workable bits left over. Rather the main result is called into question because there are no other useful and workable bits.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#35

Post by rurban »

jim777 wrote: post #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?

This is typical behavior in Japan when you question someones authority. It doesn't go well with them, it's a direct attack on their honor. You really need to go deeper with him (over dinner or so), but he refuses, so most likely he is wrong snd he knows it.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#38

Post by doall »

matthewbauer wrote: post #9

I 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?

I think Mochizuki won't have any problems with English, since he spent his school days, up to PhD in the US.

https://en.wikipedia.org/wiki/Shinichi_Mochizuki

About Hoshi, I have seen him in a conference video before, and have an impression that he isn't good at English, which can make a bit difficult in discussion.

I don't know about Scholze and Stix.

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#39

Post by Obi_Juan_Kenobi »

Slightly OT: it was very nice to read an article that made such wonderful use of links. Just about every case where material could be directly linked, it was done.

I particularly enjoyed the link to Dr. Calegari's blog post, as it was interesting to read the comments in 'real time' and compare that with the author's synthesis. Very good article!

Re: Titans of Mathematics Clash Over Epic Proof of ABC Conjecture

#40

Post by ericsoderstrom »

doitLP wrote: post #25
Moodles wrote: post #12

I have a MSc in mathematics so I am by no means an expert in mathematics proofs but I get the gist of it. To me a proof is literally a logical argument that you can follow to "believe" that a theorem is true. I do worry how many people actually understand or verify mathematics proofs. How many people have actually read and verified Perelman's or Wiles' proofs (I'm only singling them out because they're famous, not be…

> We seem to think that once a proof is published in a reputable journal then it is definitely true, but really we should only think "a small number of qualified people have read it and think it is fine" This same could be said of many other professions, medicine and psychology to start. It seems a related manifestation of the Gells-Mann Amnesia.

Math is different in that one feels there should be something close to "absolute truth." That is, given a set of axioms, it is possible to verify with complete certainty whether a proof follows from those axioms or not. Though when proofs become so long and abstruse that only a handful of people can even read them, perhaps that's no longer true. In other fields, it's more clear that nothing is known with 100% certainty. That differences of opinion or experimental error could always lead to uncertainty.
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