Our goal is to explain exactly what andrew wiles 14, with the. The work on this paper was supported by an nsf grant. The only case of fermat s last theorem for which fermat actually wrote down a proof is for the case n 4. What follows, therefore, is a sketch of much simpler and indeed more classical ideas related to fermat s last theorem. Modular elliptic curves and fermats last theorem homepages of. When andrew john wiles was 10 years old, he read eric temple bells the. The only prerequisites needed to follow the proof are some high school algebra and the ability to take derivatives of products and quotients of polynomials. The proof, takeshi saito, this is the second volume of the book on the proof of fermat s last theorem by wiles and taylor the first volume is published in the same series.
Wiless proof of fermats last theorem is a proof by british mathematician andrew wiles of a special case of the modularity theorem for elliptic curves. This book will describe the recent proof of fermat s last the orem by andrew wiles, aided by richard taylor, for graduate. Although andrew wiles proved fermat s last theorem, the following analysis is offered as a biproduct of the authors unsuccessful attempts to solve fermat s last theorem. Given the right angled triangle below, we know from pythagoras that the sides a, b and c are related by the equation. When one supercube made up of unit cubes is subtracted from a. The leading thought throughout the derivation is illustrated in fig. Nigel boston university of wisconsin madison the proof. Easier aspects of fermat s last theorem it goes without saying that the nonexpert will have a tough time getting to grips with andrew wiles proof. This deep result allowed him to reduce fermats last theorem to the shimurataniyama conjecture. In particular, this finally yields a proof of fermats last theorem. Karl rubin uc irvine fermat s last theorem ps breakfast, march 2007 23 37. Here the detail of the proof announced in the first volume is fully exposed. Wiles announces his proof in three lectures on modular forms, elliptic curves, and galois representations at a workshop at the newton institue in cambridge, england. Using some clever com mutative algebra, wiles obtains conditions for such a map to be an isomorphism.
Wiles announces his proof in three lectures on modular forms, elliptic curves, and galois representations at a workshop at the newton institue in. Why its so impressive that fermats last theorum has been. It can bepresented in a very elementary way, and it is interesting in itself. In our final lecture we give an overview of the proof of fermats last theorem. In 1986 gerhard frey places fermat last theorem at elliptic curve. After all, professor wiles had already won almost every other prize for his 1995 proof of fermat s last theorem, the most notorious problem in the history of mathematics. Jiang and wiles proofs on fermat last theorem4 vixra. The proof of the fermats last theorem will be derived utilizing such a geometrical representation of integer numbers raised to an integer power.