基礎論破ってない と本人が言っている >>316 再録 "artificial solution to the "membership equation a ∈ a"" については、[cf. the discussion of [IUTchIV], Remark 3.3.1(i)]で "大まかに言えば、基礎の公理に違反することなく「∈ ループをシミュレートする」こと(が可能)です" が結論
(参考) https://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20I.pdf Inter-universal Teichmuller TheoryI P102 (b) an isomorphism, or identification, between v [i.e., a prime of F ] and v'[i.e., a prime of K] which [manifestly — cf., e.g., [NSW], Theorem 12.2.5] fails to extend to an isomorphism between the respective prime decomposition trees over v and v'.
If one thinks of the relation “∈” between sets in axiomatic set theory as determining a "tree", then the point of view of (b) is reminiscent of the point of view of [IUTchIV],§3, where one is concerned with constructing some sort of artificial solution to the “membership equation a ∈ a” [cf. the discussion of [IUTchIV], Remark 3.3.1(i)].
https://www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20IV.pdf Inter-universal Teichmuller TheoryIV P75 Remark 3.3.1 (i) One well-known consequence of the axiom of foundation of axiomatic set theory is the assertion that “∈-loops” a∈b∈c∈...∈a can never occur in the set theory in which one works. On the other hand, there are many situations in mathematics in which one wishes to somehow “identify”mathematical objects that arise at higher levels of the ∈-structure of the set theory under consideration with mathematical objects that arise at lower levels of this ∈-structure. 略 That is to say, the mathematical objects at both higher and lower levels of the ∈-structure constitute examples of the same mathematical notion of a “set”, so that one may consider “bijections of sets” between those sets without violating the axiom of foundation. In some sense,the notion of a species may be thought of as a natural extension of this observation.
That is to say, the notion of a “species” allows one to consider, for instance, speciesisomorphisms between species-objects that occur at different levels of the ∈-structure of the set theory under consideration — i.e., roughly speaking, to “simulate ∈-loops” — without violating the axiom of foundation. (google訳) 「種」の概念により、たとえば、検討中の集合論の ∈ 構造の異なるレベルで発生する種オブジェクト間の種同型写像を考慮することができます — つまり、大まかに言えば、基礎の公理に違反することなく「∈ ループをシミュレートする」こと(が可能)です 0436132人目の素数さん2024/05/02(木) 13:49:35.86ID:u4DjJzRY>>435
・IUT論文長いので、PDFの単語検索をかけたよ。“species”で、ヒットするのはIUT Iの冒頭のP22の1か所のみで あとは論文本体には皆無で、IUT IVの付録の”§3. Inter-universal Formalism: the Language of Species”まで飛ぶ ・つまりは、プロレスで言えば、本来のリング内では“species”なしで その後に 場外のIUT IV §3で、“species”論を、望月氏は一席ぶっているんだねw ・IUT IV §3は、本来のリング外だから そこでなにかあっても、本体の部分は殆ど無関係ですよ(最悪、(着想部分? or 勘違い部分?のw)IUT IV §3と、IUT Iの冒頭のP22の1か所を削除すれば良いだけのことよ。それでも論文本体は成り立つ!)
(参考) https://www.kurims.kyoto-u.ac.jp/~motizuki/papers-japanese.html 望月新一 宇宙際Teichmuller理論 [1] Inter-universal Teichmuller Theory I: Construction of Hodge Theaters. PDF NEW !! (2020-05-18) [2] Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic Evaluation. PDF NEW !! (2020-12-23) [3] Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice. PDF NEW !! (2020-05-18) [4] Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations. PDF NEW !! (2020-04-22)
・Inter-universal Teichmuller Theory I で、“species”は冒頭の1か所のみ P22 At this point, the careful reader will note that the above discussion of the inter-universal aspects of the theory of the present series of papers depends, in an essential way, on the issue of distinguishing different “types of mathematical objects” and hence, in particular, on the notion of a “type of mathematical object”. This notion may be formalized via the language of “species”, which we develop in the final portion of [IUTchIV].
