Pierre de Fermat

Lore & Background

The couple had eight children, five surviving to adulthood. Fluent in six languages, Fermat communicated most of his work in letters, often without full proofs, leading to priority disputes with contemporaries such as Descartes and Wallis. Fermat developed a method (adequality) for determining maxima, minima, and tangents, equivalent to differential calculus, and was the first to evaluate the integral of general power functions. In number theory, he studied Pell's equation, perfect numbers, amicable numbers, and Fermat numbers, discovering Fermat's little theorem and inventing Fermat's factorization method. He popularized proof by infinite descent and developed the two-square theorem and polygonal number theorem.

Reader's Guide

Pierre de Fermat's significance lies in his foundational contributions across multiple mathematical fields, often predating later formal developments. His technique of adequality anticipated differential calculus, and his work on quadrature and tangents directly influenced Newton and Leibniz. His collaboration with Pascal established probability theory, and his principle of least time in optics shaped variational physics. Despite his amateur status as a lawyer, Fermat's insights, communicated through letters and marginal notes, have had enduring impact, though many of his claimed proofs were lost, leading to historical skepticism. Together with Descartes, he is regarded as a leading mathematician of the early 17th century.

Did You Know?

• Fermat was a lawyer at the parlement of Toulouse and a poet fluent in six languages.
• He discovered Fermat's little theorem while researching perfect numbers.
• Fermat's Last Theorem was first discovered by his son in the margin of a copy of Diophantus' Arithmetica.