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Pierre de Fermat

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Information about Pierre de Fermat
Education

Published on March 16, 2009

Author: aharning

Source: slideshare.net

Description

An overview of Pierre de Fermat's life.
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Fermatting with Numbers By: Professor April Harning History of Mathematics Course Chapter 10: 17 th Century

That’s right! Pierre de Fermat (1601-1665)

Fermat was a… Family man Lawyer Government official Mathematician

Family man

Lawyer

Government official

Mathematician

Fermat’s Life Born in France Dominique Claire de Long Siblings Married Louise de Long

Born in France

Dominique

Claire de Long

Siblings

Married Louise de Long

Fermat’s Studies Classical literature Languages Law Attended…

Classical literature

Languages

Law

Attended…

Became a … Purchased part of Toulouse’s parliament Counsellor of Local Parliament Criminal Court Chief Spokesman of the Grand Chamber

Purchased part of Toulouse’s parliament

Counsellor of Local Parliament

Criminal Court

Chief Spokesman of the Grand Chamber

Time for Mathematics Retired Contributions Geometry Infinitesimal calculus Theory of numbers Probability His friends

Retired

Contributions

Geometry

Infinitesimal calculus

Theory of numbers

Probability

His friends

Fermat’s Geometry Old Works Plane Loci Analytic Geometry Rotation of Axes Cubic and Quartic Equations Higher Dimension Curves De Linearum Curvarum cum Lineis Rectis

Old Works

Plane Loci

Analytic Geometry

Rotation of Axes

Cubic and Quartic Equations

Higher Dimension Curves

De Linearum Curvarum cum Lineis Rectis

Fermat’s Calculus Hyperbolas and Parabolas of Fermat Archimedean Spiral, r = aΘ Differentiation Maximum and Minimum Values “ Fermat, the true inventor of the differential calculus.” ~Laplace Integral Calculus

Hyperbolas and Parabolas of Fermat

Archimedean Spiral, r = aΘ

Differentiation

Maximum and Minimum Values

“ Fermat, the true inventor of the differential calculus.” ~Laplace

Integral Calculus

Fermat’s Number Theory Arithmetica Method of Infinite Descent Girard’s Assertion Fermat’s Little Theorem Fermat Numbers 65537 F 4 257 F 3 17 F 2 5 F 1 3 F 0 Primes Fermat

Arithmetica

Method of Infinite Descent

Girard’s Assertion

Fermat’s Little Theorem

Fermat Numbers

Proof of Fermat’s Little Theorem Theorem : Let p be a prime and suppose that p does not divide a . Then, Given : Prime p where p does not divide a Prove : Consider the first p-1 positive multiples of a , ( a, 2a, 3a, …,(p-1)a ) IMPOSSIBLE

Theorem : Let p be a prime and suppose that p does not divide a . Then,

Given : Prime p where p does not divide a

Prove :

Consider the first p-1 positive multiples of a , ( a, 2a, 3a, …,(p-1)a )

IMPOSSIBLE

Proof of Fermat’s Little Theorem Previous set of integers must be congruent modulo p to 1, 2, 3, …, p-1 Therefore, because p does not divide (p-1)!

Previous set of integers must be congruent modulo p to 1, 2, 3, …, p-1

Therefore, because p does not divide (p-1)!

Fermat’s Probability Gambler’s Dispute with Pascal Chevalier de Méré informed Pascal Exchange of Letters

Gambler’s Dispute with Pascal

Chevalier de Méré informed Pascal

Exchange of Letters

Fermat’s Last Theorem x n + y n = z n has no integer solutions for x , y, and z when n > 2 Famous quote, "I have discovered a truly remarkable proof which this margin is too small to contain.“ Challenged mathematicians In 1994, Andrew Wiles and Richard Taylor

x n + y n = z n has no integer solutions for x , y, and z when n > 2

Famous quote, "I have discovered a truly remarkable proof which this margin is too small to contain.“

Challenged mathematicians

In 1994, Andrew Wiles and Richard Taylor

Peaceful Death In 1665, … City of Castres Samuel, his son Accuracy of work Publications

In 1665, …

City of Castres

Samuel, his son

Accuracy of work

Publications

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