Fermat's Last Theorem - The Odyessy

It took 360 years for many generations of great mathematicians to finally prove Fermat's last theorem. The theorem itself has no practical significance even in a mathematical sense. During the struggle to prove the theorem, many new techniques were developed, new theorems were proved, in particular the Taniyama-Shimura Conjecture was proved which has tremendous implications in mathematics.

Here is the timeline of major milestones in the establishment and proof of the Fermat's last theorem according to the book "Fermat's Enigma" by Simon Singh.

600BC Pythagorean theorem

1637 Fermat's last theorem proposed

1753 First breakthrough in proving Fermat's last theorem by
Leonhard Euler for n=3

1825 Using a method proposed by Sophie Germain, Gustav Dirichlet
and A. Legndre proved Fermat's theorem for n=5

1839 Gabriel Lame proved the theorem for n=7

1847 Spectacular failures - Proof of the Fermat's last theorem
proposed by G. Lame and A. L. Cauchy was shown to be wrong by Ernst Kummer

1908 Paul Wolfskehl found a mistake in Kummer's paper and corrected it. He created Wolfskehl Prize for the first person who proves the Fermat's last theorem

1955 Taniyama-Shimura Conjecture proposed by Japanese mathematician Yutaka Taniyama and Goro Shimura about the relation between modular form and elliptic equation

1984 Gehard Frey showed that if Taniyama-Shimura Conjecture can be proved, then Fermat's last theorem is automatically proved

1986 Andrew Wiles started working on proving Taniyama-Shimura Conjecture for purpose of proving Fermat's last theorem

1988 The claimed proof by Yoichi Miyaoka was shown to be wrong

1993 Andrew Wiles announced his proof of Fermat's last theorem
1993 An error was found in Wiles' proof by referees

1994 Error fixed by Andrew Wiles and Richard Taylor

1995 The proof published in Annals of Mathematics

1997 Andrew Wiles was awarded Wolfskehl Prize