MATH 4400, History of Mathematics
Lecture 7: The early 18th Century
Professor: Peter Gibson
[email protected]
http://people.math.yorku.ca/pcgibson/math4400
October 27, 2015
Overview and historical context
The 18th century is characterized by political absolutism, by intellectual
revolution—the Enlightenment—and, in the latter part, by monumental
political revolutions. It is the period in which mathematics took on its
modern form, adopting efficient notation and sophisticated theory that
was able to treat previously unassailable problems and to begin to
understand the mechanics of the universe.
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Development of Calculus
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The dissemination of mathematics in the late 17th and early 18th
centuries rested largely on personal communication. Two incipient new
forums that emerged as important at this time were:
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The dissemination of mathematics in the late 17th and early 18th
centuries rested largely on personal communication. Two incipient new
forums that emerged as important at this time were:
the Royal Society;
P. Gibson (YorkU)
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The dissemination of mathematics in the late 17th and early 18th
centuries rested largely on personal communication. Two incipient new
forums that emerged as important at this time were:
the Royal Society;
the Acta Eruditorum.
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Leibniz was an external member of the Royal Society
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The work of Newton and Leibniz provided new tools which were taken up
by others and applied to a range of previously intractable problems.
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The work of Newton and Leibniz provided new tools which were taken up
by others and applied to a range of previously intractable problems.
A number of mathematicians who took up the mantle had the same name:
Bernoulli.
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The brachistochrone problem, posed in the Acta Eruditorum by Johann
Bernoulli, was solved by Newton, Leibniz and Jakob Bernoulli.
Later the journal backed Leibniz in his bitterly-contested rivalry with
Newton.
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Some Russian history (again)
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 proprietate
gaudentes, sive solutio problematis isoperimetrici latissimo sensu
accepti (1744)
Introductio in analysin infinitorum (1748)
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Two of Euler’s many, many works:
Methodus inveniendi lineas curvas maximi minimive proprietate
gaudentes, sive solutio problematis isoperimetrici latissimo sensu
accepti (1744)
Introductio in analysin infinitorum (1748)
Euler is often credited to bringing mathematics into its modern form.
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