Fermat's Last Theorem states that there are no whole number solutions to the equation x^n + y^n = z^n for values of n greater than two. It was solved finally by Andrew Wiles whose proof and correction to the proof were released on 25/10/1994 The Taniyama-Shimura conjecture proposed that there was a one-to-one relationship betwen the up to then completely separate branches of mathematics: Modular Forms and Elliptic Curves. Gerhard Frey showed that if Fermat's Last Theorem had a solution for n>2, it would imply the existance of a very strange Elliptic Curve - the Frey Curve. The Frey Curve was so strange that it couldn't possibly be related to a Modular Form. So proving the Taniyama-Shimura conjecture would lead to Fermat's Last Theorm. The Elliptic Curves are characterised by an infinite sequence called the E series, and the Modular forms by a similar sequence called the M series. Wiles was able to show first that the first element of each M-series matched the first element of each E-series, and finally to show that if the first N elements matched then the N+1th element matched too. This proved that Elliptic Curves and Modular forms were different aspects of the same thing, and thus the Frey Curve couldn't exist, and thus Fermat's Last Theorem is true.