Pierre de Fermat

Pierre de Fermat

Frenchman Pierre de Fermat (1601–1665) was one of the two leading mathematicians of the early 1600s, the other being 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). 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 equation 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 conjuction with others, in 1995.

A Fermat number is a positive integer of the form

F_n = 2²ⁿ + 1

where n is a nonnegative integer.

The first eight Fermat numbers are

• F₀ = 2¹ + 1 = 3
• F₁= 2² + 1 = 5
• F₂= 2⁴ + 1 = 17
• F₃ = 2⁸ + 1 = 257
• F₄ = 2¹⁶ + 1 = 65537

As of 2007, only the first 12 Fermat numbers have been completely factored see: http://www.prothsearch.net/fermat.html.