MATH 5400, History of Mathematicspcgibson/math5400/math5400files/...John Playfair (1748-1819) James Hutton (1726-1797) This set the stage for later developments... P. Gibson Math 5400

MATH 5400, History of MathematicsLecture 13: The 18th Century

Professor: Peter Gibson

January 29, 2013

Some Russian history

St. Petersburg was founded in 1703

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Peter the Great (ruled 1682-1725)

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Catherine the Great (ruled 1762-1796)

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The contemporary Prussian monarch was Frederick the Great (1740-1786)

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Which brings us to Euler (1707-1783)

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Two of Euler’s many, many works:

Methodus inveniendi lineas curvas maximi minimive proprietategaudentes, sive solutio problematis isoperimetrici latissimo sensuaccepti (1744)

Introductio in analysin infinitorum (1748)

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France during the Enlightenment

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Joseph-Louis Lagrange (1736-1813)

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Born in Turin

1755, Professor of Mathematics at the School of Artillery in Turin

1766, summoned to Berlin by Frederick the Great

1786, death of Frederick; Lagrange moves to Paris

1795, Professor at the Ecole normale

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Important works of Lagrange include:

Sur la resolution des equations numeriques (1767)

Mechanique analytique (1788)

Theorie des fonctions analytiques (1797)

Le cons sur le calcul des fonctions (1801)

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Pierre-Simon Laplace (1747-1827) was a professor at the Ecole militaire inParis.

He wrote some of the most important works of his day:

Mechanique celeste (5 volumes) (1799-1825)

Theorie analytique des probabilites (1812)

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Pierre-Simon Laplace (1747-1827) was a professor at the Ecole militaire inParis.

He wrote some of the most important works of his day:

Mechanique celeste (5 volumes) (1799-1825)

Theorie analytique des probabilites (1812)

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There were many other prominent French mathematicians besidesLagrange and Laplace:

Jean le Rond D’Alembert (1717-1783)

Adrien Marie Legendre (1752-1833)

Joseph Fourier (1768-1830)And somewhat later...

Simeon-Denis Poisson (1781-1840)

Augustin Cauchy (1789-1857)

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The Scottish Enlightenment

A period of intellectual flowering in Scotland in the 18th century.

1707 Act of Unification (creating Great Britain)

Scotland had suffered a financial collapse and was poor

Following union with England, there was established a system of publicschooling, and a revitalization of the Universities. As in Europe,intellectual culture in Scotland flourished.

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Figures of 18th century Scotland

David Hume (1711-1776)I A Treatise of Human NatureI Dialogues Concerning Natural Religion

Adam Smith (1723-1790)

I The Wealth of Nations

Robert Burns (1759-1796)

John Playfair (1748-1819)

James Hutton (1726-1797)

This set the stage for later developments...

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Adam Smith (1723-1790)I The Wealth of Nations





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MATH 5400, History of Mathematicspcgibson/math5400/math5400files/...John Playfair (1748-1819) James Hutton (1726-1797) This set the stage for later developments... P. Gibson Math 5400

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