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Ask HN: Understanding inter-universal Teichmüller theory?

13 点作者 valera_rozuvan将近 10 年前
Hi! My name is Valera Rozuvan, and I want to understand inter-universal Teichmüller theory. For those of you who never heard of this theory, please take a look at the Wikipedia&#x27;s entry https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Inter-universal_Teichm%C3%BCller_theory .<p>Why is this important? This theory might have a proof for the abc conjecture.<p>My background is in physics, optics. I finished the Taras Shevchenko National University of Kyiv. I am a hobbyist mathematician.<p>What should be my path of learning that will lead to understanding this theory? Any advice on specific texts, courses, online resources, etc. will be appreciated!

4 条评论

impendia将近 10 年前
It would take an <i>extraordinary</i> effort. I doubt there is <i>anyone</i> who could learn this material given anything less than a year of solid study -- and I am thinking of the leading researchers in the world, who are already experts in everything related. I am a professional mathematician myself, and I doubt I could manage it even within a year.<p>This is dictated by the difficulty of the subject, and it is even more so since Mochizuki&#x27;s papers are notoriously difficult to read. What I have heard from other research mathematicians is that Mochizuki doesn&#x27;t make much of an effort to make himself comprehensible, to answer questions, or in general to explain his results to the community.<p>Also please be warned that the consensus is generally that Mochizuki&#x27;s theory is probably incorrect.<p>That said, if you want to learn the stuff, there is no reference other than Mochizuki&#x27;s papers themselves. If you would like to learn some general background theory I would recommend learning some algebraic geometry, for which see Ravi Vakil&#x27;s book:<p><a href="http:&#x2F;&#x2F;math.stanford.edu&#x2F;~vakil&#x2F;216blog&#x2F;FOAGapr2915public.pdf" rel="nofollow">http:&#x2F;&#x2F;math.stanford.edu&#x2F;~vakil&#x2F;216blog&#x2F;FOAGapr2915public.pd...</a><p>and maybe Milne on etale cohmology:<p><a href="http:&#x2F;&#x2F;www.jmilne.org&#x2F;math&#x2F;CourseNotes&#x2F;LEC210.pdf" rel="nofollow">http:&#x2F;&#x2F;www.jmilne.org&#x2F;math&#x2F;CourseNotes&#x2F;LEC210.pdf</a><p>If you find that incomprehensible, start with Dummit and Foote&#x27;s <i>Abstract Algebra</i> (read it cover to cover), Neukirch&#x27;s <i>Algebraic Number Theory</i>, Atiyah and Macdonald&#x27;s <i>Commutative Algebra</i>, and Fulton and Harris&#x27;s <i>Representation Theory</i>.<p>If you indeed want to read all that, you may as well enroll in a Ph.D. program in math....
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upwg24将近 10 年前
see <a href="http:&#x2F;&#x2F;www.claymath.org&#x2F;events&#x2F;iut-theory-shinichi-mochizuki" rel="nofollow">http:&#x2F;&#x2F;www.claymath.org&#x2F;events&#x2F;iut-theory-shinichi-mochizuki</a> and <a href="https:&#x2F;&#x2F;www.maths.nottingham.ac.uk&#x2F;personal&#x2F;ibf&#x2F;files&#x2F;symcor.iut.html" rel="nofollow">https:&#x2F;&#x2F;www.maths.nottingham.ac.uk&#x2F;personal&#x2F;ibf&#x2F;files&#x2F;symcor...</a> for more information, including the 1st letter to its participants.
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asdftemp将近 10 年前
hi there, you might start with this mathoverflow thread: <a href="http:&#x2F;&#x2F;mathoverflow.net&#x2F;questions&#x2F;106560&#x2F;philosophy-behind-mochizukis-work-on-the-abc-conjecture" rel="nofollow">http:&#x2F;&#x2F;mathoverflow.net&#x2F;questions&#x2F;106560&#x2F;philosophy-behind-m...</a>
valera_rozuvan将近 10 年前
A very-very good YouTube video explaining what the abc conjecture is: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=RkBl7WKzzRw" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=RkBl7WKzzRw</a> .