Character Catalog

Fermat develops the foundations of analytic geometry, representing curves through algebraic equations, independently of and in parallel with Descartes's work.

A method for finding the maxima and minima of functions, a direct precursor to differential calculus. Newton and Leibniz drew directly from it to develop infinitesimal calculus.

The assertion that the equation xⁿ + yⁿ = zⁿ has no non-zero integer solutions for n > 2. This problem, left without a published proof, occupied mathematicians for 358 years.

A founding exchange of letters for probability theory. The two scholars formalize the 'problem of points' and lay the groundwork for modern probabilistic reasoning.

If p is a prime number and a an integer not divisible by p, then aᵖ⁻¹ ≡ 1 (mod p). This result is fundamental in modular arithmetic and modern cryptography.

Light always takes the path that minimizes its travel time. This principle foreshadows the laws of reflection and refraction and anticipates the great variational principles of physics.

Here is roughly my method for the problem of points: [...] If two players, playing several games, find themselves in a situation where the first is missing two games and the second three, and they wish to separate [...] I say that the first player should receive 11/16 of all the money.

Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere. Cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.

To find the maximum or minimum of a quantity, one must substitute A+E for A in the expression, then equate the two sides and cancel the terms containing E as a common factor, and finally set E equal to zero.

I have found a great number of beautiful and new propositions and I am still searching for more. The introduction of plane and solid loci into algebra gives me a general method for solving all problems of geometry.

City where Fermat served as a councillor at the Parliament for over thirty years. It was there that he spent his professional life and conducted most of his mathematical research.

Town in Tarn-et-Garonne where Pierre de Fermat was born around 1607. A statue dedicated to him stands in the main square as a tribute to this illustrious son of the region.

City where Fermat died on 12 January 1665, during a professional trip related to his duties as a magistrate.

Father Marin Mersenne's cell at the Convent of the Minims in Paris served as a nerve centre for European scientific exchanges. Fermat was part of this network through correspondence, and his work was regularly discussed there.

The everyday tool of both magistrate and scholar, the goose quill allowed Fermat to write his legal documents as well as his mathematical demonstrations in letters and book margins alike.

The Latin edition annotated by Bachet (1621) was Fermat's mathematical bible. It is in its margins that he wrote his famous notes, including the statement of the Last Theorem.

Classical geometry instruments, indispensable for the constructions Fermat studied, even though his algebraic methods sought to go beyond purely geometric construction.

The black robe of the councillor at the Parlement symbolized Fermat's double life: a respected jurist by day, a prolific mathematician during his leisure hours.

Candlelight was the only means of working in the evening, and Fermat spent many nocturnal hours corresponding with European scholars and developing his theorems.

Since Fermat published almost nothing, his letters to Mersenne, Pascal, Descartes, and Huygens make up the bulk of his known scientific work.