Editing History of mathematics (section)

==Mathematics during the Scientific Revolution==
{{See also|Scientific Revolution}}

===17th century===
[[File:JKepler.jpg|thumb|upright|left|[[Johannes Kepler]]]]
[[File:Gottfried Wilhelm Leibniz, Bernhard Christoph Francke.jpg|thumb|upright|right|[[Gottfried Wilhelm Leibniz]]]]
The 17th century saw an unprecedented increase of mathematical and scientific ideas across Europe. [[Tycho Brahe]] had gathered a large quantity of mathematical data describing the positions of the planets in the sky. By his position as Brahe's assistant, [[Johannes Kepler]] was first exposed to and seriously interacted with the topic of planetary motion. Kepler's calculations were made simpler by the contemporaneous invention of [[logarithm]]s by [[John Napier]] and [[Jost Bürgi]]. Kepler succeeded in formulating mathematical laws of planetary motion.<ref>{{cite book
 | last =Struik
 | first =Dirk
 | title =A Concise History of Mathematics
 | publisher =Courier Dover Publications
 | edition =3rd.
 | year =1987
 | pages =[https://archive.org/details/concisehistoryof0000stru_m6j1/page/89 89]
 | isbn =978-0-486-60255-4
 | url =https://archive.org/details/concisehistoryof0000stru_m6j1/page/89
 }}</ref>
The [[analytic geometry]] developed by [[René Descartes]] (1596–1650) allowed those orbits to be plotted on a graph, in [[Cartesian coordinates]].

Building on earlier work by many predecessors, [[Isaac Newton]] discovered the laws of physics that explain [[Kepler's Laws]], and brought together the concepts now known as [[calculus]]. Independently, [[Gottfried Wilhelm Leibniz]], developed calculus and much of the calculus notation still in use today. He also refined the [[binary number]] system, which is the foundation of nearly all digital ([[Scientific calculator|electronic]], [[Solid-state electronics|solid-state]], [[Logic gate|discrete logic]]) [[computer]]s.<ref>{{cite web |title=2021: 375th birthday of Leibniz, father of computer science |url=https://people.idsia.ch/~juergen/leibniz-father-computer-science-375.html |website=people.idsia.ch}}</ref>

Science and mathematics had become an international endeavor, which would soon spread over the entire world.<ref>Eves, Howard (1990). ''An Introduction to the History of Mathematics'', Saunders. {{ISBN|0-03-029558-0}}, p. 379, "... the concepts of calculus... (are) so far reaching and have exercised such an impact on the modern world that it is perhaps correct to say that without some knowledge of them a person today can scarcely claim to be well educated."</ref>

In addition to the application of mathematics to the studies of the heavens, [[applied mathematics]] began to expand into new areas, with the correspondence of [[Pierre de Fermat]] and [[Blaise Pascal]]. Pascal and Fermat set the groundwork for the investigations of [[probability theory]] and the corresponding rules of [[combinatorics]] in their discussions over a game of [[gambling]]. Pascal, with his [[Pascal's Wager|wager]], attempted to use the newly developing probability theory to argue for a life devoted to religion, on the grounds that even if the probability of success was small, the rewards were infinite. In some sense, this foreshadowed the development of [[utility theory]] in the 18th and 19th centuries.

=== 18th century ===
[[File:Leonhard Euler - Jakob Emanuel Handmann (Kunstmuseum Basel).jpg|right|thumb|upright|[[Leonhard Euler]]]]

The most influential mathematician of the 18th century was arguably [[Leonhard Euler]] (1707–1783). His contributions range from founding the study of [[graph theory]] with the [[Seven Bridges of Königsberg]] problem to standardizing many modern mathematical terms and notations. For example, he named the square root of minus 1 with the symbol [[Imaginary unit|<span style="font-family:times new Roman;">''i''</span>]], and he popularized the use of the Greek letter <math>\pi</math> to stand for the ratio of a circle's circumference to its diameter. He made numerous contributions to the study of topology, graph theory, calculus, combinatorics, and complex analysis, as evidenced by the multitude of theorems and notations named for him.

Other important European mathematicians of the 18th century included [[Joseph Louis Lagrange]], who did pioneering work in number theory, algebra, differential calculus, and the calculus of variations, and [[Pierre-Simon Laplace]], who, in the age of [[Napoleon]], did important work on the foundations of [[celestial mechanics]] and on [[statistics]].