French mathematician. Studied law, in Toulouse and Burdeos. In 1629 rebuilded some of the lost demonstrations of the greek
mathematician Apolonio about geometric places.
Developed an algebraic
method to treat questions of geometry using a system of coordinates.
Designed a differentiation algorithm by mean of which he could determine the maximum and minimum values of a polinomial curve, correctly assuming that when the light displaces in a higher density medium its velocity decreases, demonstrated that the path of a luminiscence ray between two points is always the one that takes less time to travel; This principle has been named for him and deduces the reflection and refraction laws.
In 1654, the principles of the probability theory. Another field in which he realized contributions was in the numbers theory. From his work important results were derivated,
related to the prime numbers theory, lot of which were expresed in form of proportions and theorems.
Developed also an ingenious method of demonstration called "infinite descent".
Fermat''s Last Theorem.
It was found on the Diofanto Arithmethic book margin and is related with the Pythagorean triples.
States that for n>2 that relation does not fulfilled. Fermat explains, "it is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain."
Many mathematicians tried to demonstrate so during long time. However, it was a mistery to know if this was true or if he was wrong.