Reply to thread

Message: <blockquote data-quote="mag123" data-source="post: 21113848" data-attributes="member: 73975">Yes , you are correct Professor Sir Andrew John Wiles proved it and his proof is over 150 pages, and uses techniques from algebraic geometry and number theory .   -----------------------------------------------------------------------------------During 21–23 June 1993 Wiles announced and presented his proof of the Taniyama–Shimura conjecture for semi-stable elliptic curves, and hence of Fermat's Last Theorem, over the course of three lectures delivered at the Isaac Newton Institute for Mathematical Sciences in Cambridge, England.[1] There was a relatively large amount of press coverage afterwards.[23]After the announcement, Katz was appointed as one of the referees to review Wiles's manuscript. In the course of his review, he asked Wiles a series of clarifying questions that led Wiles to recognise that the proof contained a gap. There was an error in one critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. The error would not have rendered his work worthless – each part of Wiles's work was highly significant and innovative by itself, as were the many developments and techniques he had created in the course of his work, and only one part was affected.[29] Without this part proved, however, there was no actual proof of Fermat's Last Theorem.Wiles and his former student Richard Taylor spent almost a year resolving this issue.[30][31] Wiles indicates that on the morning of 19 September 1994 he realised that the specific reason why the Flach approach would not work directly suggested a new approach based on his previous attempts using Iwasawa theory, which resolved the issue and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles asked three colleagues (including Faltings) to review his new proof,[11] and on 24 October 1994 Wiles submitted two manuscripts, "Modular elliptic curves and Fermat's Last Theorem"[32] and "Ring theoretic properties of certain Hecke algebras",[33] the second of which Wiles had written with Taylor and proved that certain conditions were met which were needed to justify the corrected step in the main paper.The two papers were vetted and finally published as the entirety of the May 1995 issue of the Annals of Mathematics. The new proof was widely analysed, and became accepted as likely correct in its major components.[34][35][36][37] These papers established the modularity theorem for semistable elliptic curves, the last step in proving Fermat's Last Theorem, 358 years after it was conjectured.----------------------------------------------------------------------------------------------------------------<img src="/styles/default/xenforo/smilies/default/yes.gif"  class="smilie" loading="lazy" alt=":yes:" title="Yes    :yes:" data-shortname=":yes:" /><img src="/styles/default/xenforo/smilies/default/yes.gif"  class="smilie" loading="lazy" alt=":yes:" title="Yes    :yes:" data-shortname=":yes:" /><img src="/styles/default/xenforo/smilies/default/yes.gif"  class="smilie" loading="lazy" alt=":yes:" title="Yes    :yes:" data-shortname=":yes:" />-</blockquote>

Verification: Dawasata paya keeyak thibeda?

Top Bottom