The Fermat’s Last Theorem was proposed by French mathematician Pierre de Fermat in 1637. It was one of the most difficult problems in the history of mathematics.
The Fermat’s Last Theorem is related to Pythagorean Theorem. Recall that the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of its shorter legs. That is, if and are the lengths of the legs and is the length of the hypotenuse of a right triangle, then
There are special right triangles whose side lengths are integers. Examples are triangles with side lengths (3, 4, 5), (5, 12, 13), (7, 24, 25). These triples are called Pythagorean triples. The Fermat’s Last Theorem says that you cannot find an integral triple that can satisfy the equation above for all integeral powers greater than 2. In equation form, for all integers and
, an integer greater than 2.
Despite numerous attempts, the Fermat’s Last Theorem remained unsolved for more than 300 years. In 1995, American mathematician Andrew Wiles stunned the world when he proved the 3-century enigma. It took him more than 7 years to prove the theorem. Watch the documentary above of Wiles’ inspiring journey in proving the Fermat’s Last Theorem.