Wiles's Proof of Fermat's Last Theorem

Wiles's Proof Of Fermat's Last Theorem

Wiles' proof of Fermat's Last Theorem is a proof of the modularity theorem for semistable elliptic curves released by Andrew Wiles, which, together with Ribet's theorem, provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the Modularity Theorem were almost universally considered inaccessible to proof by contemporaneous mathematicians (meaning, impossible or virtually impossible to prove using current knowledge). Wiles first announced his proof in June 1993 in a version that was soon recognized as having a serious gap in a key point. The proof was corrected by Andrew Wiles, in part via collaboration with a colleague, and the final, widely accepted, version was released by Wiles in September 1994, and formally published in 1995. The proof uses many techniques from algebraic geometry and number theory, and has many ramifications in these branches of mathematics. It also uses standard constructions of modern algebraic geometry, such as the category of schemes and Iwasawa theory, and other 20th-century techniques not available to Fermat.

The proof itself is over 100 pages long and consumed seven years of Wiles's research time. For solving Fermat's Last Theorem, he was knighted, and received other honors.