# Pierre de Fermat

Frenchman **Pierre de Fermat** (1601?–1665) was the greatest mathematician of the 17th century,^{[1]} and a contemporary of Rene Descartes. Fermat was a founder of the modern theory of numbers, discovered the fundamental principle of analytic geometry (independent of Descartes' work) and helped found the theory of probability (with Blaise Pascal). Fermat discovered proof by infinite descent. Isaac Newton credited his discovery of differential calculus to the insight of Fermat in drawing tangents.^{[2]} Fermat was homeschooled for his education.^{[3]}

By trade Fermat was a lawyer, and he pursued mathematics purely as a hobby. In that sense he is considered the greatest amateur mathematician ever.

Fermat's most famous conjecture is Fermat's Last Theorem, which was not proven until mathematician Andrew Wiles relied on the controversial Axiom of Choice and hyperbolic geometry to publish an abstract proof, in conjunction with others, in 1995.

A Fermat number is a positive integer of the form

F_{n} = 2^{2n} + 1

where n is a nonnegative integer.

The first five Fermat numbers are

- F
_{0}= 2^{1}+ 1 = 3 - F
_{1}= 2^{2}+ 1 = 5 - F
_{2}= 2^{4}+ 1 = 17 - F
_{3}= 2^{8}+ 1 = 257 - F
_{4}= 2^{16}+ 1 = 65537

As of 2007, only the first 12 Fermat numbers have been completely factored see: http://www.prothsearch.net/fermat.html. Fermat conjectured that all were prime; however, it is now believed that all but the first four are composite.