https://www.math.columbia.edu/~woit/wordpress/?p=11723 Not Even Wrong Why the Szpiro Conjecture is Still a Conjecture Posted on April 18, 2020 by woit
OP says: April 18, 2020 at 4:41 pm The comment of @naf hits the nail on the head. But I would go a step further: when confronted with a truly massive edifice of highly technical mathematics, nearly all experts need some kind of motivation to persevere beyond the final goal at the end of the tunnel. For example, a powerful heuristic to give confidence in the strategy, or some kind of intuitive guide to grab onto along the way to have a feeling of making progress (or at least interesting achievements along the way in the absence of a global guide). But here there is nothing of the sort, not even a compelling mathematical reason to believe at the outset that investing a huge amount of time is going to reap satisfying mathematical understanding. There is only patience to keep oneself going, and it can be very hard to rely on that alone after a lot of time.
This practical (albeit psychological) concern came to mind almost immediately after I was asked early on to be on the referee team for the IUT papers. I have great respect for Mochizuki’s mathematical talent, and no doubt in the sincerity of his belief that he has a proof of the main result. But I could see that the referees would not only have to check the details of an extremely long work written in a very obscure style (which didn’t provide insightful reasons for confidence in the approach being used). They would also have to engage in a herculean effort to get the writing substantially changed. It was too much, so I declined and communicated my concerns to the editorial board. (I recommended immediate rejection with a demand that the work be completely rewritten before it could be reconsidered.)
I am very sorry to see all these years later that neither the referees who were eventually obtained nor the editorial board obtained any real improvement on the clarity of the way the material is presented, not even at least an Introduction presenting key new insights in some conventional manner (to compensate for the way the technical material is presented). I hope the editors of PRIMS and the senior faculty at RIMS will reflect on their responsibility to the field of mathematics, and reconsider what they are doing. (引用終り) 以上 0139現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/19(日) 09:06:41.26ID:ijGx7lvx>>138 DeepL翻訳(一部修正)
ということは、海外の数学者では、「IUT訳分からん。RIMS訳分からん」という人多数でしょうね まあ、別スレで、ショルツ氏が納得すれば、ともかくも RIMS側が説明責任を果たす努力を怠ってはいけないと思う 0142現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/19(日) 09:56:50.80ID:ijGx7lvx>>131 Taylor Dupuy先生、いい味だしているね〜w(^^
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit (抜粋) Taylor Dupuy says: April 18, 2020 at 1:09 pm Hi Everyone,
もう1つ 「サーストンのモンスター定理(ハーケン多様体には幾何構造が入る)」(>>143&>>95) これは、もっとひどくってw(^^; (>>95) ”William Thurston was awarded the Fields medal in 1983^8, but it took about 20 years and the efforts of many authors for all details to be written down rigorously. It is worth reading Thurston’s interesting argument [Th1994] why he did not provide the detailed proof himself.” つまり、サーストン先生自身は定理の証明を書かずに ”about 20 years and the efforts of many authors for all details to be written down rigorously.” というから、まあ米国の佐藤幹夫先生みたいなものかw
説明の何百ページの文書はいらないんだ ただ、「国際会議でちゃんと説明するから」くらいでいいんだ あるいは、もし国際会議用に準備している文書があるから、それを先にリリースして 「国際会議で議論予定」でもいいけどね 0147現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/19(日) 11:37:59.79ID:ijGx7lvx>>145 追加 https://www.math.columbia.edu/~woit/wordpress/?p=11723 Not Even Wrong Why the Szpiro Conjecture is Still a Conjecture Posted on April 18, 2020 by woit (抜粋) OP says: April 18, 2020 at 8:49 pm Just to clarify: I wasn’t a referee on the IUT papers, but rather was invited to serve as one, and I declined (giving the editorial board my recommendation for how I thought would be best to proceed). As for Katz’ work as a referee on the initial FLT paper, my impression is that this only became public knowledge sometime after the fix was found and the corrected version had gone through the review process (e.g., maybe via the BBC video that was made about it).
