Fermat was born in 1601 in
Beaumont-de-Lomagne, France — the late 15th-century mansion where Fermat was born is now a museum. He was from
Gascony, where his father, Dominique Fermat, was a wealthy leather merchant and served three one-year terms as one of the four consuls of Beaumont-de-Lomagne. His mother was Claire de Long. Pierre had one brother and two sisters and was almost certainly brought up in the town of his birth. He attended the
University of Orléans from 1623 and received a bachelor in civil law in 1626, before moving to
Bordeaux. In Bordeaux, he began his first serious mathematical researches. In 1629, he gave a copy of his restoration of
Apollonius's
De Locis Planis to one of the mathematicians there. In Bordeaux, he was in contact with
Beaugrand, and during this time, he produced important work on
maxima and minima which he gave to
Étienne d'Espagnet who shared mathematical interests with Fermat. There, he became much influenced by the work of
François Viète. In 1630, he bought the office of a
councilor at the
Parlement de Toulouse, one of the High Courts of Judicature in France, and was sworn in by the Grand Chambre in May 1631. He held this office for the rest of his life. Fermat thereby became entitled to change his name from Pierre Fermat to Pierre de Fermat. On 1 June 1631, Fermat married Louise de Long, a fourth cousin of his mother Claire de Fermat (née de Long). The Fermats had eight children, five of whom survived to adulthood: Clément-Samuel, Jean, Claire, Catherine, and Louise. Fluent in six languages (
French,
Latin,
Occitan,
classical Greek,
Italian and
Spanish), Fermat was praised for his written verse in several languages and his advice was eagerly sought regarding the emendation of Greek texts. He communicated most of his work in letters to friends, often with little or no proof of his theorems. In some of these letters to his friends, he explored many of the fundamental ideas of calculus before
Newton or
Leibniz. He was a trained lawyer making mathematics more of a hobby than a profession. Nevertheless, he made important contributions to
analytical geometry, probability, number theory and calculus. Secrecy was common in European mathematical circles at the time. This naturally led to priority disputes with contemporaries such as
Descartes and
Wallis.
Anders Hald writes that, "The basis of Fermat's mathematics was the classical Greek treatises combined with Vieta's
new algebraic methods."
Work 's
Arithmetica includes Fermat's commentary, referred to as his "Last Theorem" (
Observatio Domini Petri de Fermat), posthumously published by his son. Fermat's pioneering work in
analytic geometry (
Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum) was circulated in manuscript form in 1636 (based on results achieved in 1629), predating the publication of Descartes'
La géométrie (1637), which exploited the work. This manuscript was published posthumously in 1679 in
Varia opera mathematica, as
Ad Locos Planos et Solidos Isagoge (
Introduction to Plane and Solid Loci). In
Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum, Fermat developed a method (
adequality) for determining maxima, minima, and
tangents to various curves that was equivalent to
differential calculus. In these works, Fermat obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in
quadrature. Fermat was the first person known to have evaluated the integral of general power functions. With his method, he was able to reduce this evaluation to the sum of
geometric series. The resulting formula was helpful to
Newton, and then
Leibniz, when they independently developed the
fundamental theorem of calculus. In number theory, Fermat studied
Pell's equation,
perfect numbers,
amicable numbers and what would later become
Fermat numbers. It was while researching perfect numbers that he discovered
Fermat's little theorem. He invented a factorization method —
Fermat's factorization method — and popularized the proof by
infinite descent, which he used to prove
Fermat's right triangle theorem which includes as a corollary Fermat's Last Theorem for the case
n=4. Fermat developed the
two-square theorem, and the
polygonal number theorem, which states that each number is a sum of three
triangular numbers,
four square numbers, five
pentagonal numbers, and so on. Although Fermat claimed to have proven all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including
Gauss, doubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical methods available to Fermat. His
Last Theorem was first discovered by his son in the margin in his father's copy of an edition of
Diophantus, and included the statement that the margin was too small to include the proof. It seems that he had not written to
Marin Mersenne about it. It was first proven in 1994, by
Sir Andrew Wiles, using techniques unavailable to Fermat. Through their correspondence in 1654, Fermat and
Blaise Pascal helped lay the foundation for the theory of probability. From this brief but productive collaboration on the
problem of points, they are now regarded as joint founders of
probability theory. Fermat is credited with carrying out the first-ever rigorous probability calculation. In it, he was asked by a professional
gambler why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two
dice resulted in his losing. Fermat showed mathematically why this was the case. The first
variational principle in
physics was articulated by
Euclid in his
Catoptrica. It says that, for the path of light reflecting from a mirror, the
angle of incidence equals the
angle of reflection.
Hero of Alexandria later showed that this path gave the shortest length and the least time. Fermat refined and generalized this to "light travels between two given points along the path of shortest
time" now known as the
principle of least time. For this, Fermat is recognized as a key figure in the historical development of the fundamental
principle of least action in physics. The terms
Fermat's principle and
Fermat functional were named in recognition of this role.
Death Pierre de Fermat died on 12 January 1665, at
Castres, in the present-day department of
Tarn. The oldest and most prestigious high school in
Toulouse is named after him: the Lycée Pierre-de-Fermat. French sculptor
Théophile Barrau made a marble statue named
Hommage à Pierre Fermat as a tribute to Fermat, now at the
Capitole de Toulouse. File:Fermat burial plaque.jpg|Place of burial of Pierre de Fermat in Place Jean Jaurés,
Castres. Translation of the plaque: in this place was buried on January 13, 1665, Pierre de Fermat, councillor at the Chambre de l'Édit (a court established by the
Edict of Nantes) and mathematician of great renown, celebrated for his theorem, for .|alt=Plaque at the place of burial of Pierre de Fermat File:Beaumont-de-Lomagne - Monument à Fermat.jpg|Monument to Fermat in
Beaumont-de-Lomagne in
Tarn-et-Garonne, southern France File:Capitole Toulouse - Salle Henri-Martin - Buste de Pierre de Fermat.jpg|Bust in the Salle Henri-Martin in the
Capitole de Toulouse File:Fermats will.jpg|
Holographic will handwritten by Fermat on 4 March 1660, now kept at the Departmental Archives of
Haute-Garonne, in
Toulouse. == Assessment of his work ==