Pierre de Fermat in the encyclopedia

Looking in the Encyclopedia Americana, Pierre de Fermat is regarded solely as a French Mathematician. On August  20, 1601 he was born in Beaumont-de-Lomangne, France. He studied at the University of Toulouse, followed by the University of Orleans where he received a law degree. While looking at a professional career as a lawyer and legislator, he had activities that also appealed to him. Some of these include mathematics, holding a reputation as a classicist, and also a poet. The encyclopedia entry contains two sections about his mathematical career, one for Algebraic Analysis and the other for Number Theory. 
His work in Algebraic Analysis, inspired by François Viète, was made possible by the recent view of symbolic algebra which allowed arithmetic and geometry to be treated in a similar manner. He had a strong focus on treating problems with respect to the algebraic theory of equations, and combined this with work in Geometry to create analytic geometry at the same time as Descartes. Fermat managed to algebraically with use of geometric information find tangents to curves. Fermat's other discoveries relating to curves and the information that could be found by revolving a solid around a coordinate axis paved the way to what is a big part of Calculus, both differential and integral. However he is discredited of inventing Calculus due to his failure to recognize the relationship between finding the inverse and the area under are inversely related to one another. 
Many of Fermat's most famous contributions stem from his work in Number theory. Two of his proofs mentioned are "Fermat's theorem" and "Fermat's last theorem". While some of these contributions were not made use of during his life, Euler, Legendre, and Gauss and other mathematicians made extensive contributions with them and caused them to be more well known. Fermat also helped found probability theory and although did not focus on many physical applications, used his method to find maxima and minima to develop Fermat's principle.

Mahoney, Michael. "Fermat, Pierre de." Encyclopedia Americana. International ed. ed. 2006. Print.