Pierre de Fermat (pronounced Fair-mah) (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, southwestern France, and a mathematician who is given credit for his contribution towards the development of modern calculus. With his insightful theorems Fermat created the modern theory of numbers. The depth of his work can be gauged by the fact that many of his results were not proved for over a century after his death, and one of them, the Last Theorem, took more than three centuries to prove.

By the time he was 30, Pierre was a civil servant whose job was to act as a link between petitioners from Toulouse to the King of France and an enforcer of royal decrees from the King to the local people. Evidence suggests he was considerate and merciful in his duties. [citation needed]

Since he was also required to act as an appeal judge in important local cases, he did everything he could to be impartial. To avoid socializing with those who might one day appear before him in court, he became involved in mathematics and spent as much free time as he could in its study. He was so skilled in the subject that he could be called a professional amateur.

He was mostly isolated from other mathematicians, though he wrote regularly to two English mathematicians, Digby and Wallis. He also corresponded with French mathematician, Father Mersenne who was trying to increase discussion and the exchange of ideas among French mathematicians. One was Blaise Pascal who, with Fermat, established a new branch of math - probability theory.

Besides probability theory, Fermat also helped lay the foundations for calculus, an area of math that calculates the rate of change of one quantity in relation to another, for example velocity and acceleration. In particular, he is the precursor of differential calculus with his method of finding the greatest and the smallest ordinates of curved lines, analogous to that of the then unknown differential calculus.

Fermat himself was secretive and, since he rarely wrote complete proofs or explanations of how he got his answers, was mischievously frustrating for others to understand. He loved to announce in letters that he had just solved a problem in math but then refused to disclose its solution, leaving it for others to figure out.

Fermat's passion in math was in yet another branch - number theory, the relationship among numbers. While he was studying an ancient number puzzle book, he came up with a puzzle of his own that has been called Fermat's Last Theorem. Mathematicians worked for over three centuries to find its answer, but no one succeeded until 1994. Andrew Wiles, an English mathematician, created a proof and published it 330 years after Fermat's death in 1665.

Although he carefully studied and drew inspiration from Diophantus, Fermat inaugurated a different tradition. Diophantus was content to find a single solution to his equations, even if it was a fraction. Fermat was only interested in integer solutions to his diophantine equations and he looked for all solutions of the equation. He also proved that certain equations had no solution, an activity which baffled his contemporaries.

He studied Pell's equation and Fermat, perfect, and amicable numbers. It was while researching perfect numbers that he created Fermat's little theorem.

He created the principle of infinite descent and Fermat's factorization method.

He created the two-square theorem, and the polygonal number theorem, which states that each number is a sum of 3 triangular numbers, 4 square numbers, 5 pentagonal numbers, ...

He was the first to evaluate the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to summing geometric series. The formula that resulted was a key hint to Newton and Leibniz when they independently developed the fundamental theorems of calculus.

Although Fermat claimed to be able to prove all his arithmetical results, few of his proofs (if he had them) have survived. And considering that some of the results are so difficult (especially considering the mathematical tools at his disposal) many, including Gauss, believe that Fermat was unable to do so.

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, he discovered the fundamental principle of analytic geometry. Through his correspondence with Blaise Pascal, he was a co-founder of the theory of probability.

Fermat was born at Beaumont-de-Lomagne, 58 kilometers (36 miles) north-west of Toulouse, France. He died at Castres, 79 kilometers (49 miles) east of Toulouse. The oldest and most prestigious high-school in Toulouse is called Pierre de Fermat. This high-school has preparatory classes for engineering and business schools (grandes écoles), and is ranked in the top 10 of France's best preparatory classes. The late 15th century mansion where Fermat was born in Beaumont-de-Lomagne is now a museum.