Bluff your way in Fermat's Last Theorem


The proof

Annals of Mathematics, 2nd Series, 141 (3), May 1995, pp. 443–572

Front Matter

Andrew Wiles, "Modular elliptic curves and Fermat's last theorem," pp. 443–551

Andrew Wiles and Richard Taylor, "Ring-theoretic properties of certain Hecke algebras," pp. 553–572

Back Matter

Alternative version of the Wiles paper and the Wiles-Taylor paper (courtesy of Derek Buchanan).


A review

"I think that if you were lost on a desert island and you had only this manuscript then you would have a lot of food for thought. You would see all of the current ideas of number theory. You turn to a page and there's a brief appearance of some fundamental theorem by Deligne and then you turn to another page and in some incidental way there's a theorem by Helegouarch — all of these things are just called into play and used for a moment before going on to the next idea."

 

Kenneth A. Ribet


Also of interest: the proof of Shimura-Taniyama-Weil conjecture

Fred Diamond, "On deformation rings and Hecke rings," Annals of Mathematics, 2nd Series, 144 (1), July 1996, pp. 137–166

Brian Conrad, Fred Diamond and Richard Taylor, "Modularity of certain potentially Barsotti-Tate Galois representations," Journal of the American Mathematical Society, 12 (2), 1999, pp. 521–567

Christophe Breuil, Brian Conrad, Fred Diamond and Richard Taylor, "On the modularity of elliptic curves over Q: wild 3-adic exercises," Journal of the American Mathematical Society, 14 (4), 2001, pp. 843–939


The bluffer's guide to Fermat's Last Theorem

The papers above are provided for the benefit of those without access to JSTOR or JAMS but would nevertheless like to know what the proof of the most celebrated theorem in Mathematics looks like.

However, if you don't have easy access to JSTOR or the AMS periodicals, then the likelihood is that you aren't a professional number theorist or arithmetic geometer. So, like yours truly, you won't have much chance of understanding the papers above. In which case you may wish to check out the following (much more readable) expositions:


Allan Adler, Lecture notes on Fermat's last theorem, University of Rhode Island, June 7–August 12, 1993 (original files available here)

Avner Ash and Robert Gross, "Generalized non-abelian reciprocity laws: a context for Wiles' proof," Bulletin of the London Mathematical Society, 32 (4), July 2000, pp. 385–397.

David Cox, "Introduction to Fermat's last theorem," American Mathematical Monthly, 101 (1), January 1994, pp. 3–14

Charles Daney, The mathematics of Fermat's last theorem, 1996 (original files available here)

Gerd Faltings, "The proof of Fermat's last theorem by R. Taylor and A. Wiles," Notices of the American Mathematical Society, 42 (7), July 1995, pp. 743–746

Fernando Gouvêa, "A marvelous proof," American Mathematical Monthly, 101 (3), March 1994, pp. 203–222

Israel Kleiner, "From Fermat to Wiles: Fermat's Last Theorem becomes a theorem," Elemente der Mathematik, 55 (1), February 2000, pp. 19–37

Barry Mazur, "Number theory as gadfly," American Mathematical Monthly, 98 (7), August-September 1991, pp. 593–610

Barry Mazur, "On the passage from local to global in number theory," Bulletin of the American Mathematical Society, 29 (1), July 1993, pp. 14–50

Kenneth Ribet, "Galois representations and modular forms," Bulletin of the American Mathematical Society, 32 (4), October 1995, pp. 375–402

Karl Rubin and Alice Silverberg, "A report on Wiles' Cambridge lectures," Bulletin of the American Mathematical Society, 31 (1), July 1994, pp. 15–38

Richard Taylor, "Galois representations," Annales de la FacultÚ des Sciences de Toulouse, SÚrie 6, XIII (1), 2004, pp. 73–119.

Richard Taylor, "Galois representations," Proceedings of the International Congress of Mathematicians 2002, 1, pp. 449–474


Links

The Mathematics of Fermat's Last Theorem (by Charles Daney)

Fermat's Last Theorem — the story, the history and the mystery (by David Shay)




Contact: Comments on this page are welcome. Please write to L.H.Lim@dpmms.cam.ac.uk.