MATH 5400, History of Mathematics - Lecture 8: Euler, Topology and

MATH 5400, History of Mathematics
Lecture 8: Euler, Topology and Analysis
Professor: Peter Gibson
[email protected]
http://people.math.yorku.ca/pcgibson/math5400
November 17, 2016
Background
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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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 placement
of masts on sailing ships
1727 moved to St. Petersburg, to join Daniel Bernoulli at the
St. 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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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 of
Frederick the Great
1742 letter from Goldbach with his famous conjecture
1744 Methodus inveniendi lineas curvas maximi minimive proprietate
gaudentes, sive solutio problematis isoperimetrici latissimo sensu
accepti
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. Peter’s
Academy, writing many, many books.
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Some contemporaries
Benjamin Franklin (1706-1790)
George Washington (1732-1799)
Robespierre (1758-1794)
Captain Cook (1728-1779)
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Political Turmoil in France
The Age of Enlightenment was a precursor to radical political
developments in France (and elsewhere) toward the end of the 18th
century.
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Political Turmoil in France
The Age of Enlightenment was a precursor to radical political
developments in France (and elsewhere) toward the end of the 18th
century.
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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 XVI (1793)
the Reign of Terror (1793-1794)
military adventures outside of France
coup d’état by Napolean Bonaparte (1799)
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The Reign of Terror saw tens of thousands of summary executions
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Napoléon, who was in power from 1799-1815 conquered much of Europe
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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 Scool of Artillery in Turin
1766, summoned to Berlin by Frederick the Great
“it is necessary that the greatest geometer of Europe should live near
the 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 résolution des équations numériques (1767)
Méchanique analytique (1788)
Théorie des fonctions analytiques (1797)
Leçons sur le calcul des fonctions (1801)
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There were many other prominent French mathematicians besides
Lagrange:
Jean le Rond d’Alembert (1717-1783)
Adrien-Marie Legendre (1752-1833)
Joseph Fourier (1768-1830)
Siméon-Denis Poisson (1781-1840)
Augustin Cauchy (1789-1857)
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Pierre-Simon Laplace (1747-1827) was a professor at the Ecole militaire in
Paris.
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He wrote some important mathematical works of the time:
Méchanique céleste (5 volumes) (1799-1825)
Théorie analytique des probabilités (1812)
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