Mathematics during the Scientific Revolution(17th century)

The 17th century saw an unprecedented increase of mathematical and scientific ideas across Europe. Galileo伽利略 observed the moons of Jupiter木星的卫星 in orbit轨道 about that planet, using a telescope based on a toy imported from Holland. Tycho Brahe第谷·布拉赫 had gathered an enormous quantity of mathematical data describing the positions of the planets in the sky. By his position as Brahe's assistant, Johannes Kepler约翰内斯·开普勒 was first exposed to and seriously interacted with the topic of planetary motion行星运动. Kepler's calculations were made simpler by the contemporaneous同时发生的 invention of logarithms对数 by John Napier and Jost Bürgi约翰·纳皮尔和约瑟夫·本吉. Kepler succeeded in formulating mathematical laws of planetary motion. The analytic geometry developed by René Descartes勒内·笛卡尔 (1596–1650) allowed those orbits to be plotted on a graph, in Cartesian coordinates笛卡尔坐标系. Building on earlier work by many predecessors, Isaac Newton discovered the laws of physics explaining Kepler's Laws, and brought together the concepts now known as calculus微积分. Independently, Gottfried Wilhelm Leibniz戈特弗里德·威廉·莱布尼茨, who is arguably one of the most important mathematicians of the 17th century, developed calculus and much of the calculus notation still in use today. Science and mathematics had become an international endeavor努力, which would soon spread over the entire world. In addition to the application of mathematics to the studies of the heavens天体？, applied mathematics began to expand into new areas, with the correspondence来往信件 of Pierre de Fermat and Blaise Pascal皮埃尔·德·费马和布莱斯·帕斯卡. Pascal and Fermat set the groundwork for the investigations学术研究 of probability theory and the corresponding rules of combinatorics组合学规则 in their discussions over a game of gambling赌博. Pascal, with his wager赌注, 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预示着 the development of utility theory in the 18th–19th century.