Timeline for Why certain diophantine equations are interesting (and others are not) ?
Current License: CC BY-SA 2.5
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| Dec 20, 2015 at 17:52 | comment | added | PrimeRibeyeDeal | @MinhyongKim this was another nice answer, in typical style. I was intrigued by your comment about Mochizuki's perspective on additive and multiplicative structures through fundamental groups. Could you say a bit more about that? | |
| Oct 25, 2010 at 17:19 | comment | added | Hailong Dao | Dear Minhyong, thank you for this wonderful answer. I found what you added on Oct 22 particularly inspiring. | |
| Oct 25, 2010 at 16:12 | history | edited | Minhyong Kim | CC BY-SA 2.5 |
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| Oct 23, 2010 at 0:34 | comment | added | Minhyong Kim | Dear Matt, Thanks for your comments. I can't think of a good equation off-hand either, but I hear of nice ones once in a while and then forget about them. Michael Stoll told me about an amusing one that was called the 'box equation,' I think. Maybe someone knowledgeable can remind me what it was. I'm probably just revealing my own ignorance with the comments on Goldbach. But I did sneakily prepare myself for your objection by writing that it is likely to gain in respectability. | |
| Oct 22, 2010 at 17:38 | comment | added | Emerton | ... Fermat got a lot of its cachet because of the way it was entwined with the entire history of algebraic number theory.) Incidentally, has Goldbach ever been unfashionable or unrespectable? It seems to be entwined with the history of analytic number theory in a way at least somewhat analogous to Fermat's connection with algebraic number theory. | |
| Oct 22, 2010 at 17:35 | comment | added | Emerton | Dear Minhyong, I like the preliminary discussion that you have added. Perhaps it's reasonable to distinguish "interesting to oneself" and "interesting to many others at this moment in time". If one's taste or intuition suggests that studying a particular equation is important or interesting, then it may well make sense to study that equation. But I think it is true that, at the present time, there aren't any particular Diophantine equations that are valued for their own sake (i.e. as a problem to be solved in their own right), in the way that Fermat was before it was solved. (And even ... | |
| Oct 22, 2010 at 16:22 | history | edited | Minhyong Kim | CC BY-SA 2.5 |
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| Oct 18, 2010 at 16:17 | history | edited | Minhyong Kim | CC BY-SA 2.5 |
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| Oct 18, 2010 at 13:39 | history | edited | Minhyong Kim | CC BY-SA 2.5 |
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| Oct 18, 2010 at 13:28 | history | answered | Minhyong Kim | CC BY-SA 2.5 |