tag:blogger.com,1999:blog-8070362.post111674811453254407..comments2023-06-05T14:03:50.121+05:30Comments on Death Ends Fun: Marginal at bestDilip D'Souzahttp://www.blogger.com/profile/08221707482541503243noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-8070362.post-1128517218645355122005-10-05T18:30:00.000+05:302005-10-05T18:30:00.000+05:30Here's more information on a new proof of Fermat's...Here's more information on a new proof of Fermat's Last Theorem, due to Khare, Wintenberger and Dieulefait (it also mentions a related conjecture of Serre):<BR/><BR/>http://www.matematicalia.net/Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1117476777371448522005-05-30T23:42:00.000+05:302005-05-30T23:42:00.000+05:30Dilip,Many Many thanks for discussing mathematics ...Dilip,<BR/><BR/>Many Many thanks for discussing mathematics and science in general. I find very lonely in my land where none is interested in talking science. <BR/>You have done very good background reading, I'm happy, otherwise you would not have known the famed Taniyama-Shimura conjecture. <BR/>It is also worth mentioning that by the time he got a conclusive proof, Wiles crossed that magic age-limit of 40 for Fields medal, but still got one special prize. <BR/><BR/>If it interests you, there is another "star work" in the horizon sone by a young Russian Mat'cian Grisha Perelman. This is also a proof of a famous conjecture - Poincare' conjecture in geometry. I'm more familiar with this than Fermat's theorem. Still if you could write a few words about this in future, will be grateful.<BR/><BR/>A student of theor. physics.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1117028477635366872005-05-25T19:11:00.000+05:302005-05-25T19:11:00.000+05:30Really enjoyed this blog!I recently started a blog...Really enjoyed this blog!<BR/><BR/>I recently started a blog that you might be interested in (it is not as well written).<BR/><BR/>I am an amateur who is using a series of blogs to trace the history of Fermat's Last Theorem from Fermat's notes in the margin to Wiles' proof. My focus is on the mathematics and proofs. The goal is to present a series of proofs in the same format as Euclid's Elements.<BR/><BR/>I would be very interested in any comments that you have:<BR/>http://fermatslasttheorem.blogspot.com<BR/><BR/>Cheers,<BR/><BR/>-LarryLegacy Userhttps://www.blogger.com/profile/02600423550336034710noreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116929479833101422005-05-24T15:41:00.000+05:302005-05-24T15:41:00.000+05:30Rohit -- There may not be more to talk about that ...Rohit -- There may not be more to talk about that identity than what Wiki does.<BR/><BR/>Suresh -- I thought Dilip did not miss that point. In fact he stressed that point:<BR/><I><BR/>There were some gaps in his work, but over the next couple of years, he took care of those. His eventual proof, like Fermat's, was also a little longer than a margin could contain: it actually filled an entire 130-page issue of the journal Annals of Mathematics.<BR/></I><BR/><BR/>Also he linked to Wiles and Taylor-Wiles.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116928844610768932005-05-24T15:30:00.000+05:302005-05-24T15:30:00.000+05:30Dear Dilip,A follow up on my earlier comment about...Dear Dilip,<BR/><BR/>A follow up on my earlier comment about natural numbers. First<BR/><BR/>(cube root 4)cubed plus (cube root 4)cubed<BR/>=2 cubed<BR/><BR/>would always give you a solution for n=3. And you can do this for any power. I picked squares just to show that even finding the Pythagorean triplets reduces to a trviality if one allows arbitrary numbers on the real line as possible solutions. It is restricting the problem to natural numbers that makes it really hard.<BR/><BR/>To give a more precise history: Wiles announced the proof of his theorem in 1993. There was a serious gap. It was resolved in August 1994 by a the paper of <BR/>Rcihard Taylor and Andrew Wiles in the same volume of the Annals of Mathematics cited by you. Incidentally, C. Khare (at that time in TIFR, Mumbai) and R. Ramakrishna subsequently developed their own approach to the Taylor-Wiles systems,<BR/>as they are known. C. Khare's work has recently gone "beyond" FLT. Check out<BR/><BR/>http://www.hindu.com/2005/04/25/stories/2005042506530100.htm<BR/><BR/>RaviAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116920471506381932005-05-24T13:11:00.000+05:302005-05-24T13:11:00.000+05:30Hi