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Pierre de Fermat

Pierre de Fermat IPA: [pjɛːʁ dəfɛʁ'ma] (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. 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 the then unknown differential calculus, as well as his research into the theory of numbers. He also made notable contributions to analytic geometry and probability. Image File history File links Broom_icon. ... In the public domain by age This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... In the public domain by age This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... is the 229th day of the year (230th in leap years) in the Gregorian calendar. ... Events February 8 - Robert Devereux, 2nd Earl of Essex, rebels against Elizabeth I of England - revolt is quickly crushed February 25 - Robert Devereux beheaded Jesuit Matteo Ricci arrives in China Bad harvest in Russia due to rainy summer Dutch troops drive Portuguese from Málaga Battle of Kinsale, Ireland Births... is the 12th day of the year in the Gregorian calendar. ... Year 1665 (MDCLXV) was a common year starting on Thursday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Sunday of the 10-day slower Julian calendar). ... For the fish called lawyer, see Burbot. ... This article is for the Ancien Régime institution. ... New city flag (Occitan cross) Traditional coat of arms Motto: (Occitan: For Toulouse, always more) Location Coordinates Time Zone CET (GMT +1) Administration Country Region Midi-Pyrénées Department Haute-Garonne (31) Intercommunality Community of Agglomeration of Greater Toulouse Mayor Jean-Luc Moudenc  (UMP) (since 2004) City Statistics Land... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... For other uses, see Calculus (disambiguation). ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ... Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers and contains many open problems that are easily understood even by non-mathematicians. ... Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra. ... Probability is the likelihood that something is the case or will happen. ...

With his gift for number relations (Diophantus) and his ability to find proofs for his theorems, Fermat essentially created the modern theory of numbers. The quality of his work can be gauged by the fact that many of his results were not proved for over a century after his death, and one of them, his Last Theorem, took more than three centuries to prove. It was the convention among mathematicians in his day to challenge each other to prove a result, often not publishing their own proof to retain an advantage in such competitions. Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... Pierre de Fermats conjecture written in the margin of his copy of Arithmetica proved to be one of the most intriguing and enigmatic mathematical problems ever devised. ...

Although he carefully studied, and drew inspiration from Diophantus, Fermat began a different tradition. Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his diophantine equations, and he looked for all possible solutions. He also often proved that certain equations had no solution, which usually baffled his contemporaries. In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. ...

He studied Pell's equation, Fermat, perfect, and amicable numbers. It was while researching perfect numbers that he discovered the little theorem. Pells equation is any Diophantine equation of the form where n is a nonsquare integer. ... In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer. ... In mathematics, a perfect number is defined as an integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors not including the number. ... Amicable numbers are two numbers so related that the sum of the proper divisors of the one is equal to the other, unity being considered as a proper divisor but not the number itself. ... Fermats little theorem (not to be confused with Fermats last theorem) states that if p is a prime number, then for any integer a, This means that if you start with a number, initialized to 1, and repeatedly multiply, for a total of p multiplications, that number by...

He invented the proof technique of infinite descent, and a factorization method which has been named for him. In mathematics, a proof by infinite descent is a particular kind of proof by mathematical induction. ... With Fermats factoring method, one tries to represent an odd integer as the difference of two squares: . That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N. Furthermore, each odd number has such a representation. ...

He also 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 mathematics, Pierre de Fermats theorem on sums of two squares states that an odd prime number p is expressible as with x and y integers, if and only if For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and... Every positive integer is a sum of at most -polygonal numbers. ... Lagranges four-square theorem, also known as Bachets conjecture, was proved in 1770 by Joseph Louis Lagrange. ...

He was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, 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 mathematics, a geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. ... The fundamental theorem of calculus specifies the relationship between the two central operations of calculus, differentiation and integration. ...

Although Fermat claimed to have proved 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 tools available to Fermat. His famous Last Theorem was first discovered by his son in the margin on his father's copy of an edition of Diophantus, and included the statement that the margin was too small to include the proof. He had not bothered to inform even Mersenne of it. Johann Carl Friedrich Gauss or Gauß ( ; Latin: ) (30 April 1777 – 23 February 1855) was a German mathematician and scientist of profound genius who contributed significantly to many fields, including number theory, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. ...

Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, he discovered the fundamental principles of analytic geometry. With Blaise Pascal, he was a founder of the theory of probability. “Descartes” redirects here. ... Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of geometry using the principles of algebra. ... Blaise Pascal (pronounced ), (June 19, 1623 – August 19, 1662) was a French mathematician, physicist, and religious philosopher. ... Probability theory is the mathematical study of probability. ...

Fermat was secretive and a recluse. His only contact with the wider mathematical community aside from a brief exchange of letters with Pascal, was Marin Mersenne. However as Mersenne operated a correspondence network of sorts with other European thinkers, Fermat's results became widely distributed.^[1] Marin Mersenne, Marin Mersennus or le Père Mersenne (September 8, 1588 – September 1, 1648) was a French theologian, philosopher, mathematician and music theorist. ...

