Pierre de Fermat

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Pierre de Fermat
Pierre de Fermat.jpg
BornBetween 31 October and 6 December 1607[a]
Died(1665-01-12)12 January 1665
(aged 57)
EducationUniversity of Orléans (LL.B., 1626)
Known forContributions to number theory, analytic geometry, probability theory
Folium of Descartes
Fermat's principle
Fermat's little theorem
Fermat's Last Theorem
Fermat's "difference quotient" method[1]
(See full list)
Scientific career
FieldsMathematics and law
InfluencesFrançois Viète, Gerolamo Cardano, Diophantus

Pierre de Fermat (French: [pjɛːʁ də fɛʁma]; between 31 October and 6 December 1607 [a] – 12 January 1665) was a French lawyer[3] at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' Arithmetica.


Fermat was born in 1607 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.[2] Pierre had one brother and two sisters and was almost certainly brought up in the town of his birth.[citation needed]

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, and in 1629 he gave a copy of his restoration of Apollonius's De Locis Planis to one of the mathematicians there. Certainly, 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 clearly shared mathematical interests with Fermat. There he became much influenced by the work of François Viète.[citation needed]

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.[4][5][6]

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. Fermat 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.[7] Secrecy was common in European mathematical circles at the time. This naturally led to priority disputes with contemporaries such as Descartes and Wallis.[8]



Pierre de Fermat

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),[10] predating the publication of Descartes' famous La géométrie (1637), which exploited the work.[11] This manuscript was published posthumously in 1679 in Varia opera mathematica, as Ad Locos Planos et Solidos Isagoge (Introduction to Plane and Solid Loci).[12]

In Methodus ad disquirendam maximam et minimam and in De tangentibus linearum curvarum, Fermat developed a method (adequality) for determining maxima, minima, and tangents to various curves that was equivalent to differential calculus.[13][14] 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.[15] The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.[citation needed]


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 famous 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.[citation needed]

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.[16] 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.[17]

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.[18] 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.[19] 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.[20]


Pierre de Fermat died on January 12, 1665, at Castres, in the present-day department of Tarn.[21] The oldest and most prestigious high school in Toulouse is named after him: the Lycée Pierre-de-Fermat [fr]. French sculptor Théophile Barrau made a marble statue named Hommage à Pierre Fermat as a tribute to Fermat, now at the Capitole de Toulouse.

Assessment of his work[edit]




See also[edit]


  1. ^ a b Most sources give Fermat's birth year as 1601, however recent research suggests this was the year a half-brother called Piere was born and, working backwards from the stated age at death, gives 1607 as his birth year.[2] Piere died before Pierre was born.


  1. ^ Benson, Donald C. (2003). A Smoother Pebble: Mathematical Explorations, Oxford University Press, p. 176.
  2. ^ a b "When Was Pierre de Fermat Born? | Mathematical Association of America". www.maa.org. Retrieved 2017-07-09.
  3. ^ W.E. Burns, The Scientific Revolution: An Encyclopedia, ABC-CLIO, 2001, p. 101
  4. ^ "Fermat, Pierre De". www.encyclopedia.com. Retrieved 2020-01-25.
  5. ^ Davidson, Michael W. "Pioneers in Optics: Pierre de Fermat". micro.magnet.fsu.edu. Retrieved 2020-01-25.
  6. ^ "Pierre de Fermat's Biography". www.famousscientists.org. Retrieved 2020-01-25.
  7. ^ Larson, Ron; Hostetler, Robert P.; Edwards, Bruce H. (2008). Essential Calculus: Early Transcendental Functions. Boston: Houghton Mifflin. p. 159. ISBN 978-0-618-87918-2.
  9. ^ Faltings, Gerd (1995). "The proof of Fermat's last theorem by R. Taylor and A. Wiles" (PDF). Notices of the American Mathematical Society. 42 (7): 743–746. MR 1335426.
  11. ^ "Pierre de Fermat | Biography & Facts". Encyclopedia Britannica. Retrieved 2017-11-14.
  15. ^ Paradís, Jaume; Pla, Josep; Viader, Pelegrí (2008). "Fermat's method of quadrature". Revue d'Histoire des Mathématiques. 14 (1): 5–51. MR 2493381. Zbl 1162.01004. Archived from the original on 2019-08-08.
  18. ^ Kline, Morris (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press. pp. 167–168. ISBN 978-0-19-501496-9.
  23. ^ Simmons, George F. (2007). Calculus Gems: Brief Lives and Memorable Mathematics. Mathematical Association of America. p. 98. ISBN 978-0-88385-561-4.
  24. ^ Weil 1984, p.104
  25. ^ Weil 1984, p.105

Works cited[edit]

  • Weil, André (1984). Number Theory: An approach through history From Hammurapi to Legendre. Birkhäuser. ISBN 978-0-8176-3141-3.

Further reading[edit]

External links[edit]