Dilip, you missed the coda. As it turns out, W...Hi Dilip,<BR/> you missed the coda. As it turns out, Wiles was not done. there were serious problems in his proof that needed to be fixed, and were finally resolved a few years later in papers by Wiles and Taylor. <BR/><BR/><A HREF="http://mathworld.wolfram.com/FermatsLastTheorem.html" REL="nofollow">More here</A><BR/><BR/>Nice job on the article. Your science writing is infrequent but always a pleasure. as a math blogger, I appreciate the company :)Suresh Venkatasubramanianhttps://www.blogger.com/profile/15898357513326041822noreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116920038462455882005-05-24T13:03:00.000+05:302005-05-24T13:03:00.000+05:30Ravi, I almost picked up Simon Singh's book some m...Ravi, I almost picked up Simon Singh's book some months ago, after reading a good review somewhere. Don't know why I didn't. But now that you've mentioned it again, I will make sure to get it. (Kraktik, is that the book you had in mind?) Have you read <A HREF="http://www.amazon.com/exec/obidos/ASIN/0312381859/qid=1116919293/sr=2-1/ref=pd_bbs_b_2_1/102-3567769-1058551" REL="nofollow">A History of Pi"</A>? Quite a delight.<BR/><BR/>Also, you're right about natural numbers, but the thing about these articles is, I need to limit what I will explain, what concepts I write about. I took the easy way, assuming that most people who read this would understand "number" to mean "natural number".<BR/><BR/>One more thing: while I get your point, the solution you offer is not what the equation (Fermat's) asks for. The theorem holds for powers greater than 2.<BR/><BR/>Anurag, I have not read "Schrodingers Kittens", tell me more. Why not make a trip from Pune here and drop it off...?<BR/><BR/>Fadereu old chum, "like a good teacher"?! I think I had better revise how I write about science after that! I know little about Euler's Identity, despite your Wiki pointer. Anand, you wanna be the teacher?Dilip D'Souzahttps://www.blogger.com/profile/08221707482541503243noreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116914743683016362005-05-24T11:35:00.000+05:302005-05-24T11:35:00.000+05:30Dear Dilip,Perhaps you could have emphasised that ...Dear Dilip,<BR/><BR/>Perhaps you could have emphasised that <BR/>the you are talking only about "natural<BR/>numbers" when trying to find solutions to <BR/>your equations. Otherwise,<BR/><BR/>(root 2) squared plus (root 2) squared= 4<BR/><BR/>is always possible. Incidentally, the best popular account of the Fermat Saga is due to Simon Singh (Fermat's enigma). Also due to him is an excellent BBC documentary on the subject.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116852697200160382005-05-23T18:21:00.000+05:302005-05-23T18:21:00.000+05:30Hi Dilip, I love the way write about science, like...Hi Dilip, I love the way write about science, like a good teacher. <BR/><BR/>As a faithful student, I demand a post on the Euler's Identity, and here's the <A HREF="http://en.wikipedia.org/wiki/Euler's_identity" REL="nofollow">wikipedia entry</A>.Anonymoushttps://www.blogger.com/profile/05074262977593006257noreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116830077418311792005-05-23T12:04:00.000+05:302005-05-23T12:04:00.000+05:30I'd have loved to be there, too. Sigh.You seem to ...I'd have loved to be there, too. Sigh.<BR/><BR/>You seem to like science and mathematics a lot, Dilip. Have you read "Schrodinger's kittens"? It's a must read...Anuraghttps://www.blogger.com/profile/15081668599890491146noreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116825942033460422005-05-23T10:55:00.000+05:302005-05-23T10:55:00.000+05:30Marginal at best! This is perhaps the best title t...Marginal at best! This is perhaps the best title that I've seen recently.<BR/><BR/>Nice post, Dilip.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8070362.post-1116786741742644382005-05-23T00:02:00.000+05:302005-05-23T00:02:00.000+05:30Funny you should mention it ... I read a most intr...Funny you should mention it ... I read a most intriguing book on this about a year back, it was called "Fermat's Last Theorem - The most intriguing problem in mathematics" or something to that effect ( I know for certain it wasn't that exactly ). They go on to discuss it right from the time of hte Greeks down to Andrew Wiles.<BR/><BR/>KRAKTIK.k.r.a.k.t.i.khttps://www.blogger.com/profile/07674366816838476546noreply@blogger.com