Pierre de Fermat

Born: 1601
Died: 1665
Title: Prince of Amateur Mathematicians / Father of Number Theory

The Greatest "Amateur Player" in History

Fermat's day job was as a lawyer and judge; mathematics was just his hobby. He didn't like publishing papers, preferring to scribble in the margins of books and then send letters challenging other mathematicians.

Core Contributions - Deep Analysis

Fermat's Last Theorem

While reading Arithmetica, he wrote in the margin: "$x^n + y^n = z^n$ (when $n > 2$) has no integer solutions. I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

This "too narrow to contain" note puzzled mathematicians worldwide for 358 years, until it was finally proven by Andrew Wiles in 1994. (In fact, Fermat likely did not have a proof, or his proof was incorrect.)

Fermat's Little Theorem

A fundamental theorem in number theory that states: if $p$ is a prime number and $a$ is an integer not divisible by $p$, then $a^{p-1} \equiv 1 \pmod{p}$.

The Birth of Probability Theory

Through correspondence with Pascal, he solved the "problem of points" (dividing stakes), laying the foundation for modern probability theory.

Legacy

Fermat established number theory as a serious field of study. His "Last Theorem" became one of the most famous unsolved problems in mathematics, inspiring generations of mathematicians. His work in probability theory, done through correspondence with Pascal, created an entirely new branch of mathematics.