(参考) https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments Not Even Wrong Latest on abc Posted on April 3, 2020 by woit W says: April 19, 2020 at 9:53 am 0156132人目の素数さん2020/04/20(月) 13:14:27.34ID:nSShSe+M ΘとかΘ±ell とか D-Θ±ell ってどう翻訳すればいいんだろうな? 0157現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/20(月) 13:22:03.00ID:jS1N2Wjo>>136 >IUT論文において、サーストン怪物定理の図8(>>95)みたいなの >これが欲しいね
そうそう 追加で 1.IUT用語辞書 or 定義集(含む本論文ページへのヒモつけ) 2.インデックス(上記と重なる部分あるが、しっかり整備要。用語のみならず、数学記号も) 3.IUT用語と標準数学用語との対比表(差分を表示)(上記と重なる部分もあるが、しっかり整備すること)
そこはアブストラクトじゃんかw(^^; で http://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf INTER-UNIVERSAL TEICHMULLER THEORY I: CONSTRUCTION OF HODGE THEATERS Shinichi Mochizuki April 2020 P6 In some sense, the main goal of the present paper may be thought of as the construction of Θ±ell NF-Hodge theaters [cf. Definition 6.13, (i)] P7 one may associate a D-Θ±ell NF-Hodge theater [cf. Definition 6.13, (ii)] (引用終り)
結論:この文書には "Θ±ell"の詳しい記載なし
そこで、下記山下先生のレビューが役に立つのです〜(^^ これ、IUTの前の準備文書が含まれているから、調べるのに便利だということに気付いたのです http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2019Jul5.pdf A PROOF OF THE ABC CONJECTURE AFTER MOCHIZUKI By Go Yamashita preprint. last updated on 8/July/2019. (注意:文字化けがあるので、必ず原文見て下さい!) P14 We write M ell ⊂ M ell ̄ for the fine moduli stack of elliptic curves and its canonical compactification.
結論:これより、ell:elliptic curve です
P199 § 10. Hodge Theatres. In this section, we construct Hodge theatres after fixing an initial Θ-data (Section 10.1). More precisely, we construct Θ±ell NF-Hodge theatres (In this survey, we shall refer to them as ◇□-Hodge theatres). A Θ±ellNF-Hodge theatre (or a ◇□-Hodge theatre) will be obtained by “gluing” (Section 10.6) ・a ΘNF-Hodge theatre, which has a F*l-symmetry, is related to a number field, of arithmetic nature, and is used to Kummer theory for NF (In this survey, we shall refer to it as a -Hodge theatre, Section 10.4) and
P200 ・a Θ±ell-Hodge theatre, which has a F x±-symmetry, is related to an elliptic curve, of geometric nature, and is used to Kummer theory for Θ (In this survey, we shall refer to it as a -Hodge theatre, Section 10.5) Separating the multiplicative (◇) symmetry and the additive (□) symmetry is also important (cf. [IUTchII, Remark 4.7.3, Remark 4.7.6]). ΘNF-Hodge theatre F*l-symmetry (◇) arithmetic nature Kummer theory for NF Θ±ell-Hodge theatre Fx±l-symmetry (□) geometric nature Kummer theory for Θ
結論: "Θ±ell"で、 Θは Θ-data (Section 10.1). 分かったのはここまで 多分、§ 10. Hodge Theatres. をもう少し読み込めば、±の意味( + and - か、あるいは + or - か、多分前者と思う)などはっきりすると思う NFも、Kummer theory for NF とあるので、もう少し読み込めば、はっきりすると思うけどね
https://books.google.co.jp/books?id=81QeCwAAQBAJ&printsec=frontcover&dq=Teichmuller+Mochizuki&hl=ja&sa=X&ved=0ahUKEwjR3tP7hffoAhVPPnAKHVZeDbIQ6AEIKDAA#v=onepage&q=Teichmuller%20Mochizuki&f=false Foundations of p-adic Teichmuller Theory 著者: Shinichi Mochizuki ASM 1999 0173現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 07:44:51.24ID:/78llOaT>>170 訂正と追加 訂正 >>167はすぐその下とダブりで消す
追加 "NF"について 下記P12 the abbreviations NF for "number field" ですね(^^ http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2019Jul5.pdf A PROOF OF THE ABC CONJECTURE AFTER MOCHIZUKI By Go Yamashita preprint. last updated on 8/July/2019. (注意:文字化けがあるので、必ず原文見て下さい!) P12 Number Fields and Local Fields: In this survey, we define a number field to be a finite extension of Q (i.e., we exclude infinite extensions). We define a mixed characteristic (or non-Archimedean) local field to be a finite extension of Qp for some p. We use the abbreviations NF for "number field", MLF for "mixed characteristic local field", and CAF for "complex Archimedean field" (i.e., a topological field isomorphic to C). For a topological field k which is isomorphic to R or C, we write j _ jk : k ! R>=0 for the absolute value associated to k, i.e., the unique continuous map such that the restriction of j_jk to k determines a homomorphism k ! R>0 with respect to the multiplicative structures of k and R>0, and jnjk = n for n ∈ Z>=0. We write π ∈ R for the mathematical constant pi (i.e., π = 3:14159 ・ ・ ・ ). (引用終り)
今回の件で 山下先生の下記 http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2019Jul5.pdf A PROOF OF THE ABC CONJECTURE AFTER MOCHIZUKI By Go Yamashita preprint. last updated on 8/July/2019.
