Almost every mathematician at the time had previously considered both Fermat's Last Theorem and the Modularity Theorem either impossible or virtually impossible to prove, even given the most cutting edge developments.
One culmination of the pursuit ofpure mathematics is the affirmative answer to Fermat's Last Theorem, whose proof was found using the Modern Number Theory.
From 1993 to 1994, Andrew Wiles provided a proof of the modularity theorem for semistable elliptic curves, which, together with Ribet's theorem,provided a proof for Fermat's Last Theorem.
Grothendieck's use of these universes(whose existence cannot be proved in ZFC) led to some uninformed speculation that étale cohomology andits applications(such as the proof of Fermat's last theorem) needed axioms beyond ZFC.
In the afternoon-only program on September 8, Kazuhiko Aso of the Graduate School of Mathematical Sciences, University of Tokyo, described how he came to discover audio tapes of lectures given at the"Tokyo-Nikko Symposium"(the 1955international conference that paved the way for solution of Fermat's Last Theorem, which had gone unsolved for 300 years), and also discussed digitization of the tapes-a topic of global import.
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