History of Mathematicspeople.math.yorku.ca/pcgibson/math4400/math4400files/Lecture_12… · Euler...

History of MathematicsEuler and Lagrange

Peter Gibson

November 12, 2016

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)

Read Euler, he is the master of us all.

-Laplace

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Biographical details

Born near Basel, Switzerland; father was a clergyman

tutored as a boy by Johann Bernoulli

entered the University of Basel at age 14

obtained a Master’s degree in philosophy; entered divinity school;switched to mathematics

1727 won an international competition for analysis of the placementof masts on sailing ships

1727 moved to St. Petersburg, to join Daniel Bernoulli at theSt. Petersburg Academy

his original post was for physiology and medicine

1733 obtained the chair in mathematics

had diverse duties as an employee of the state (preparing maps,advising the navy, testing fire engines...)

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Aside: the Bernoulli family

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1735 solved the Basel problem, first posed in 1644

1738 lost sight in his right eye

1739 Mechanica

1741 moved to the new Berlin Academy, under the patronage ofFrederick the Great

1742 letter from Goldbach with his famous conjecture

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

1748 Introductio in analysin infinitorum

1760-1762 Letters to a German Princess

1766 return to Russia

1771 lost sight in his left eye

1783 worked on hot air balloons, the moons of Uranus

Euler was hugely prolific, dominating the Journal of the St. PetersburgAcademy, writing many, many books.

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Some contemporaries

Benjamin Franklin (1706-1790)

George Washington (1732-1799)

Maximilien Robespierre (1758-1794)

Captain James Cook (1728-1779)

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Political Turmoil in FranceThe Age of Enlightenment was a precursor to radical politicaldevelopments in France (and elsewhere) toward the end of the 18thcentury.

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Political Turmoil in FranceThe Age of Enlightenment was a precursor to radical politicaldevelopments in France (and elsewhere) toward the end of the 18thcentury.

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The French Revolution changed completely the political landscape

the Tennis Court Oath, followed by the storming of the Bastille (1789)

the execution of Louis XIV (1793)

the Reign of Terror (1793-1794)

military adventures outside of France

coup d’etat by Napolean Bonaparte (1799)

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The Reign of Terror saw tens of thousands of summary executions

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Napoleon, who was in power from 1799-1815 conquered much of Europe

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Napoleon suffered a defeat in 1812 on the Russian front.

In 1814, after further defeats, he abdicated and was exiled to Elba.

He escaped, returned to Marseille, and regained power before finallybeing defeated at Waterloo by a coalition of British and Prussianforces.

He was then exiled to St. Helena, where he died in 1821.

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Despite the political turmoil, French mathematics flourished.

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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“it is necessary that the greatest geometer of Europe should live nearthe greatest of kings”

1786, death of Frederick; Lagrange moves to Paris

1795, professor at the Ecole normale

1797, professor at the Ecole polytechnique

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Important works of Lagrange

Sur la resolution des equations numeriques (1767)

Mechanique analytique (1788)

Theorie des fonctions analytiques (1797)

Lecons sur le calcul des fonctions (1801)

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There were many other prominent French mathematicians besidesLagrange:

Jean le Rond d’Alembert (1717-1783)

Adrien-Marie Legendre (1752-1833)

Joseph Fourier (1768-1830)

Simeon-Denis Poisson (1781-1840)

Augustin Cauchy (1789-1857)

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

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He wrote some important mathematical works of the time:

Mechanique celeste (5 volumes) (1799-1825)

Theorie analytique des probabilites (1812)

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