Peirre de Fermat was an intuitive genius. Although he was an amateur mathematician, he was solely responsible for modernizing number theory. He made major contributions toward developing calculus, in-particular he developed the concept of minima, maxima, and tangents to curved lines. It is interesting that Fermat and Descartes were often at odds with each other, trying to discredit one another. Fermat is probably best known for Fermat's Last Theorem, which was more recently proved by Andrew Wiles (see my blog post for more about this).
Sources:
Golden, John. "Pierre de Fermat. Grand Valley State University. 2014
"Pierre De Fermat." Fermat Biography. University of St. Andrews Scotland, n.d. Web. 14 June 2014
"Pierre De Fermat." Wikipedia. Wikimedia Foundation, 15 June 2014. Web. 16 June 2014. <http://en.wikipedia.org/wiki/Pierre_de_Fermat>
Golden, John. "Pierre de Fermat. Grand Valley State University. 2014
"Pierre De Fermat." Fermat Biography. University of St. Andrews Scotland, n.d. Web. 14 June 2014
"Pierre De Fermat." Wikipedia. Wikimedia Foundation, 15 June 2014. Web. 16 June 2014. <http://en.wikipedia.org/wiki/Pierre_de_Fermat>