後ろに、Appendix A〜Cも付けてあって C.4. On the Prime Number Theorem. C.5. On the Residual Finiteness of Free Groups. とか、基本的な知識の補足もある C.6. Some Lists on Inter-universal Teichmuller Theory とかは、IUTの重要な記号の一覧ですかね
P366 A.3. Hodge-Arakelov-theoretic Comparison Theorem.で ”Note that these can be considered as a discrete analogue of the calculation of Gaussian integral is a Gaussian distribution (i.e., j → j^2) in the cartesian coordinate is a calculation in the polar coordinate ・・・” とか、望月先生の講演ネタで使っていた話の解説もあるな
P358 ”Proof. Theorem follows from the definitions.(QED)” には、笑った(^^; すぐ後に、”A rough picture of the final multiradial representation is as follows:”と部分解説が続くのだけれど だったら、解説の後に、 ”Proof. Theorem follows from the definitions.(QED)”に持ってこないとねぇー ここ (P352) ”The following the Main Theorem of inter-universal Teichmuller theory: Theorem 13.12. (Multiradial Algorithms via LGP-Monoids/Frobenioids, [IUTchIII, Theorem 3.11]) ” なんだけど、例のCor 3.12に直結するところだしね
Cor 3.12は P359 ”Corollary 13.13. (Log-volume Estimates for -Pilot Objects, [IUTchIII, Corollary 3.12]) We write -| log(θ)|∈ R ∪{+∞}” あと P360 ”Then we obtain -| log(q)|< -| log(θ)|” で、IUT III Cor3.12 になるけどねw(^^; (Proof.は、その直後から4ページほどある) 山下サーベイ論文は、それなりに面白いわ(^^ 0178現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 11:54:52.77ID:QPCMXF1q <転載> Inter-universal geometry と ABC予想 50 https://rio2016.5ch.net/test/read.cgi/math/1586907848/882 なお、ショルツ氏の最終意見は下記です、ご参照ください(^^ 半歩、IUT側へ譲歩していますよw(^^;
https://www.math.columbia.edu/~woit/wordpress/?p=11709#comments woitブログ (抜粋) Peter Scholze says: April 17, 2020 at 7:15 pm PS: I just realized that maybe the following information is worth sharing. Namely, as an outsider one may wonder that the questions being discussed at length in these comments (e.g., the issue of distinct copies etc.) are very far from the extremely intricate definitions in Mochizuki’s manuscripts (his notation is famously forbidding, some of it surfaced in Taylor’s comments), and feel almost philosophical, so one might wonder that one is not looking at the heart of the matter. However, the discussions in Kyoto went along extremely similar lines, and these discussions were actually very much led, certainly initially, by Mochizuki. He first wanted to carefully explain the need for distinct copies, by way of perfections of rings, and then of the log-link, leading to discussions rather close to the one I was having with UF here. He agreed that one first has to understand these basic points before it makes sense to introduce all further layers of complexity. (I should add that we did also go through the substance of the papers, but kept getting back at how this reflects on the basic points, as we all agreed that this is the key of the matter.) 0179現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 12:19:05.83ID:QPCMXF1q>>178 追加
