tag:blogger.com,1999:blog-3722233.post6876765130667206397..comments2023-09-24T02:44:04.210-05:00Comments on Computational Complexity: When did Mathematicians realize that Fermat did not have a proof of FLT?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-3722233.post-43740972207545719182015-10-11T17:03:06.651-05:002015-10-11T17:03:06.651-05:00Isn't it a little weird to ask when did people...Isn't it a little weird to ask when did people stop believing Fermat had a proof.<br /><br />Presumably the confidence that Fermat didn't have a proof has grown in an almost continuous manner as time passed and no such proof emerged. I would now assign a very very low probability to him having a proof but surely not zero and that will continue to decrease over time.<br /><br />Are you assuming that there was some critical event or time period in which there was a sudden drop in this probability?TruePathhttps://www.blogger.com/profile/00124043164362758796noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-26674919330730477062015-09-22T07:25:40.054-05:002015-09-22T07:25:40.054-05:00(This is Bill Gasarch)
The episoe was Shown in 198...(This is Bill Gasarch)<br />The episoe was Shown in 1989 but took place in the far future. The writers didn't<br />know that FLT would be solved soon, so I don't really call that an error on their parts. After it aired I asked Larry washington, an number theorist when FLT would be solved and he said ``in the next 10 years'' which I call a very good estimate.<br />I also asked him about Rieman: ``not in my lifetime' and <br />Goldbach `in your lifetime but not my lifetime'Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-24699031418755152112015-09-22T06:07:05.630-05:002015-09-22T06:07:05.630-05:00In 1989 FLT was still open. In 1989 FLT was still open. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-50872625982054550452015-09-21T21:58:32.676-05:002015-09-21T21:58:32.676-05:00I recall my abstract algebra professor in undergra...I recall my abstract algebra professor in undergraduate giving me the modern version of a *specific false proof* of FLT using some basic algebraic number theory (trying to solve the equations over various rings like Z[\sqrt{-3}] and whatnot). He said that experts agree this is probably the technique that Fermat thought he had found for FLT, but because he did not write it down and check it thoroughly enough he did not see his mistake (that such and such elements used are not prime in whatever ring). I cannot remember the specific details.j2kunhttps://www.blogger.com/profile/08041921049916424212noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-85402880195373569832015-09-21T17:17:51.809-05:002015-09-21T17:17:51.809-05:00This used to be a FAQ in sci.math something I used...This used to be a FAQ in sci.math something I used to maintain in a previous life:<br /><br />https://cs.uwaterloo.ca/~alopez-o/math-faq/node26.html#SECTION00414000000000000000Alex Lopez-Ortizhttps://www.cs.uwaterloo.ca/~alopez-onoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-3302715232510364222015-09-21T11:24:19.035-05:002015-09-21T11:24:19.035-05:00Hi Bill,
I think that Singh does not make any sta...Hi Bill,<br /><br />I think that Singh does not make any statement to this effect in Fermat's Enigma. If anything, he in fact reiterates (or at least that's what I recall) what we all feel -- Fermat thought that he had a proof, but which must have been incorrect.<br /><br />I would feel that with this Simpson's thing really your option 3 should be the explanation. This is most likely (and perhaps unfortunately) done with the intention of making the story "better".Grad Studenthttp://www.google.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-47085663748196969282015-09-21T10:10:53.932-05:002015-09-21T10:10:53.932-05:00not an expert in this area but my understanding is...not an expert in this area but my understanding is that there is some rough proof that "elementary" techniques cannot succeed related to the complex mathematical framework built up over last few decades (would like to know more details on that myself). ie a sort of impossibility proof. but interpreting those can be very tricky as RJLipton has argued in his blog.vznhttp://vzn1.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-2577419657062120002015-09-21T09:24:24.054-05:002015-09-21T09:24:24.054-05:00I don't know about the history after Fermat (i...I don't know about the history after Fermat (if anyone knows, Singh does). However, on Fermat himself, the consensus is that Fermat believed he had a proof, but later discovered it had a flaw in it, possibly when it came time to actually work out the details.<br /><br />It's interesting to speculate what "proof" Fermat thought he had.Pseudonymhttps://www.blogger.com/profile/04272326070593532463noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-35923592355638367482015-09-21T09:16:33.127-05:002015-09-21T09:16:33.127-05:00My guess is that for a while they thought he had a...My guess is that for a while they thought he had a proof and so they worked to figure out what it was knowing what they knew about his other work of the time and came upon an attempt or two that had subtle errors and figured out that he thought he had a proof but then when he went to formalize it realized he didn't and he moved on with his life. We it seems did not.Anonymousnoreply@blogger.com