Pierre de Fermat

FermatPierre FermatFermat, Pierre dede Fermat, PierreFermat's PrincipleP. Fermat
Pierre de Fermat (between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer 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.wikipedia
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Adequality

adequal
Pierre de Fermat (between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer 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 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.
Adequality is a technique developed by Pierre de Fermat in his treatise Methodus ad disquirendam maximam et minimam (a Latin treatise circulated in France c. 1636) to calculate maxima and minima of functions, tangents to curves, area, center of mass, least action, and other problems in calculus.

Fermat's Last Theorem

Fermat’s Last TheoremLast Theorema long-standing problem
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.
The proposition was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica; Fermat added that he had a proof that was too large to fit in the margin.

Calculus

infinitesimal calculusdifferential and integral calculusclassical calculus
Pierre de Fermat (between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer 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.
Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal error term.

Diophantus

Diophantus of AlexandriaDiophantosDiophantus the Arab
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.
While reading Claude Gaspard Bachet de Méziriac's edition of Diophantus' Arithmetica, Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem.

Maxima and minima

maximumminimumlocal maximum
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.
Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.

Analytic geometry

analytical geometryCartesian geometrycoordinate geometry
He made notable contributions to analytic geometry, probability, and optics.
Analytic geometry was independently invented by René Descartes and Pierre de Fermat, although Descartes is sometimes given sole credit.

Probability

probabilisticprobabilitieschance
He made notable contributions to analytic geometry, probability, and optics.
Aside from the elementary work by Cardano, the doctrine of probabilities dates to the correspondence of Pierre de Fermat and Blaise Pascal (1654).

Number theory

number theoristcombinatorial number theorytheory of numbers
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. 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.
Pierre de Fermat (1607–1665) never published his writings; in particular, his work on number theory is contained almost entirely in letters to mathematicians and in private marginal notes.

Differential calculus

differentialdifferentiationcalculus
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. 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.
For their ideas on derivatives, both Newton and Leibniz built on significant earlier work by mathematicians such as Pierre de Fermat (1607-1665), Isaac Barrow (1630–1677), René Descartes (1596–1650), Christiaan Huygens (1629–1695), Blaise Pascal (1623–1662) and John Wallis (1616–1703).

Fermat number

Fermat primesFermat numbersGeneralized Fermat prime
In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers.
In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form

Fermat's factorization method

Fermat factorizationFermat factorization method
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's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares:

Tangent

tangent linetangentialtangents
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.
In the 1630s Fermat developed the technique of adequality to calculate tangents and other problems in analysis and used this to calculate tangents to the parabola.

Toulouse

Toulouse, FranceTolosaToulousain
Pierre de Fermat (between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer 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.
Several notable Toulousains have been scientists, such as Jean Dausset, 1980 winner of the Nobel Prize in Physiology or Medicine; 17th-century mathematician Pierre de Fermat, who spent his life in Toulouse, where he wrote Fermat's Last Theorem and was a lawyer in the city's Parlement; Paul Sabatier, 1912 winner of the Nobel Prize in Chemistry; Albert Fert, 2007 winner of the Nobel Prize in Physics who grew up in Toulouse where he attended the and Jean Tirole, owner of the 2014 Nobel Prize in Economic Sciences, chairman and founder of the Toulouse School of Economics along with Jean-Jacques Laffont.

Fermat's theorem on sums of two squares

two-square theoremFermat's two-square theoremFermat's theorems
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.
In additive number theory, Fermat's theorem on sums of two squares states that an odd prime p can be expressed as:

René Descartes

DescartesCartesianRene Descartes
This naturally led to priority disputes with contemporaries such as Descartes and Wallis.
In La Géométrie, Descartes exploited the discoveries he made with Pierre de Fermat, having been able to do so because his paper, Introduction to Loci, was published posthumously in 1679.

Fermat's little theorem

Fermat's TheoremFermat little theoremFermat's "little theorem
It was while researching perfect numbers that he discovered Fermat's little theorem.
The theorem is named after Pierre de Fermat, who stated it in 1640.

University of Orléans

University of OrleansOrléansUniversité d'Orléans
He attended the University of Orléans from 1623 and received a bachelor in civil law in 1626, before moving to Bordeaux.

Fermat's right triangle theorem

hereproof by Fermat
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.

Beaumont-de-Lomagne

Lomagne
Fermat was born in the first decade of the 17th century in Beaumont-de-Lomagne, France—the late 15th-century mansion where Fermat was born is now a museum.
The eminent mathematician Pierre de Fermat, famous for Fermat's Last Theorem, was born in Beaumont in either 1601 or 1607.

Proof by infinite descent

infinite descentMethod of infinite descentdescent
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.
The method was much later developed by Fermat, who coined the term and often used it for Diophantine equations.

Apollonius of Perga

ApolloniusApollonius of PergeApollonian
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.
Since Pappus gives somewhat full particulars of its propositions, this text has also seen efforts to restore it, not only by P. Fermat (Oeuvres, i., 1891, pp.

Blaise Pascal

PascalPascal, BlaisePascalian
Through their correspondence in 1654, Fermat and Blaise Pascal helped lay the foundation for the theory of probability.
Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of 16, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.

Amicable numbers

amicable numberamicableamicable pairs
In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers.
Thābit ibn Qurra's formula was rediscovered by Fermat (1601–1665) and Descartes (1596–1650), to whom it is sometimes ascribed, and extended by Euler (1707–1783).

Pell's equation

Pell equationPell equationsPellian equation
In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers.
Pierre de Fermat found how to solve the equation and in a 1657 letter issued it as a challenge to English mathematicians.

Fermat polygonal number theorem

polygonal number theoremFermat's polygonal number theorem
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.
The theorem is named after Pierre de Fermat, who stated it, in 1638, without proof, promising to write it in a separate work that never appeared.