Timeline for Philosophy behind Mochizuki's work on the ABC conjecture
Current License: CC BY-SA 3.0
12 events
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| Nov 16, 2017 at 22:15 | comment | added | Samantha Y | @DavidRoberts just wanted to say that your optimistic comment was very uplifting, and on a personal level, encouraged me to go back and not only take another stab at trying to understand IUT, but also led me to realize my understanding of colimits was woefully inadequate! exactly the point of Mathoverflow comments, and MO in general, in my humble opinion | |
| Sep 19, 2012 at 0:02 | comment | added | Felipe Voloch | @Vesselin: I'm sorry I voted to close. Your answers (and the others too) are quite interesting, but it's a matter of principle. | |
| Sep 18, 2012 at 20:10 | comment | added | Vesselin Dimitrov | My apology for sounding argumentative in relating my impression from Mochizuki's papers: it was not my intention, and I should not have used the word "disagree." | |
| Sep 18, 2012 at 11:05 | comment | added | Minhyong Kim | Deane Yang mentioned this post on Facebook, remarking that Vesselin Dimitrov 'dared to disagree' with me. Of course Deane meant this in a good humored way. But still, I copy here my reply, in case there's any misunderstanding: Hi Deane, 'Dare to disagree' is a strong term! I still haven't had any time to really look at Mochizuki, so it's quite likely I said something stupid that was noted by Dimitrov. I'll try to look at it more carefully soon, but I hope it doesn't take much daring for people to disagree with me (in general). | |
| Sep 18, 2012 at 1:01 | comment | added | David Roberts♦ | This sounds like sensible mathematics, far from the cries of 'no one has any idea what he's doing!' reported in the press. Creating new mathematical objects that are formal (co)limits of existing objects without the required (co)limits is a long-established tradition (e.g. negative numbers! but more recently stacks etc). | |
| Sep 17, 2012 at 21:42 | comment | added | Pasten | (cont.) The table in page 27 of IUTT-I gives an idea of what are the roles played by some of the main objects introduced by Mochizuki (and as VD pointed out, the hyperbolic curve "is" the number field, not the elliptic curve). Anybody can read this directly from the paper, but the only reason why I am mentioning it is the following: I was very curious about the papers (as everybody else), but the first couple pages seemed very intimidating. However, after spending some time with the papers on Frobenioids then the introduction of IUTT-I became readable after all. I hope this suggestion helps! | |
| Sep 17, 2012 at 21:28 | comment | added | Pasten | For people wanting to known more details without having to read all the 500 pages: the answer provided by VD is a nice survey of the first 16 pages of IUTT-I (avoiding technicalities of how the several types of Hodge theaters are actually constructed, or what are the prime-strips). For the interested reader, the first 27 pages of IUTT-I indeed give a very good introduction. However, it is better to get used with the language of Frobenioids FIRST, otherwise the exposition can be intimidating. Unfortunately, it does not hint on the actual "source of inequality" (I mean, not beyond analogies). | |
| Sep 17, 2012 at 16:35 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Sep 17, 2012 at 15:07 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Sep 17, 2012 at 15:02 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Sep 17, 2012 at 14:41 | history | edited | Vesselin Dimitrov | CC BY-SA 3.0 |
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| Sep 17, 2012 at 14:34 | history | answered | Vesselin Dimitrov | CC BY-SA 3.0 |