Simon singh also produced a rather good tv documentary on it for horizon, a rare example of maths being made the subject of a tv programme. Pdf the story of fermats last theorem researchgate. They speak of it in awed terms and consider it to be an even more difficult problem than fermat s last theorem, which was finally proven by andrew wiles in 1995. Fermat s last theorem flt, 1637, states that if n is an integer greater than 2, then it is impossible to find three natural numbers x, y and z where such equality is met being x,y0 in xn. This book will describe the recent proof of fermat s last theorem by andrew wiles, aided by richard taylor, for graduate students and faculty with a reasonably broad background in algebra. We propose in the rest of this article to sketch how galois theory is used in the proof of. The twoway the mathematics problem he solved had been lingering since 1637. If you are having trouble logging in, email your instructor. Computer verification of wiles proof of fermats last theorem. When studying elliptic curves, there is in theory nothing lost. Fermats last theorem a mathematical mystery youtube. One of his contributions was the idea of congruence arithmetic. View fermat s last theorem research papers on academia. Both fermat s last theorem and the modularity theorem were almost.
Why its so impressive that fermats last theorum has been. Fermat s last theorem by simon singh fourth estate, 1997. Elliptic curves, modularity, and fermats last theorem. 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.
The only case of fermat s last theorem for which fermat actually wrote down a proof is for the case n 4. Professor who solved fermat s last theorem wins maths abel prize. Nigel boston university of wisconsin madison the proof. Fermats last theorem to view the content on this page, click here to log in using your course website account. The last person i investigated was carl friedrich gauss 17771855. The story of a riddle that confounded the worlds greatest minds for. If r s t 0, then the coefficients of the weierstrass equation transform as ai aiui. As for modular forms, we will mostly cover the basic definitions. In particular, this finally yields a proof of fermats last theorem. Fermat s last theorem, the most notorious problem in the history of mathematics. We will show that for large values of n, fermats theorem holds. Modular elliptic curves and fermats last theorem pdf. As it has been mentioned in dr who, star trek, the simpsons and the liz hurley blockbuster bedazzled, i would hope that most people would know the intricacies of fermat s last theorem. Fermats little theorem robinson 6 to be careful, though, not to get too far ahead here in what is meant to provide a background to the history of fermats little theorem.
Galois representations and the theorem of fermatwiles. Formalize and verify by computer a proof of fermats last theorem, as proved by a. It has all the makings of a great mystery a 17th century genius, an ancient greek text, and a 10 year old boy, who in the 1960s was determined to solve the mystery of a 350 year old maths. In the riemann hypothesis, acclaimed author karl sabbagh interviews some of the worlds finest mathematicians who have spent their lives working on. Modular elliptic curves and fermats last theorem homepages of.