Fermat's Last Theorem
Pierre de Fermat
Pierre de Fermat, b. Aug. 17, 1601, d. Jan. 12, 1665, who was a lawyer and government official in Toulouse. However, he is better known as a great French mathematician who made important discoveries in analytical geometry and number theory and also worked on probability theory and optics.
In 1636, Fermat presented a system of analytic geometry similar to the one that Descartes would propose a year later. Fermat's greatest work was in number theory. He was especially interested in the properties of prime numbers and in the determination of families of solutions to sets of similar problems. About his most famous theorem, known as Fermat's last theorem, Fermat wrote in the margin of his copy of the works of Apollonius: "I have discovered a truly remarkable proof (of this theorem) which this margin is too small to contain." The theorem has still not been proved, although current number-theory conjectures seem to imply its validity
The Last Theorem
The ancient Greeks knew there are many whole-number solutions of the equation x² + y² = z² (for example, 3² + 4² = 5²). But Fermat wrote in the margin of a book that there is no whole-number solution of xn + yn =z n if n is greater than 2. Fermat noted that he had found a wonderful proof of this fact, but that there was not enough room to write it down.
Baffling the Mathematicians
After three centuries of attempts, no other mathematician has been able to establish that this general proposition is true. Mathematicians long were baffled by the statement, for they were unable either to prove or to disprove it, although the statement had been proved for many specific values of n. Using sophisticated tools from algebraic geometry, the English mathematician Andrew Wiles, with help from his former student, Richard Taylor, devised a proof of Fermat's last theorem that was published in 1995 in the journal Annals of Mathematics. Unfortunately, they found an error in their calculations and Fermat's last theorem has not been proven yet.