・Inter-universal Teichmuller Theory I,IIは、皆無
・Inter-universal Teichmuller Theory IVは、§3で出てくるが、§3はあくまで付け足し解説で、IUTの本体数学外 §3. Inter-universal Formalism: the Language of Species 0441132人目の素数さん2024/05/02(木) 16:48:39.95ID:MGx3IZdS>>440 >IUT論文長いので、PDFの単語検索をかけたよ。 >“species”で、ヒットするのは >IUT Iの冒頭のP22の1か所のみで >あとは論文本体には皆無で、 >IUT IVの付録の”§3. Inter-universal Formalism: the Language of Species”まで飛ぶ >つまりは、プロレスで言えば、 >本来のリング内では“species”なしで >その後に 場外のIUT IV §3で、 >“species”論を、望月氏は一席ぶっているんだね >IUT IV §3は、本来のリング外だから >そこでなにかあっても、本体の部分は殆ど無関係ですよ
・下記のIUT IVの下記P6(Introduction内)より ”As one constructs sets at new levels of the ∈-structure of some model of axiomatic set theory — e.g., as one travels along vertical or horizontal lines of the log-theta-lattice! — one typically encounters new schemes, which give rise to new Galois categories, hence to new Galois or ´etale fundamental groups, which may only be constructed if one allows oneself to consider new basepoints, relative to new universes. ”
(参考) https://www.kurims.kyoto-u.ac.jp/~motizuki/papers-japanese.html 望月新一 宇宙際Teichmuller理論 [1] Inter-universal Teichmuller Theory I: Construction of Hodge Theaters. PDF NEW !! (2020-05-18) [2] Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic Evaluation. PDF NEW !! (2020-12-23) [3] Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice. PDF NEW !! (2020-05-18) [4] Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations. PDF NEW !! (2020-04-22)
・Inter-universal Teichmuller Theory I で、“univers”のカ所 P21 It is this fundamental aspect of the theory of the present series of papers — i.e., of relating the distinct set-theoretic universes associated to the distinct fiber functors/basepoints on either side of such a non-ring/scheme-theoretic filter — that we refer to as inter-universal. P33 Thus, from the point of view of “coarsifications of 2-categories of 1-categories” [cf. [FrdI], Appendix, Definition A.1, (ii)], an “isomorphism C →D” is precisely an “isomorphism in the usual sense” of the [1-]category constituted by the coarsification of the 2-category of all small 1-categories relative to a suitable universe with respect to which C and D are small.
・Inter-universal Teichmuller Theory IV で、“univers”のカ所 (P2からのIntroduction内) P6 As one constructs sets at new levels of the ∈-structure of some model of axiomatic set theory — e.g., as one travels along vertical or horizontal lines of the log-theta-lattice! — one typically encounters new schemes, which give rise to new Galois categories, hence to new Galois or ´etale fundamental groups, which may only be constructed if one allows oneself to consider new basepoints, relative to new universes. In particular, one must continue to extend the universe, i.e., to modify the model of set theory, relative to which one works. Here, we recall in passing that such “extensions of universe” are possible on account of an existence axiom concerning universes, which is apparently attributed to the “Grothendieck school” and, moreover, cannot, apparently, be obtained as a consequence of the conventional ZFC axioms of axiomatic set theory [cf. the discussion at the beginning of §3 for more details]. On the other hand, ultimately in the present series of papers [cf. the discussion of [IUTchIII], Introduction], we wish to obtain algorithms for constructing various objects that arise in the context of the new schemes/universes discussed above — i.e., at distant Θ±ell NF-Hodge theaters of the log-theta-lattice — that make sense from the point of view of the original schemes/universes that occurred at the outset of the discussion. Again, the fundamental tool that makes this possible, i.e., that allows one to express constructions in the new universes in terms that makes sense in the original universe is precisely the species-theoretic formulation — i.e., the formulation via settheoretic formulas that do not depend on particular choices invoked in particular universes — of the constructions of interest
P7 If,instead of working species-theoretically, one attempts to document all of the possible choices that occur in various newly introduced universes that occur in a construction, then one finds that one is obliged to work with sets, such as sets obtained via set-theoretic exponentiation, of very large cardinality. (§3にある個所は略す) (引用終り) 以上 0470132人目の素数さん2024/05/02(木) 21:25:43.78ID:e13eGB1v>>465 >それはあくまでモチベーション理解の話だよ >abc予想の証明に宇宙際なんか必要ないと俺は思ってる >IUTについて適度に考えるのは無駄にはならないとも思ってる
・全面同意 ・宇宙際は、望月氏が発想・着想でこだわっているだけと思う ・適度に流さないと "artificial solution to the "membership equation a ∈ a""などに こだわっても仕方ない気がする 0471132人目の素数さん2024/05/02(木) 21:31:17.14ID:2SgEedok >その証明はどこにある?
