| Description |
Fermat's Last Theorem (FLT) states that if n is an integer greater than three, the equation xn + yn = zn has no integer solutions with xyz 6= 0. This incredible statement eluded proof for over three-hundred years: in that time, mathematicians developed numerous tools which finally proved FLT in 1995. In this paper, we introduce some of the essential objects which enter the proof - especially modular forms, elliptic curves, and Galois representations - with an emphasis on precisely stating the Shimura-Taniyama Conjecture and explaining how its proof finally settled FLT. We o↵er proofs whenever they clarify a definition or elucidate an idea, but generally prefer examples and exposition which make concrete a truly beautiful body of mathematical theory. |
