Fermat "In Mathematical Circles"

While glancing over a book called "In Mathematical Circles" by Howard Eves one can find many interesting discoveries by mathematicians. Oddly enough when examining the book there is no reference of Pierre de Fermat in any section containing Pascal as opposed to most other sources always mentioning them together. Instead, Eves devotes an entire section titled "René Descartes and Pierre de Fermat" to their foundations of analytic geometry, life, and independent mathematical achievements. Fermat is given a section in this portion of the book dedicated to his early life. Pierre de Fermat is stated to be born near Toulouse in 1601 and the son of  leather merchant. Fermat is said to of received his early education at home. The book then jumps to his age of 30 then he obtained the position of Councillor for the parliament at Toulouse. After his retirement he worked in mathematics until he died in Castres in 1665. Due to his contributions in many fields of mathematics he is considered to be the greatest French mathematician of the seventeenth century, and even more so universally considered one of the greatest number theorists to ever live. After discussing some of Decartes work and death, Eves begins to discuss "The Fermat Numbers". In this section Eves states that Fermat believed he had found a formula for finding primes. However this was shown to be false by a counter example created by Leonhard Euler. The formula has been modified to believe to be true for composite numbers. These numbers by this formula are considered to be Fermat Numbers. Other connections have been made with Fermat Numbers.

Fermat also created a method known as "Fermat's method of infinite descent" This is sometimes viewed as a proof method that is the reverse of mathematical induction.

Finally the book concludes with a section of Fermat's last theorem. While this section contains most of the information as seen in the other sources examined, what is interesting about this source is at the time written it had not been solved with. Hence this source talks about math mathematicians sending in proofs for specific values of n, and how many integers n the theorem has been verified for by use of super computers. The book also lists some rewards that were being placed at the time for proofs of the theorem or for just finding if it was true for large values of .

Eves, Howard Whitley. In mathematical circles; a selection of mathematical stories and anecdotes. Boston: Prindle, Weber & Schmidt, 1969. Print.