| Pierre de Fermat | |
 Pierre de Fermat | |
| Born | Beaumont-de-Lomagne, France |
|---|---|
| Died | 12 January 1665 (aged 63) Beaumont-de-Lomagne, France |
| Residence | France |
| Nationality | French |
| Fields | Mathematician and Law |
| Known for | Analytic geometry Probability Fermat's Last Theorem |
Pierre de Fermat IPA: [pjɛːʁ dəfɛʁ'ma] (August 17, 1601 or 1607/8[1] – 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. Beaumont-of-Lomagne is a commune in France, located in the Département of Tarn-et-Garonne and the Region of Midi-Pyrénées This article is about the country For a topic outline on this subject see List of basic France topics. Events 475 - Basiliscus becomes Byzantine Emperor, with a coronation ceremony in the Hebdomon palace in Constantinople Beaumont-of-Lomagne is a commune in France, located in the Département of Tarn-et-Garonne and the Region of Midi-Pyrénées This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. This article is about the country For a topic outline on this subject see List of basic France topics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Law is a system of rules enforced through a set of Institutions used as an instrument to underpin civil obedience politics economics and society Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry Probability is the likelihood or chance that something is the case or will happen Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like Events 986 - A Byzantine army was destroyed in the pass of Trajan's Gate by the Bulgarians under the Comitopuli Events 475 - Basiliscus becomes Byzantine Emperor, with a coronation ceremony in the Hebdomon palace in Constantinople This article is about the country For a topic outline on this subject see List of basic France topics. A lawyer, according to Black's Law Dictionary, is "a person learned in the law as an attorney, Counsel or Solicitor; a person This article is for the Ancien Régime institution For the post-Revolutionary and present-day institution see French Parliament. Toulouse ( pronounced in standard French, and in the local accent ( Occitan: Tolosa, pronounced) is a city in southwest This article is about the country For a topic outline on this subject see List of basic France topics. A mathematician is a person whose primary area of study and research is the field of Mathematics. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives 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. Differential Calculus, a field in Mathematics, is the study of how functions change when their inputs change Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes He also made notable contributions to analytic geometry, probability, and optics. Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry Probability is the likelihood or chance that something is the case or will happen
Contents |
Life and work
Fermat was born at Beaumont-de-Lomagne, 58 kilometers (36 miles) north-west of Toulouse, France. Beaumont-of-Lomagne is a commune in France, located in the Département of Tarn-et-Garonne and the Region of Midi-Pyrénées Beaumont-of-Lomagne is a commune in France, located in the Département of Tarn-et-Garonne and the Region of Midi-Pyrénées Toulouse ( pronounced in standard French, and in the local accent ( Occitan: Tolosa, pronounced) is a city in southwest This article is about the country For a topic outline on this subject see List of basic France topics. The late 15th century mansion where Fermat was born in Beaumont-de-Lomagne is now a museum. Beaumont-of-Lomagne is a commune in France, located in the Département of Tarn-et-Garonne and the Region of Midi-Pyrénées
In 1631, Fermat received the title of councilor at the High Court of Judicature in Toulouse, which he held for the rest of his life. Fluent in Latin, 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. [2]
Work
Fermat's pioneering work in analytic geometry, Ad Locos Planos et Solidos Isagoge, was circulated in manuscript form in 1636, predating the publication of Descartes' famous La géométrie. This manuscript was published posthumously in 1679.
In Methodus ad disquirendam maximam et minima and in De tangentibus linearum curvarum, Fermat developed a method for determining maxima, minima, and tangents to various curves that was equivalent to differentiation. [3] In these works, Fermat also obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature. [4]
Fermat 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. In Mathematics, a geometric series is a series with a constant ratio between successive terms. [5] The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements The fundamental theorem of calculus specifies the relationship between the two central operations of Calculus, differentiation and integration.
