Pierre de Fermat (August 17, 1601-January 12, 1665) was a French lawyer and amateur mathematician. His mathematical achievements are no worse than any professional mathematician and he is known as the "King of Amateur Mathematicians." He seems to be most interested in number theory and contributed to the establishment of modern calculus.

Fermat's father was a wealthy leather merchant. Fermat was born in Beaumont-de-Lomagne, Tarn-Garonne, in a house that is now the Fermat Museum. After entering the University of Toulouse in the mid-1620s, he moved to Bordeaux, where he began his first formal mathematical studies, and met the mathematician Jean Beaugrand. There were many mathematical exchanges between them, which remained unchanged after Fermat moved to Toulouse. After that, he met mathematicians such as Pierre de Caqueville, Maran Mason, and René Descartes, and exchanged many letters. Many of Fermat's mathematical achievements were born in these letters.

His famous saying was: "I found a wonderful proof, but I didn't write it down because the blank space was too small."

He died in Custer in 1665. Fermat did not often publish his research formally, and only after his death did his son organize it into a book called Varia Opera.

Achievements: Optics, Fermat's Principle, Calculus, Fermat's Lemma, Analytical Geometry

Fermat re-established Apollonius's geometric analysis with algebraic methods, opening up the path to analytical geometry.

Fermat's system is quite different from modern ones. For example, Fermat only uses one axis and only accepts positive answers. Descartes was often the founder of analytic geometry in later generations, mainly because Fermat did not publish his works.

probability theory

The discussion in Fermat and Pascal's letter in 1654 was the beginning of probability theory.

In 1656, his exchange with Christian Huygens, the official founder of probability theory, led Huygens to increase his interest in probability.

Number Theory: Fermat's Last Theorem (Fermat's Last Theorem), Fermat's Small Theorem, Fermat's Sum of Squares Theorem, Fermat Number, Fermat Spiral, etc.

Fermat's achievements in the field of number theory are significant, including:

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Fermat's little theorem: a ^ p - a ¡Ô 0 (mod p), where p is a prime number and a is a positive integer, its proof is relatively simple. In fact, it is a special case of Euler's theorem. Euler's theorem says: a ^ ¦Õ (n) - 1 ¡Ô 0 (mod n), a, n are all positive integers, ¦Õ (n) is Euler's function, representing the number of positive integers less than n that are coprime with n (its expression has been derived by Euler and can be found in the entry "Euler's formula").