www.DeepL.com/Translator(無料版) 部分修正 Peter Scholze says: April 17, 2020 at 7:15 pm PS: 以下の情報は共有する価値があるのではないかと思っています。 つまり、部外者からは、これらのコメントで長々と議論されている疑問は、以下のようなものではないかと思うでしょう。 望月の論文にある非常に複雑な定義で (e.g., the issue of distinct copies etc.) (望月の表記は禁止されていることで有名で (ここは原英文も意味不明です)、テイラーのコメントにもその一部が登場している) ほとんど哲学的な感じで、問題の核心を見ていないのではないかと疑問に思うかもしれません。 しかし、京都での議論は非常に似たような線をたどっていた、この議論は実際には、最初は確かに望月によって次のようにリードされていました。 彼はまず、the need for distinct copies, by way of perfections of rings, and then of the log-link を丁寧に説明しようとしていて、私がここでUFと議論していたのと同じような議論になった。 彼は、最初にこれらの基本的な点を理解してからでないと 複雑な他のすべての階層を導入することに意味がないとしていた。 (ここで論文の内容についても議論したが、基本的な点をどう反映させているのかということに戻ってきて、これが問題の鍵であるということに全員が同意した。) (引用終り) 0180現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 12:28:38.49ID:QPCMXF1q>>179 補足
これをさらに要約すると 1.ショルツ先生は、これ以前は、IUT全然だめと言っていた 2.このコメントで、望月の論文にある非常に複雑な定義が問題で、自分が反例として出した例とは、すれ違いの可能性があることだけは認めた 3.このスレ違いは、京都でもあって、いまのWoitブログのDupuy氏やUF氏の指摘の議論と似た展開であったことを思い出した 4.そして、”(I should add that we did also go through the substance of the papers, but kept getting back at how this reflects on the basic points, as we all agreed that this is the key of the matter.)” と結んでいる。つまり、もうちょっと、望月論文を読まないといけない (あるいは、原文は過去形で、ちゃんと読めてないところがあって、それが、”the key of the matter”だと)
どこをどう読んだらそう読める? むしろショルツの認識は京都で議論した時点から全く変わっていないということだろ 0182現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 15:45:34.50ID:QPCMXF1q>>181 違う ショルツ氏は思い出したんだよ 京都の議論を そして、いまのDupuyとUF氏の指摘と同じだと いう そして、>>178 (e.g., the issue of distinct copies etc.) are very far from the extremely intricate definitions in Mochizuki’s manuscripts (his notation is famously forbidding, some of it surfaced in Taylor’s comments), and feel almost philosophical, so one might wonder that one is not looking at the heart of the matter. ってこと
要するに、繰り返すが feel almost philosophical, so one might wonder that one is not looking at the heart of the matter. ってこと
で、私なりに咀嚼して解説すると これ お経みたいなものだということ
門前の小僧習わぬ教を読む 習えば、お経が読めるんだよ
戻ると 例えば ”feel almost philosophical, so one might wonder that one is not looking at the heart of the matter.” が、ある人から見れば、(わけわからん)お経でも ちゃんと、仏教の修行をした坊さんとか 分かる人が見れば 「これは ありがたい仏の教えだ」となるわけ
1.ショルツ氏も、21世紀の数学の論文において、「自分を基準にして、自分が読める論文にしろ」(それが査読の条件だ)とは言っていない 2.いままで、ショルツ氏が言ってきたことは、「自分なりに読んで、IUT Cor3.12はおかしい。矛盾があって、IUTは根本的に不成立!」と言ってきた 3.>>178の”Peter Scholze says: April 17, 2020 at 7:15 pm”は、望月氏の論文はお経で、”feel almost philosophical, so one might wonder that one is not looking at the heart of the matter.” まで 後退したってこと。つまり、上記の2の ”自分なりに読んで” の部分が成り立っていないことに、いまさらながら 気付いたってこと 4.ショルツ氏が読めない (お経のような)論文書いてどうするんだという意見は認めるとしても 上記2と3とは、決定的に違うよ 5.そして、お経じゃなく、読める論文にしてくれというのも分かる。でも、それは 論文が成立しているか不成立か とは違う議論だよ
>feel almost philosophical, so one might wonder that one is not looking at the heart of the matter. これは「(このコメントを見ている人にとって)このブログでの議論はほとんど哲学的に感じられ、問題の核心を見ていないと思うかもしれません。」 ってことだよ その後に続く部分は、「でもそうじゃないよ」っていう弁明だよ
あと、 >>179 で >(望月の表記は禁止されていることで有名で (ここは原英文も意味不明です)、テイラーのコメントにもその一部が登場している) って書いているけど、ここは「テイラーのコメントにあるように、このブログで望月の記号をそのまま書き込むことはできない」くらいの意味 該当する「テイラーのコメント」は恐らくこれのことだろう >Taylor Dupuy says: >April 14, 2020 at 5:30 pm >… >(last time I tried a double underline it didn’t work out so I’m using double prime this time, >here we need to take an analytification or formal scheme with log structure) >… https://www.math.columbia.edu/~woit/wordpress/?p=11709&cpage=2#comment-236043 0187132人目の素数さん2020/04/21(火) 16:48:59.01ID:RBkmWQJ3 JAXAの表現では137億年どまり。さて?
