Pierre de Fermat

Pierre de Fermat (1607–1665) was a French mathematician whose work helped shape number theory, probability, and analytic geometry. His name is attached to Fermat’s Last Theorem and Fermat’s little theorem.

Number theory: The branch of mathematics concerned with integers and their properties. Fermat’s conjectures and theorems helped establish number theory as a central mathematical field.
Fermat's Last Theorem: The theorem that no positive integers satisfy xⁿ + yⁿ = zⁿ for any integer n greater than two. Fermat claimed to have a proof of this equation’s impossibility; Andrew Wiles proved it centuries later.
Blaise Pascal: A French mathematician, physicist, and philosopher who lived from 1623 to 1662. Pascal and Fermat exchanged letters about games of chance, helping establish probability theory.
Parlement of Toulouse: A French sovereign court based in Toulouse before the Revolution. Fermat earned his living as a magistrate there while pursuing mathematics outside his official duties.
Algebraic number theory: The study of number-theoretic questions using algebraic structures such as number fields and rings. The eventual proof of Fermat’s Last Theorem drew on tools developed in this branch.
Analytic geometry: The study of geometric problems using coordinates and algebraic equations. Fermat developed methods connecting equations with curves independently of René Descartes.
Fermat's little theorem: For a prime p and integer a not divisible by p, aᵖ⁻¹ is congruent to one modulo p. This concise result exemplifies Fermat’s contributions to modular arithmetic and prime numbers.
René Descartes: A French philosopher and mathematician who developed a coordinate-based approach to geometry. Descartes and Fermat independently developed analytic geometry, though their methods and public reputations differed.
University of Orléans: A French university founded in the Middle Ages and known for teaching law. Fermat studied law at Orléans before becoming a counselor in the Parlement of Toulouse.
Modular arithmetic: Arithmetic in which integers are considered equivalent when they have the same remainder modulo a fixed number. Fermat’s little theorem became a foundational result in arithmetic modulo primes.

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