Timeline for On the history of the Artin Reciprocity Law
Current License: CC BY-SA 3.0
9 events
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| Jul 4, 2016 at 20:27 | vote | accept | Asvin | ||
| Jul 4, 2016 at 2:04 | comment | added | post.as.a.guest | Furthermore, Lang also indicates that Weil (1974) was annoyed by conjectures in general, particularly with the so-called Mordell conjecture due to there being not a shred of evidence for/against it (Lang queries the "so-called" here (as it being not due to Mordell?), but I think Weil just means that calling it a "conjecture" in the formal sense is not completely warranted w/o evidence). So I think that is more prevalent to his view, rather than anything about the modularity conjecture, or reciprocity. | |
| Jul 4, 2016 at 1:30 | comment | added | post.as.a.guest | As Lang (Notices Nov 1995) relates from Shimura, regarding the conversation of Weil's initial doubts: firstly, Taniyama opines that modular functions are themselves not enough, and then Weil says that he thinks the picture with elliptic curves in general should be completely different and mysterious (even more than uniformization by automorphic functions). Calling this the "Shimura-Taniyama conjecture" at this point in 1955 seems rather anachronistic. The later words at a IAS party (1962-4) by Weil are more direct and pointed, with the famous "both are denumerable" comment. | |
| Jul 3, 2016 at 20:17 | comment | added | Timothy Chow | This is pure speculation, but I think that Artin reciprocity is one of those things that seems "too good to be true." Any expert eventually develops, through long experience, an intuition as to what sorts of conjectures are too optimistic. For example, if I recall correctly, S.-T. Yau initially thought that mirror symmetry, as proposed by the physicists, seemed too good to be true. Of course, while the experts are usually right, they are sometimes wrong, and that's when we get some of the most electrifying discoveries in mathematics. | |
| Jul 3, 2016 at 20:13 | answer | added | Franz Lemmermeyer | timeline score: 17 | |
| Jul 3, 2016 at 18:55 | history | edited | Asvin | CC BY-SA 3.0 |
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| Jul 3, 2016 at 18:46 | history | edited | GH from MO |
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| Jul 3, 2016 at 18:45 | comment | added | GH from MO | Interestingly, according to Shimura, Weil had doubts about (or saw little reason to believe in) the Shimura-Taniyama conjecture, which is a result of similar character. BTW, I think your question is most appropriate on this site, so don't worry about that. | |
| Jul 3, 2016 at 17:58 | history | asked | Asvin | CC BY-SA 3.0 |