Contributions

Fermat is considered to be one of the 'fathers' of analytic geometry. (Along with Descartes.)

Fermat along with Blaise Pascal is also considered to be one of the founders of probability theory.

Fermat also made contributions in the field of optics and provided a law on light travel and made wrote a few papers about calculus well before Isaac Newton and Gottfried Leibniz were actually born.

Fermat's most important work was done in the development of modern number theory which was one of his favorite areas in math. He is best remembered for his number theory, in particular for Fermat's Last Theorem. This theorem states that: x^n + y^n = z^n  has no non-zero integer solutions for x, y and z when n is greater than 2.
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