The most interesting of the three mathematicians would have to be Pierre de Fermat, not only because his advances were so great, but because of his nationalism. Fermat was an ingenious mathematician who specialized in solving problems that were posed to him, and creating problems to challenge other people. One of the things he enjoyed was sending the English mathematicians problems that they could not solve. Although Fermat discovered many relations between numbers, he is best known for what is called Fermat's Last Theorem. The theorem states that for any integers x, y, z > 0 and any integer n > 2 the equation xⁿ + yⁿ = zⁿ has no (integer) solutions. This is obviously not true for n=2 because 3² + 4² = 9 +16 = 25 = 5². Many of Fermat's theorems were not discovered with a proof. In the case of this theorem, Fermat said that he had proved it, but the proof was too big for the margins of the paper he had written the theorem on. This theorem was recorded by Fermat some time before 1660. The reason the theorem is known as Fermat's Last Theorem is because it was the last one to be proven to be true or false. The former was done in the 1990's by Andrew Wiles, more that 330 years after Fermat had stated it. Although it is believed that Fermat did not actually prove it, people think that he thought he had proved it and he may have proved it for the cases when n = 3 or n = 4. It is now common for mathematicians to say that they solved a problem, but couldn't fit the proof in the margins, when they are unsure of how to actually solve the problem in reference to Fermat.

         Most of the advances done by these mathematicians did not affect the math world in the 17^th Century, because they were very much ahead of their time. Descartes did affect mathematics in a different way do to the popularity of his research and his influence on mathematicians in the later 17^th and 18^th Centuries. None of these mathematicians could be declared as more important than the others to modern mathematics, because of how much has come from their research. Pascal's Triangle is still being studied today and the research that had been done to prove Fermat's Last Theorem is invaluable. These mathematicians probably did not know the extent of their influence on mathematics and it is still unknown how their results and findings will change mathematics in the future. And the work that these mathematicians did help inspire math throughout France and assemble France into one of the Worlds major mathematical societies in the seventeenth, eighteenth, and nineteenth centuries.