In number theory, Fermat studied Pell's equation, Fermat numbers, perfect, and amicable numbers. Pell's equation is any Diophantine equation of the form x^2-ny^2=1\ where n is a nonsquare integer and x In Mathematics, a Fermat number, named after Pierre de Fermat who first studied them is a positive integer of the form F_{n} = 2^{2^{ In mathematics a perfect number is defined as a positive integer which is the sum of its proper positive Divisors that is the sum of the positive divisors excluding Amicable numbers are two different Numbers so related that the sum of the Proper divisors of the one is equal to the other one being considered It was while researching perfect numbers that he discovered the little theorem. Fermat's little theorem (not to be confused with Fermat's last theorem) states that if p is a Prime number, then for any Integer a He also invented a factorization method which has been named for him as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. Fermat 's factorization method is based on the representation of an odd Integer as the Difference of two squares: N = a^2 - In Mathematics, a proof by infinite descent is a particular kind of proof by Mathematical induction. Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like Fermat 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 Number theory, Pierre de Fermat 's theorem on sums of two squares states that an odd prime p is expressible as p = x^2 In Mathematics, the Fermat polygonal number theorem states every positive integer is a sum of at most n n- Polygonal numbers That is every A triangular number is the sum of the n Natural numbers from 1 to n. Lagrange's four-square theorem, also known as Bachet's conjecture, was proven in 1770 by Joseph Louis Lagrange. A pentagonal number is a Figurate number that extends the concept of triangular and Square numbers to the Pentagon, but unlike the first
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. Johann Carl Friedrich Gauss (ˈɡaʊs, Gauß Carolus Fridericus Gauss ( 30 April 1777 – 23 February 1855) was a German 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. It was not proved until 1994, using techniques unavailable to Fermat.
Although he carefully studied, and drew inspiration from Diophantus, Fermat began a different tradition. The Capitole de Toulouse is the seat of the municipal administration of the French city of Toulouse. Diophantus of Alexandria ( Greek: b between 200 and 214 d between 284 and 298 AD sometimes called "the father of Algebra " a title some claim should 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 general solutions. In Mathematics, a Diophantine equation is an indeterminate Polynomial Equation that allows the variables to be Integers only He also often proved that certain equations had no solution, which usually baffled his contemporaries. In Mathematics, and more specifically Set theory, the empty set is the unique set having no ( Zero) members
Through his correspondence with Blaise Pascal in 1654, Fermat and Pascal helped lay the fundamental groundwork for the theory of probability. Blaise Pascal (blɛz paskal (June 19 1623 &ndash August 19 1662 was a French Mathematician, Physicist, and religious Philosopher Probability is the likelihood or chance that something is the case or will happen From this brief but productive collaboration on the problem of points, they are now regarded as joint founders of probability theory. The problem of points, also called the problem of division of the stakes, is a classical problem in Probability theory. [6]
Fermat's principle of least time (which he used to derive Snell's law in 1657) was the first variational principle [7] enunciated in physics since Hero of Alexandria described a principle of least distance in the first century CE. In Optics, Fermat's principle or the principle of least time is the idea that the path taken between two points by a ray of light is the path that can be In Optics and Physics, Snell's law (also known as Descartes' law or the law of refraction) is a formula used to describe the relationship A variational principle in physics is an alternative method for determining the state or dynamics of a physical system by identifying it as an extremum (minimum maximum or saddle point Hero (or Heron) of Alexandria ( Ήρων ο Αλεξανδρεύς) (c In this way, Fermat is recognized as a key figure in the historical development of the fundamental principle of least action in physics. This article discusses the history of the principle of least action The term Fermat functional was named in recognition of this role. [8]
Death
He died at Castres, age 63, 79 kilometers (49 miles) east of Toulouse. A holographic will is a will and testament that has been entirely handwritten and signed by the Testator. Events 51 - Nero, later to become Roman Emperor, is given the title Princeps iuventutis (head of the youth Haute-Garonne ( Occitan: Nauta Garona; English: Upper Garonne) is a department in the southwest of France named after the Toulouse ( pronounced in standard French, and in the local accent ( Occitan: Tolosa, pronounced) is a city in southwest Castres ( Castras in the Languedocian dialect of Occitan language) is a town and commune of Languedoc in south-western France Toulouse ( pronounced in standard French, and in the local accent ( Occitan: Tolosa, pronounced) is a city in southwest The oldest, and most prestigious, college in Toulouse is named after him - the Pierre de Fermat. Toulouse ( pronounced in standard French, and in the local accent ( Occitan: Tolosa, pronounced) is a city in southwest
Assessment of his work