Holographic will handwritten by Fermat on March 4, 1660 — kept at the Departmental Archives of Haute-Garonne, in Toulouse

House in Beaumont-de-Lomagne where Fermat was born; now Fermat Museum

Statue of Fermat, in Beaumont-de-Lomagne

Fermat was born at Beaumont-de-Lomagne, 58 kilometers (36 miles) north-west of Toulouse, France. He died at Castres, 79 kilometers (49 miles) east of Toulouse. The oldest, and most prestigious, college in Toulouse is named after him -- the Pierre de Fermat. The late-15th-century mansion where Fermat was born in Beaumont-de-Lomagne is now a museum. Image File history File links File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A holographic will is a will and testament that has been entirely handwritten and signed by the testator. ... is the 63rd day of the year (64th in leap years) in the Gregorian calendar. ... // Events January 1 - Colonel George Monck with his regiment crosses from Scotland to England at the village of Coldstream and begins advance towards London in support of English Restoration. ... Haute-Garonne is a département in the southwest of France named after the Garonne river. ... New city flag (Occitan cross) Traditional coat of arms Motto: (Occitan: For Toulouse, always more) Location Coordinates Time Zone CET (GMT +1) Administration Country Region Midi-Pyrénées Department Haute-Garonne (31) Intercommunality Community of Agglomeration of Greater Toulouse Mayor Jean-Luc Moudenc  (UMP) (since 2004) City Statistics Land... This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... Statue of Pierre de Fermat, in Beaumont-de-Lomagne. ... Statue of Pierre de Fermat, in Beaumont-de-Lomagne. ... New city flag (Occitan cross) Traditional coat of arms Motto: (Occitan: For Toulouse, always more) Location Coordinates Time Zone CET (GMT +1) Administration Country Region Midi-Pyrénées Department Haute-Garonne (31) Intercommunality Community of Agglomeration of Greater Toulouse Mayor Jean-Luc Moudenc  (UMP) (since 2004) City Statistics Land... Castres (Castras in the Languedocian dialect of Occitan language) is a town and commune of Languedoc in south-western France. ... New city flag (Occitan cross) Traditional coat of arms Motto: (Occitan: For Toulouse, always more) Location Coordinates Time Zone CET (GMT +1) Administration Country Region Midi-Pyrénées Department Haute-Garonne (31) Intercommunality Community of Agglomeration of Greater Toulouse Mayor Jean-Luc Moudenc  (UMP) (since 2004) City Statistics Land... New city flag (Occitan cross) Traditional coat of arms Motto: (Occitan: For Toulouse, always more) Location Coordinates Time Zone CET (GMT +1) Administration Country Region Midi-Pyrénées Department Haute-Garonne (31) Intercommunality Community of Agglomeration of Greater Toulouse Mayor Jean-Luc Moudenc  (UMP) (since 2004) City Statistics Land...

See also

In number theory, Eulers theorem (also known as the Fermat-Euler theorem or Eulers totient theorem) states that if n is a positive integer and a is coprime to n, then aφ(n) ≡ 1 (mod n) where φ(n) is Eulers totient function and mod denotes the congruence... Pierre de Fermats conjecture written in the margin of his copy of Arithmetica proved to be one of the most intriguing and enigmatic mathematical problems ever devised. ... Fermats little theorem (not to be confused with Fermats last theorem) states that if p is a prime number, then for any integer a, This means that if you start with a number, initialized to 1, and repeatedly multiply, for a total of p multiplications, that number by... Fermats theorem is a theorem in real analysis, named after Pierre de Fermat. ... In mathematics, a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer. ... Fermats principle assures that the angles given by Snells law always reflect lights quickest path between P and Q. Fermats principle in optics states: This principle was first stated by Pierre de Fermat. ... Fermats spiral (also known as a parabolic spiral) follows the equation in polar coordinates. ... A pseudoprime is a probable prime (an integer which shares a property common to all prime numbers) which is not actually prime. ... This is a list of people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics. ... In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. ... A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. ... The Fermat prize of mathematical research rewards research works in fields where the contributions of Pierre de Fermat have been decisive: Statements of Variational Principles Foundations of Probability and Analytical Geometry Number theory. ...

Bibliography

• Singh, Simon (2002). Fermats Last Theorem. Fourth Estate Ltd. ISBN 1-84115-791-0. 
• Mahoney, Michael Sean (1994). The mathematical career of Pierre de Fermat, 1601 - 1665. Princeton Univ. Press. ISBN 0-691-03666-7. 

Footnotes

1. ^ Fermat's Enigma: The Epic Quest to Solve the World's Greatest Mathematical Problem. Singh, Simon. Anchor. 1998.

External links

• O'Connor, John J; Edmund F. Robertson "Pierre de Fermat". MacTutor History of Mathematics archive.  
• The Life and times of Pierre de Fermat (1601 - 1665) from W. W. Rouse Ball's History of Mathematics
• The Mathematics of Fermat's Last Theorem
• Fermat's Achievements