https://www.math.columbia.edu/~woit/wordpress/?p=11723 Not Even Wrong Why the Szpiro Conjecture is Still a Conjecture Posted on April 18, 2020 by woit (抜粋) KS says: April 20, 2020 at 11:32 am For more sociological understanding , please let me put about some curious social situation around this issue in Japan. On the official announcement of acceptance of the papers in Kyoto, two mathematicians Tamagawa and Kashiwara attended there, and Tamagawa is actually well-known expert in the anabelian geometry.But It seems likely that he can not explain about the mathematical matter of IUT in public so far. In addition , Rigid geometer Fumiharu Kato already published the book “in 2019” about IUT “treated as correct theory” for general audience amazingly, but actually it wouldn’t be sufficient to offer any insight for professional mathematicians.Furthermore , as Tamagawa is , he also has never wrote any rigorous mathematical papers about IUT as far as I know at present. These facts seems to be indeed mysterious that is , ” whoever did understand and can defense the theory sufficiently?” .
Anyway needless to say , since IUTT use too many and overlevel terminology ,so that if it cannot be expressed with crucial idea for proof , other mathematicians wouldn’t accept it at all. 0195現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 18:09:57.50ID:QPCMXF1q>>194 なお、補足しておくが 私は、KS says に大賛成 RIMSがちゃんと、IUTが成り立つことの説明責任を果たせということ それやってほしいね 0196132人目の素数さん2020/04/21(火) 18:16:20.98ID:RBkmWQJ3 LabCuspってラブカスプっていうの?ラボカスプっていうの? Lab Cuspって分けてGoogleで翻訳するとラボカスプって出るんだけど。 0197現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 18:29:26.20ID:QPCMXF1q>>196 さあ、LabCusp と Lab Cusp と ラボカスプ との使い分けね それは、文脈依存だから、Googleで翻訳では無理ってことじゃない? 0198現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/21(火) 18:31:57.55ID:QPCMXF1q>>195 補足
ついでに補足しておくと >>182より "(e.g., the issue of distinct copies etc.) are very far from the extremely intricate definitions in Mochizuki’s manuscripts (his notation is famously forbidding, some of it surfaced in Taylor’s comments), and feel almost philosophical, so one might wonder that one is not looking at the heart of the matter."
数学者の議論では、よく「最初に定義を確認しましょう」なんてやりますよね で、ショルツ先生、2年後になって "(e.g., the issue of distinct copies etc.) are very far from the extremely intricate definitions in Mochizuki’s manuscripts (his notation is famously forbidding, some of it surfaced in Taylor’s comments), and feel almost philosophical, so one might wonder that one is not looking at the heart of the matter." って、どういうこと? その議論の場で、定義を確認すれば良かったのに〜w 定義の確認をせずに議論して、Woitブログで、”feel almost philosophical, so one might wonder that one is not looking at the heart of the matter."とは、なんでしょうかね〜?(^^
そういうことは言わないの 弘法も筆の誤り、フィールズ賞のショルツ先生も、 定義の確認をしないで議論して、 2年後に”(e.g., the issue of distinct copies etc.) are very far from the extremely intricate definitions in Mochizuki’s manuscripts (his notation is famously forbidding, some of it surfaced in Taylor’s comments), and feel almost philosophical,” と宣うのです 正直でいい そういうことは、みなあるものですよ 0211現代数学の系譜 雑談 ◆e.a0E5TtKE 2020/04/22(水) 07:57:54.59ID:s+irHIkm>>210 >>IUTが何か知らないけど応援しています >同意 >同じですw(^^;
https://www.math.columbia.edu/~woit/wordpress/?p=11723 Not Even Wrong Why the Szpiro Conjecture is Still a Conjecture Posted on April 18, 2020 by woit (抜粋) Jay Watt says: April 21, 2020 at 12:23 pm I have been following this drama for quite a while now and there’re a couple of things I just don’t get:
1. Why do people assume that the referees (if there were any) really understood the papers and should thus come out and explain it? Most of you have been refereeing papers yourself. Do you read and check every line? That’s impossible, and I’m open about this in every report I write. Even if you do think you got it all, does your judgment make the paper correct? We’re all just humans and prone to make errors. As an amusing reminder, here’s an (incomplete) list of “incomplete proofs”: https://en.wikipedia.org/wiki/List_of_incomplete_proofs. 以下略