Pierre de Fermat

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Pierre de Fermat
Pierre de Fermat, 17th century painting by unknown author
Bornc. 1607
Beaumont-de-Lomagne, France
Died(1665-01-12)12 January 1665
(aged 57)
Castres, France
EducationUniversity of Orléans (BCL, 1626)
Known forContributions to number theory, analytic geometry, probability theory
Folium of Descartes
Fermat's principle
Fermat's little theorem
Fermat's Last Theorem
Adequality
Fermat's "difference quotient" method[1]
(See full list)
Scientific career
FieldsMathematics and law

Pierre de Fermat (French:

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. He was also a lawyer[3] at the Parlement of Toulouse, France
.

Biography

Pierre de Fermat, 17th century painting by Rolland Lefebvre [fr]

Fermat was born in 1607[a] 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

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.[4]

In 1630, he bought the office of a

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.[5][6][7]

Fluent in six languages (

analytical geometry, probability, number theory and calculus.[8] Secrecy was common in European mathematical circles at the time. This naturally led to priority disputes with contemporaries such as Descartes and Wallis.[9]

new algebraic methods."[10]

Work

The 1670 edition of Diophantus'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),[11] predating the publication of Descartes' famous La géométrie (1637), which exploited the work.[12] This manuscript was published posthumously in 1679 in Varia opera mathematica, as Ad Locos Planos et Solidos Isagoge (Introduction to Plane and Solid Loci).[13]

In Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum, Fermat developed a method (

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.[16] The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.[citation needed]

In number theory, Fermat studied

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 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

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.[18]

The first

principle of least action in physics. The terms Fermat's principle and Fermat functional were named in recognition of this role.[21]

Death

Pierre de Fermat died on January 12, 1665, at Castres, in the present-day department of Tarn.[22] 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.

  • Plaque at the place of burial of Pierre de Fermat
    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,
    an + bn ≠ cn for n>2
  • Monument to Fermat in Beaumont-de-Lomagne in Tarn-et-Garonne, southern France
    Monument to Fermat in Beaumont-de-Lomagne in Tarn-et-Garonne, southern France
  • Bust in the Salle Henri-Martin in the Capitole de Toulouse
    Bust in the Salle Henri-Martin in the Capitole de Toulouse
  • Holographic will handwritten by Fermat on 4 March 1660, now kept at the Departmental Archives of Haute-Garonne, in Toulouse
    Holographic will handwritten by Fermat on 4 March 1660, now kept at the Departmental Archives of Haute-Garonne, in Toulouse

Assessment of his work

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. According to Peter L. Bernstein, in his 1996 book Against the Gods, Fermat "was a mathematician of rare power. He was an independent inventor of analytic 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 with Blaise Pascal, he made a significant contribution to the theory of probability. But Fermat's crowning achievement was in the theory of numbers."[23]

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."[24]

Of Fermat's number theoretic work, the 20th-century mathematician

descent which is rightly regarded as Fermat's own."[25] 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 the group theoretical properties of the rational points on a standard cubic."[26]
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.

See also

Notes

  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.

References

  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. ^ Chad (2013-12-26). "Pierre de Fermat Biography - Life of French Mathematician". Totally History. Retrieved 2023-02-22.
  5. ^ "Fermat, Pierre De". www.encyclopedia.com. Retrieved 2020-01-25.
  6. ^ Davidson, Michael W. "Pioneers in Optics: Pierre de Fermat". micro.magnet.fsu.edu. Retrieved 2020-01-25.
  7. ^ "Pierre de Fermat's Biography". www.famousscientists.org. Retrieved 2020-01-25.
  8. ISBN 978-0-618-87918-2
    .
  9. ISBN 978-1-4432-9487-4
    .
  10. MR 1335426
    .
  11. ^ Daniel Garber, Michael Ayers (eds.), The Cambridge History of Seventeenth-century Philosophy, Volume 2, Cambridge University Press, 2003, p. 754 n. 56.
  12. ^ "Pierre de Fermat | Biography & Facts". Encyclopedia Britannica. Retrieved 2017-11-14.
  13. ISBN 978-0393040029
  14. ^ Pellegrino, Dana. "Pierre de Fermat". Retrieved 2008-02-24.
  15. ^ Florian Cajori, "Who was the First Inventor of Calculus" The American Mathematical Monthly (1919) Vol.26
  16. Zbl 1162.01004. Archived from the original
    on 2019-08-08.
  17. ^ O'Connor, J. J.; Robertson, E. F. "The MacTutor History of Mathematics archive: Pierre de Fermat". Retrieved 2008-02-24.
  18. ^ Eves, Howard. An Introduction to the History of Mathematics, Saunders College Publishing, Fort Worth, Texas, 1990.
  19. ISBN 978-0-19-501496-9
    .
  20. ^ "Fermat's principle for light rays". Archived from the original on March 3, 2016. Retrieved 2008-02-24.
  21. S2CID 115984858
    .
  22. ISSN 0036-6978
    . Vol 9, No 4, pp. 209-228.
  23. ISBN 978-0-471-12104-6
    .
  24. ISBN 978-0-88385-561-4
    .
  25. ^ Weil 1984, p.104
  26. ^ Weil 1984, p.105

Works cited

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

Further reading

External links

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