Andrew Wiles proves Fermat's Last Theorem, conjectured by Pierre de Fermat in 1637 and open for 357 years: there are no positive integer solutions to the equation xⁿ + yⁿ = zⁿ for any exponent n greater than 2. Wiles presents an initial version of the proof at a conference in Cambridge in June 1993, but an error detected during peer review requires a substantial correction; the final, correct version, developed together with his former student Richard Taylor, is published in May 1995 in two joint papers in Annals of Mathematics. The proof proceeds by an indirect route: it proves a sufficient case of the Taniyama-Shimura-Weil conjecture on the relationship between elliptic curves and modular forms, from which Fermat's theorem follows as a corollary thanks to earlier work by Ken Ribet (1986) connecting both problems. Having exceeded the 40-year age limit set for the Fields Medal, Wiles was not eligible for the prize; in 1998 the International Mathematical Union instead awarded him a special IMU silver plaque, a distinction created specifically to recognize this achievement outside the usual Fields Medal framework.