Famous Quote:
"I have a truly marvelous demonstration of this proposition which this margin is too small to contain."
-Pierre de Fermat
Contents
1. Bio-Data
2. Introduction
3. Family
4. Education
5. Work
6. Contribution
7. Death
8. Conclusion
9. Reference
Bio-data
Name : Pierre de Fermat
Born : August 17, 1601, Beaumont-de-Lomagne, France
Died : January 12, 1665, Castres, France
Parents : Dominique Fermat, Françoise Cazeneuve Fermat
Spouse : Louise Long Fermat
Education : University of Orléans (1623–1626)
Residence : France
Nationality : French
Fields : Mathematics and law
Known for : Number Theory,
Analytic Geometry,
Fermat’s Principle,
Probability,
Fermat’s Last Theorem,
Ad equality.
Special name :
1.Founder of the modern theory of numbers,
2. one of the 'fathers' of analytic geometry Along with Rene' Descartes,
3. along with Blaise Pascal is also considered to be one of the founders of
probability theory.
Introduction
Pierre de Fermat was a French lawyer at the Parlement of Toulouse, France, and an amateur 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 the 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 Fermat's Last Theorem, which he described in a note at the margin of a copy of Diophantus' Arithmetica. Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, Fermat discovered the fundamental principle of analytic geometry. His methods for finding tangents to curves and their maximum and minimum points led him to be regarded as the inventor of the differential calculus. Through his correspondence with Blaise Pascal he was a co-founder of the theory of probability.
Family
Fermat's father, Dominique Fermat, was a wealthy merchant in wheat and cattle and was three times for one year one of the four consuls of Beaumont-de-Lomagne. His mother was either Françoise Cazeneuve or Claire de Long. Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth. Fermat had five children. The eldest, Clément-Samuel, inherited his father's office of councillor.
Life and Education
Little is known of Fermat’s early life and education. He was of Basque origin and received his primary education in a local Franciscan school. He studied law, probably at Toulouse and perhaps also at Bordeaux. Having developed tastes for foreign languages, classical literature, and ancient science and mathematics.
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.
Fermat followed the custom of his day in composing conjectural “restorations” of lost works of antiquity. By 1629 he had begun a reconstruction of the long-lost Plane Loci of Apollonius, the Greek geometer of the 3rd century bc. He soon found that the study of loci, or sets of points with certain characteristics, could be facilitated by the application of algebra to geometry through a coordinate system. Meanwhile, Descartes had observed the same basic principle of analytic geometry, that equations in two variable quantities define plane curves. Because Fermat’s Introduction to Loci was published posthumously in 1679, the exploitation of their discovery, initiated in Descartes’s Géométrie of 1637, has since been known as Cartesian geometry.
In 1631 Fermat received the baccalaureate in law from the University of Orléans.
BUST IN THE SALLE DES ILLUSTRES IN CAPITOLE DE TOULOUSE
Work
He served in the local parliament at Toulouse, becoming councillor in 1634. Sometime before 1638 he became known as Pierre de Fermat, though the authority for this designation is uncertain. In 1638 he was named to the Criminal Court.
Contribution
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. The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.
In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers. It was while researching perfect numbers that he discovered the little theorem. He invented a factorization method—Fermat's factorization method—as well as the proof technique of infinite descent, which he used to prove 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 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 methods 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 Marin Mersenne of it. It was not proved until 1994 by Sir Andrew Wiles, using techniques unavailable to Fermat.
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 general solutions. He often proved that certain equations had no solution, which usually baffled his contemporaries.
Through his correspondence with Pascal in 1654, Fermat and Pascal helped lay the fundamental groundwork 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. 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 subsequently proved why this was the case mathematically.
Fermat's principle of least time (which he used to derive Snell's law in 1657) was the first variational principle enunciated in physics since Hero of Alexandria described a principle of least distance in the first century CE. In this way, 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.
Fermat's most important work was done in the development of modern number theory which was one of his favorite areas in math. He is best remembered for his number theory, in particular for Fermat's Last Theorem. This theorem states that: xn + yn = zn has no non-zero integer solutions for x, y and z when n is greater than 2.
Analyses of curves
Fermat’s study of curves and equations prompted him to generalize the equation for the ordinary parabola ay = x2, and that for the rectangular hyperbola xy = a2, to the form an - 1y = xn. The curves determined by this equation are known as the parabolas or a hyperbola of Fermat according as n is positive or negative. He similarly generalized the Archimedean spiral r = aθ. These curves in turn directed him in the middle 1630s to an algorithm, or rule of mathematical procedure, that was equivalent to differentiation. This procedure enabled him to find equations of tangents to curves and to locate maximum, minimum, and inflection points of polynomial curves, which are graphs of linear combinations of powers of the independent variable. During the same years, he found formulas for areas bounded by these curves through a summation process that is equivalent to the formula now used for the same purpose in the integral calculus. Such a formula is:
Death
Place of burial of Pierre de Fermat in Place Jean Jaurés, Castres, France. Translation of the plaque: in this place was buried on January 13, 1665, Pierre de Fermat, councilor of the chamber of Edit [Parlement of Toulouse] and mathematician of great renown, celebrated for his theorem,
an + bn ≠ cn for n>2
Pierre de Fermat died at Castres, Tarn 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 tribute to Fermat, now at the Capitole of Toulouse.
Conclusion
Fermat was the first person known to have evaluated the integral of general power functions. French sculptor Théophile Barrau carved a marble statue of de Fermat which stands in Toulouse.
The above two images are the stamp and the coin which have the Fermat’s photo on it.Fermat is a good mathematician and also he served many things for Maths.
Reference
1.http://www.mirror.co.uk/news/technology-science/technology/pierre-de-fermat-10-things-185140#ixzz2cyu3Iyf0
2.http://www.britanica.com/ebchecked/topic/204668/pierre-de-fermat
3.https://www.google.co.in/search?q=Fermat&source=lnms&tbm=isch&sa=X&ei=Y7r0UvPmF4eikwWZ5oH4Cw&ved=0CAcQ_AUoAQ&biw=1366&bih=624#facrc=_&imgdii=_&imgrc=l7BCphW2SWOIwM%253A%3Bf6vv0RCfcC7xyM%3Bhttp%253A%252F%252Fwww.apa.org%252FImages%252Ffull-fermat_tcm7-92824.jpg%3Bhttp%253A%252F%252Fwww.apa.org%252Fabout%252Fapa%252Farchives%252Fcoins-02.aspx%3B1998%3B1392
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