Inter-universal geometry と ABC予想 (応援スレ) 77

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 77 (1002ﾚｽ)
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614: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/11/09(日) 13:56:22.21 ID:QrKJGO9s

>>576
>IUTについては
>かみ合う議論が難しい

巡回ご苦労さまです
全くです
下記の 2020 by woit での Peter Scholzeと Taylor Dupuyとの論争も
結局は、かみ合わなかった

(参考)
https://www.math.columbia.edu/~woit/wordpress/?p=11709
Latest on abc Posted on April 3, 2020 by woit
Davide Castelvecchi at Nature has the story this morning of a press conference held earlier today at Kyoto University to announce the publication by Publications of the Research Institute for Mathematical Sciences (RIMS) of Mochizuki’s purported proof of the abc conjecture.
This is very odd. As the Nature subheadline explains, “some experts say author Shinichi Mochizuki failed to fix fatal flaw”.

Peter Scholze says:
April 6, 2020 at 9:28 am
I have been weighing back and forth commenting again on this matter. However, the news in that last comment by David J. Littleboy convinced me that it might be good, even if futile, to say something again.

I may have not expressed this clearly enough in my manuscript with Stix, but there is just no way that anything like what Mochizuki does can work. (I would not make this claim as strong as I am making it if I had not discussed this for with Mochizuki in Kyoto for a whole week; the following point is extremely basic, and Mochizuki could not convince me that one dot of it is misguided, during that whole week.) It strikes deep into my heart to think that in the name of pure mathematics, an institute could be founded for research on such questions, and I sincerely hope that this will not come back to haunt pure mathematics.

The reason it cannot work is a theorem of Mochizuki himself.
略
I’m really frustrated with the current situation. What EricB reports from the Asahi Shinbun also sounds deeply troubling, effectively arguing along national lines; again, this strikes deep into my heart. I’m really quite surprised by the strong backing that Mochizuki gets from the many eminent people (who I highly respect) at RIMS.
If I can in any way help to mitigate the situation, I’d be most happy to.

Taylor Dupuy says:
April 6, 2020 at 1:00 pm
Hi Peter!
First, hope your pandemic is going well. Mine is going ok. Hard to get things done without daycare.
Second, let me say that for hyperbolic curves over a p-adic field K (with no extra hypotheses like strictly Belyi type or Belyi type or canonical lift) that pi_1(Z) “determines” Z is open. Also, I personally would advocate against using words like “determines”, “reconstructs”, etc that have been causing sooo many problems in discussing all of these things.

http://rio2016.5ch.net/test/read.cgi/math/1761878205/614

618: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2025/11/09(日) 14:24:55.46 ID:QrKJGO9s

>>614 補足
>下記の 2020 by woit での Peter Scholzeと Taylor Dupuyとの論争も
>結局は、かみ合わなかった

1）Scholzeちゃんも、若い
　「”radical simplifications”という明白な ストローマン論法」>>565
　が、彼は 若いから 数学外道だと 分っていない
　正しいと 信じ込んでいる。だから、Taylor Dupuyとの論争が かみ合わない
2）例えば O–Takegoshi L2 extension theorem https://en.wikipedia.org/wiki/Ohsawa%E2%80%93Takegoshi_L2_extension_theorem
　”・・・  Kensho Takegoshi in 1987,[1] using what have been described as ad hoc methods involving twisted Laplace–Beltrami operators, but simpler proofs have since been discovered.[2] ( Siu (2011))
　Many generalizations and similar results exist, and are known as theorems of Ohsawa–Takegoshi type.”
3）このように、”simpler proofs have since been discovered”は、良いのです
　だが、「証明をsimplificationしたら 証明にギャップが出来ました」というN大の学生が居たら？
　O先生も「あ然、ぼう然、がく然」ｗ でしょう。O先生「おまえ 本当にN大 数学科生か？」とｗ
　つまり、”simpler proofs”は是なれど、”simplification→ギャップ出来た”は 原理的に不可なのです

この簡単な理屈が、若いScholze氏は 理解できていない！
彼は「証明をsimplificationしたら 証明にギャップが出来ました」という 非数学のディベート論法を
公式の数学主張として 持ち込んで 使った 史上初の数学者かも知れない

http://rio2016.5ch.net/test/read.cgi/math/1761878205/618

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