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. Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry or analytical geometry, is the study of Geometry With Blaise Pascal, he was a founder of the theory of probability. Blaise Pascal (blɛz paskal (June 19 1623 &ndash August 19 1662 was a French Mathematician, Physicist, and religious Philosopher Probability theory is the branch of Mathematics concerned with analysis of random phenomena
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. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements "[9]
Of Fermat's number theoretic work, the great 20th century mathematician André Weil wrote that ". André Weil should not be confused with two other mathematicians with similar names Hermann Weyl (1885-1955 who made substantial contributions . . what we possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. In Algebraic geometry, an algebraic curve is an Algebraic variety of dimension one In Mathematics, an elliptic curve is a smooth, projective Algebraic curve of genus one on which there is a specified point O It naturally falls into two parts; the first one . . . may conveniently be termed a method of ascent, in contrast with the descent which is rightly regarded as Fermat's own. In Mathematics, a proof by infinite descent is a particular kind of proof by Mathematical induction. "[10] 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. Group theory is a mathematical discipline the part of Abstract algebra that studies the Algebraic structures known as groups. In Number theory, a K - rational point is a point on an Algebraic variety where each coordinate of the point belongs to the field K. "[11] 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
Bibliography
- Mahoney, Michael Sean (1994). In Number theory, Euler's theorem (also known as the Fermat-Euler theorem or Euler's totient theorem) states that if n is a positive Integer Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like Fermat's little theorem (not to be confused with Fermat's last theorem) states that if p is a Prime number, then for any Integer a Fermat's 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 F_{n} = 2^{2^{ In Optics, Fermat's principle or the principle of least time is the idea that the path taken between two points by a ray of light is the path that can be Fermat's spiral (also known as a parabolic Spiral) follows the equation r = \pm\theta^{1/2}\ 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 amateur mathematicians —people whose primary vocation did not involve mathematics (or In Mathematics, a Diophantine equation is an indeterminate Polynomial Equation that allows the variables to be Integers only In Number theory, a Prime number p is a Sophie Germain prime if 2 p + 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 The mathematical career of Pierre de Fermat, 1601 - 1665. Princeton Univ. Press. ISBN 0-691-03666-7.
- Singh, Simon (2002). Fermat's Last Theorem. Fourth Estate Ltd. ISBN 1-84115-791-0.
- Weil, André (1984). Number Theory: An approach through history From Hammurapi to Legendre. Birkhäuser. ISBN 0817631410.
References
- ^ Klaus Barner (2001): How old did Fermat become? Internationale Zeitschrift für Geschichte und Ethik der Naturwissenschaften, Technik und Medizin. ISSN 0036-6978. Vol 9, No 4, pp. 209-228.
- ^ Weil, André (1984). Number Theory: An approach through history From Hammurapi to Legendre. Birkhäuser, 38. ISBN 0817631410.
- ^ Pellegrino, Dana. Pierre de Fermat. Retrieved on 2008-02-24. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 303 - Galerius, Roman Emperor, publishes his edict that begins the persecution of Christians in his portion of the
- ^ Mahoney, Michael Sean (1994). The Mathematical Career of Pierre de Fermat, 1601-1665. Princeton University Press, 239-245. ISBN 0691036667.
- ^ Paradís, Jaume; Pla, Josep & Viader, Pelagrí, Fermat’s Treatise On Quadrature: A New Reading, <http://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID848544_code386779.pdf?abstractid=848544&mirid=5>. Retrieved on 24 February 2008
- ^ O'Connor, J. J. & Robertson, E. F. , The MacTutor History of Mathematics archive: Pierre de Fermat, <http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Fermat.html>. Retrieved on 24 February 2008
- ^ Fermat’s principle for light rays. Retrieved on 2008-02-24. 2008 ( MMVIII) is the current year in accordance with the Gregorian calendar, a Leap year that started on Tuesday of the Common Events 303 - Galerius, Roman Emperor, publishes his edict that begins the persecution of Christians in his portion of the
- ^ Červený, V. (July 2002). "Fermat's Variational Principle for Anisotropic Inhomogeneous Media". Studia Geophysica et Geodaetica 46 (3): 567. doi:. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.
- ^ Simmons, George F. (2007). Calculus Gems: Brief Lives and Memorable Mathematics. Mathematical Association of America, 98. ISBN 0883855615.
- ^ Weil, André (1984). Number Theory: An approach through history From Hammurapi to Legendre. Birkhäuser, 104. ISBN 0817631410.
- ^ Weil, André (1984). Number Theory: An approach through history From Hammurapi to Legendre. Birkhäuser, 105. ISBN 0817631410.
External links
- O'Connor, John J. & Robertson, Edmund F. , “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
- Very whole history of the last Fermat's theorem (french)
| Persondata | |
|---|---|
| NAME | Fermat, Pierre de |
| ALTERNATIVE NAMES | |
| SHORT DESCRIPTION | French mathematician and lawyer |
| DATE OF BIRTH | August 17, 1601 |
| PLACE OF BIRTH | Beaumont-de-Lomagne, France |
| DATE OF DEATH | January 12, 1665 |
| PLACE OF DEATH | Castres, France |
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