Fermat was born in 1601[a] inBeaumont-de-Lomagne, France — the late 15th-century mansion where Fermat was born is now a museum. He was fromGascony, 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.[3] Pierre had one brother and two sisters and was almost certainly brought up in the town of his birth.[citation needed]
He attended theUniversity of Orléans from 1623 and received a bachelor in civil law in 1626, before moving toBordeaux. In Bordeaux, he began his first serious mathematical researches. In 1629, he gave a copy of his restoration ofApollonius'sDe Locis Planis to one of the mathematicians there. In Bordeaux, he was in contact withBeaugrand, and during this time, he produced important work onmaxima and minima which he gave toÉtienne d'Espagnet who shared mathematical interests with Fermat. There, he became much influenced by the work ofFrançois Viète.[5]
In 1630, he bought the office of acouncilor at theParlement 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.[6][7][8]
Fluent in six languages (French,Latin,Occitan,classical Greek,Italian andSpanish), 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 beforeNewton orLeibniz. He was a trained lawyer making mathematics more of a hobby than a profession. Nevertheless, he made important contributions toanalytical geometry, probability, number theory and calculus.[9] Secrecy was common in European mathematical circles at the time. This naturally led to priority disputes with contemporaries such asDescartes andWallis.[10]
Anders Hald writes that, "The basis of Fermat's mathematics was the classical Greek treatises combined with Vieta'snew algebraic methods."[11]
The 1670 edition ofDiophantus'sArithmetica includes Fermat's commentary, referred to as his "Last Theorem" (Observatio Domini Petri de Fermat), posthumously published by his son.
Fermat's pioneering work inanalytic 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),[12] predating the publication of Descartes'La géométrie (1637), which exploited the work.[13] This manuscript was published posthumously in 1679 inVaria opera mathematica, asAd Locos Planos et Solidos Isagoge (Introduction to Plane and Solid Loci).[14]
InMethodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum, Fermat developed a method (adequality) for determining maxima, minima, andtangents to various curves that was equivalent todifferential calculus.[15][16] 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 inquadrature.
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 ofgeometric series.[17] The resulting formula was helpful toNewton, and thenLeibniz, when they independently developed thefundamental theorem of calculus.[citation needed]
Although Fermat claimed to have proven all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, includingGauss, doubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical methods available to Fermat. HisLast Theorem was first discovered by his son in the margin in his father's copy of an edition ofDiophantus, and included the statement that the margin was too small to include the proof. It seems that he had not written toMarin Mersenne about it. It was first proven in 1994, bySir Andrew Wiles, using techniques unavailable to Fermat.[citation needed]
Through their correspondence in 1654, Fermat andBlaise Pascal helped lay the foundation for the theory of probability. From this brief but productive collaboration on theproblem of points, they are now regarded as joint founders ofprobability theory.[18] Fermat is credited with carrying out the first-ever rigorous probability calculation. In it, he was asked by a professionalgambler 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 twodice resulted in his losing. Fermat showed mathematically why this was the case.[19]
The firstvariational principle inphysics was articulated byEuclid in hisCatoptrica. It says that, for the path of light reflecting from a mirror, theangle of incidence equals theangle of reflection.Hero of Alexandria later showed that this path gave the shortest length and the least time.[20] Fermat refined and generalized this to "light travels between two given points along the path of shortesttime" now known as theprinciple of least time.[21] For this, Fermat is recognized as a key figure in the historical development of the fundamentalprinciple of least action in physics. The termsFermat's principle andFermat functional were named in recognition of this role.[22]
Pierre de Fermat died on 12 January 1665, atCastres, in the present-day department ofTarn.[23] The oldest and most prestigious high school inToulouse is named after him: the Lycée Pierre-de-Fermat. French sculptorThéophile Barrau made a marble statue namedHommage à Pierre Fermat as a tribute to Fermat, now at theCapitole de Toulouse.
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 theEdict of Nantes) and mathematician of great renown, celebrated for his theorem, an +bn ≠cn forn > 2.
Together withRené Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. According toPeter L. Bernstein, in his 1996 bookAgainst the Gods, Fermat "was a mathematician of rare power. He was an independent inventor ofanalytic geometry, he contributed to the early development of calculus, he did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence withBlaise Pascal, he made a significant contribution to the theory of probability. But Fermat's crowning achievement was in the theory of numbers."[24]
Regarding Fermat's work in analysis,Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents".[25]
Of Fermat's number theoretic work, the 20th-century mathematicianAndré Weil wrote that: "what we possess of his methods for dealing withcurves ofgenus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. It naturally falls into two parts; the first one ... may conveniently be termed a method of ascent, in contrast with thedescent which is rightly regarded as Fermat's own".[26] Regarding Fermat's use of ascent, Weil continued: "The novelty consisted in the vastly extended use which Fermat made of it, giving him at least a partial equivalent of what we would obtain by the systematic use of thegroup theoretical properties of therational points on a standard cubic".[27] With his gift for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers.
Fermat made a number of mistakes. Some mistakes were pointed out by Schinzel and Sierpinski.[28] In his letter toPierre de Carcavi, Fermat said that he had proved that the Fermat numbers are all prime. Euler pointed out that 4,294,967,297 is divisible by 641. Also, see Weil, in "Number Theory".[29]
^abMost sources give Fermat's birth year as 1601; Some sources give Fermat's birth year as 1607, however, recent research suggests this was the year a half-brother called Piere was born.[3] Piere died after Pierre was born.
^Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H. (2008).Essential Calculus: Early Transcendental Functions. Boston: Houghton Mifflin. p. 159.ISBN978-0-618-87918-2.
^Ball, Walter William Rouse (1888).A short account of the history of mathematics. General Books LLC.ISBN978-1-4432-9487-4.{{cite book}}:ISBN / Date incompatibility (help)
^Daniel Garber, Michael Ayers (eds.),The Cambridge History of Seventeenth-century Philosophy, Volume 2, Cambridge University Press, 2003, p. 754, n. 56.
^Comptes Rendus of the Academy of Sciences of Paris, Volume 249, pages 1604-1605, of 28 October 1959. See Schinzel and Sierpinski, Sur quelques propositions fausses de P. Fermat.