(3) 圏の幾何:これについては、私の論文 ・Categorical representation of locally noetherian log schemes ・Categories of log schemes with archimedean structures ・Conformal and Quasiconformal Categorical Representation of Hyperbolic Riemann Surfaces
それから、講演のレクチャーノート ・「A Brief Survey of the Geometry of Categories (岡山大学 2005年5月)」 を参照して下さい。簡単にまとめると、スキーム(または、log schemeやarchimedeanな構造付きのlog scheme)や双曲的リーマン面の構造は、そのような対象たちが定義する圏(=‘category')の圏論的構造 だけで決まるという話です。
Awards He declined the $100,000 "New Horizons in Mathematics Prize" of the 2016 Breakthrough Prizes.[33] His turning down of the prize received some media attention.[34]
[34] Woit, Peter (9 November 2015). "2016 Breakthrough Prizes". Not Even Wrong. Department of Mathematics at Columbia University. Retrieved 3 August 2018. https://www.math.columbia.edu/~woit/wordpress/?p=8088 2016 Breakthrough Prizes Posted on November 9, 2015 by woit
This year I think Peter Scholze set a remarkable example by turning down a prize, a move which unfortunately has gotten little attention in the media. I hope his action causes people to take a closer look at this gift horse. Instead of just celebrating the shower of cash and attention, research mathematicians may want to consider whether, just as they changed direction with the physics prize, Milner and Zuckerberg perhaps should be encouraged to listen to Scholze and move in a different direction.
Update: On the math side, David Nadler gave a beautiful talk about Langlands/geometric Langlands, ending with a prediction for the future that a central role will be played by Peter Scholze’s work, including recent ideas on what Nadler calls “Arithmetic conformal field theory”. He suggested that 50 years from now, Hartshorne and other graduate textbooks on algebraic geometry will be replaced with new ones based on Scholze’s perfectoid spaces. Maybe if they hadn’t offered Scholze money they could have gotten him to talk about this stuff…
Update: The question this raises, which may have something to do with Peter Scholze’s refusal to participate, is “what if good scientists don’t want to be celebrities?” The impulse to do science and mathematics at the highest level and the impulse to be a celebrity may just be two very different, incompatible things.
The New York Times article doesn’t mention the Scholze story, but it does discuss the young student, Ryan Chester, who was given a $400,000 award for making a film about special relativity. 0494132人目の素数さん2024/05/05(日) 16:12:29.39ID:fBCTdg1W >・証明が正しいかどうか判定するのは、各人決定可能だが 各人は無意味なので不要 >・しかし、その各人の判断が正しいかどうかは、時間が経たないとわからない 判断は人ではなく規則によるので、時間は無関係
https://en.wikipedia.org/wiki/Field_with_one_element Field with one element Monoid schemes Deitmar's construction of monoid schemes[25] has been called "the very core of F1‑geometry",[16] as most other theories of F1‑geometry contain descriptions of monoid schemes. Morally, it mimicks the theory of schemes developed in the 1950s and 1960s by replacing commutative rings with monoids. The effect of this is to "forget" the additive structure of the ring, leaving only the multiplicative structure. For this reason, it is sometimes called "non-additive geometry".
