Timeline for The first complete proof of the Kronecker-Weber theorem
Current License: CC BY-SA 3.0
7 events
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| Sep 6, 2011 at 11:15 | comment | added | Franz Lemmermeyer | I agree with both of your objections. Weber's proof was a proof, but it had a gap, which was pointed out to him by Frobenius, whose observation was incorporated into the corrigenda of Weber's third proof. BTW, at least in the above quote in Spanish, Gray talks not about the "first proof", but about the "first valid proof". | |
| Aug 31, 2011 at 19:31 | comment | added | anon | We are talking about Weber's proof, not Kronecker's. I'm strongly objecting to Gray's statement "it is also not true that the first proof is due to Weber" (and also to the sort of mentality that leads to such statements). I also object to his statement that "Weber's mistake was not found until 1979". How would he know? Not everyone writes a paper every time they find a mistake. | |
| Aug 31, 2011 at 17:48 | comment | added | Franz Lemmermeyer | Well, sometimes the giants do not prove the great theorems. There's a paper of Kronecker in which he "proves" that primes splitting completely in a normal extension K/Q have density 1/(K:Q). Actually he doesn't prove anything. Even worse, I am not able to tell whether some of his statements are conjectures or whether he actually thought he had a proof. I would certainly vote it to be one of the best papers he wrote, but filling the gaps, at least in this case, is not for pygmies, neither early nor late in the day. | |
| Aug 31, 2011 at 15:14 | comment | added | anon | Well, they are questioning whether Weber proved the theorem, and even whether it should be called the Kronecker-Weber theorem. If you look hard enough, you can find errors in a great many proofs: the giants prove the great theorems; the pygmies fix their proofs. | |
| Aug 31, 2011 at 12:39 | comment | added | Franz Lemmermeyer | Among the errors in one of Weber's proof not pointed out by Neumann is his theorem that in cyclic extensions of number fields with prime power degree, a prime that ramifies must ramify completely. Of course he could have circumvented this "result" had someone pointed out to him that it was nonsense. Even Goldbach managed to prove that -1 is not a square modulo primes 4n+3 after Euler had politely corrected about a dozen errors in his attempts to do so. And as far as I can see, no one so far has disputed the depth of Kronecker's (and, perhaps to a lesser degree, Weber's) ideas. | |
| Aug 31, 2011 at 11:54 | history | edited | anon | CC BY-SA 3.0 |
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| Aug 31, 2011 at 0:45 | history | answered | anon | CC BY-SA 3.0 |