 
Pierre de Fermat (1601–1665) was a French magistrate with a passion for numbers. Although he published little, he was recognized as an excellent mathematician by his peers. Fermat posed questions that have shaped mathematics ever since. He had a reputation as one of the leading mathematicians in the world at the time; however, he is best remembered for his work in number theory Fermat is responsible for one of the most famous statements in the history of mathematics. While reading someone's mathematical treatise, Fermat wrote in the book’s margin: “To divide a cube into two cubes, a fourth power, or in general any power whatever into two powers of the same denomination above the second is impossible.” He added that “I have assuredly found an admirable proof of this, but the margin is too narrow to contain it.” In symbols, he was claiming that if n is larger than 2, there are no whole numbers x, y, z such that xn + yn = zn, a statement that came to be known as 'Fermat’s Last Theorem'. For three and a half centuries, it defeated all who attempted to prove it, leaving it with the reputation as the most famous unsolved problem in mathematics. If n is 2, the statement is x2 + y2 = z2, and obviously this does work; it's essentially the Pythagorean Theorem, and has easily been proven. For statements with higher powers, such as x3 + y3 = z3 and x4 + y4 = z4, Fermat said that these have no whole number solutions, and that has been proven. However, Fermat's assertion that the statement xn + yn = zn will never have whole number solutions, for any power n, had never been proven. Unsuccessful attempts to prove the theorem over a 300 year period led to a wealth of other mathematical discoveries. But Fermat's theorem remained elusive. Finally, in 1995, the theorem was proven true by Andrew Wiles, with help from Richard Taylor. Wiles succeeded where so many before him had failed, with a 130-page proof that is incredibly complex; one that certainly would not fit into any margin! |