コンヌ/コンサニのように、サクセッサsを使って s;s = s として標数1を定義すれば、足し算がベキ等である半体 B = {0, 1} を作れます(「「掛け算ありき」から見えるエキゾチックな世界と真実の世界」参照)。しかしBは、ティッツが求めていた“体”にはなりません。 0509132人目の素数さん2024/05/05(日) 18:04:25.20ID:3WXRkfeI>>508 通報 0510132人目の素数さん2024/05/05(日) 18:08:48.71ID:3WXRkfeI>>1 荒らしはご遠慮願います。 応援スレとの棲み分けにより、 0511132人目の素数さん2024/05/05(日) 18:25:17.99ID:ylWsIAzF Dupuyって元々Buiumっていう独創的な師匠の理論を研究してたんだよな それを捨ててIUTに飛び込んだ。三流数学者らしい目利きの無さだよ 0512132人目の素数さん2024/05/05(日) 18:52:46.22ID:W9ChYFnD デュプイとケドラヤはIUTに関しては、その発言にあまり影響力はないだろう。超一流という感じがしない。 0513132人目の素数さん2024/05/05(日) 18:52:59.04ID:kUby5rl+ あんな三流ばかりから証言集めるなんて、 NHKもレベル低いな 0514132人目の素数さん2024/05/05(日) 19:08:13.53ID:3WXRkfeI>>513 いや、加藤文元と玉川が IUTTは新しい数学で全く新しい 未完成の理論と証言した。 0515132人目の素数さん2024/05/05(日) 19:09:11.03ID:W9ChYFnD Will SawinとM先生が対談すればいいのにね。 0516132人目の素数さん2024/05/05(日) 19:09:53.67ID:W9ChYFnD Will SawinとM先生が対談すればいいのにね。 0517132人目の素数さん2024/05/05(日) 20:55:42.31ID:kUby5rl+ ああいえばDupuy, こう言えばJoshi 望月真理教 0518132人目の素数さん2024/05/06(月) 09:11:14.87ID:hi35vIbq カトブンが望月新一を持ち上げる理由は知らんが どうせろくでもない理由だろう 玉川は正直言って望月新一と関わり合いたくないと思ってるが、 真相を暴露すると最悪京大数解研が取り潰しになるので 黙っていろと◯原とか🌲が3つの人とかから口止めされている そんなところだろう 0519132人目の素数さん2024/05/06(月) 09:12:43.39ID:hi35vIbq 望月新一のABC予想解決論文の受理は明らかな不正査読なのだが この事実が明るみに出れば確実に数解研はつぶされる 霊長類研究所と同じ 一発アウトの極悪案件 0520132人目の素数さん2024/05/06(月) 09:40:22.46ID:lw/xQ19x 明るみには出てる もう今回の論文が外部に査読を回してなどいないのは明らか でもその事を一々騒ぎ立てる数学者もいない 結局のところこの手の問題は“中の人”の人間性に対する信頼で担保するしかない “生の卵”を安心して食べるにはその生産工程全部で監視カメラをつけるなんて不可能だから結局その工程に関わっているであろう名前も知らない人々を信頼するしかない そんな一見途方もないと思える事でも「日本なら大丈夫、日本人なら大丈夫」と言ってもらえてた、それは日本人として誇れるもののひとつだった 今回の話はそんな日本への、日本人への信頼をグチャグチャに叩き壊してくれた もう最低でもprimsは廃刊すべき 0521132人目の素数さん2024/05/06(月) 11:29:02.14ID:hi35vIbq>>520 >「日本なら大丈夫、日本人なら大丈夫」 それ世界を知らないヤツの妄想 0522132人目の素数さん2024/05/06(月) 11:36:42.38ID:lw/xQ19x そうか? 日本でなら生卵食べれるって話割と聞くよ 0523132人目の素数さん2024/05/06(月) 12:27:43.23ID:mEg4Fk3z まあ小さな抗議として数理研集会の論文乞食アンケートはずいぶん前から無視してる、 旅費出させた時もな笑 0524132人目の素数さん2024/05/06(月) 12:30:51.05ID:mEg4Fk3z>>518 Zen大学設立認可のための神輿でしょ、神輿は軽くてパーがいい♪ 理事として報酬たんまりもらってるはずなのに それをまったく説明しないのは不誠実極まりないよね。 まあある数論の人は彼のことを悪魔に魂売ったって言ってたな 0525132人目の素数さん2024/05/06(月) 14:59:35.05ID:yTnsNAbo “Will Sawin was born in Malden, Massachusetts, in October 1993. He was a child prodigy who finished learning the high school mathematics curriculum by the age of eight. The famous mathematician Serge Lang of Yale University came to Sawin’s elementary school to meet him, following which Sawin started taking BSc classes at Yale University at the tender age of ten. He was concurrently working on his high school and Yale University curricula, and in 2011, at the age of seventeen, he simultaneously received both his high school diploma and his undergraduate degree from Yale, majoring both in mathematics and economics. He was awarded the George Beckwith undergraduate prize at Yale for proficiency in mathematics or astronomy.