The Development of Mathematics Throughout the Centuries by Evans Brian

Author:Evans, Brian
Language: eng
Format: epub
Publisher: Wiley
Published: 2014-02-23T16:00:00+00:00

CHAPTER 12

European Mathematics: The 17th Century

The 17th century was perhaps the greatest century for mathematical advancements. It was during this century of accomplishment that the Scientific Revolution continued onward and people were able to see the world and universe in more ways than they ever had before, with the inventions of the microscope and telescope. Before the start of this century, William Shakespeare, perhaps the greatest writer in the English language, began writing some of the world's most famous plays such as Romeo and Juliet and A Midsummer Night's Dream. The major cities in the English North American colonies, such as New York, Boston, and Philadelphia, began to develop, and great colleges were founded in America, including Harvard in Massachusetts and William and Mary in Virginia. During this century, Oliver Cromwell temporarily overthrew the English monarch. On the European continent, the Thirty Years' War was waged between Protestants and Catholics in the Holy Roman Empire.

During this century was seen the great development of analytic geometry, probability, and calculus. As mentioned in the last chapter, much of this advancement may have been due to the widespread dissemination of knowledge through the mass production of books and journals, which was enabled by the printing press. We begin our exploration of the 17th century with a very important mathematician and philosopher, René Descartes.

René Descartes, who was born in 1596 in the western part of central France in a town now named after him, is called the “Father of Modern Philosophy” for his great works in 17th-century philosophy. Along with Pierre de Fermat, Descartes developed analytic geometry, an area in mathematics that combines algebraic ideas on a geometric plane with equations representing curves; because of this, Descartes is called the “Father of Analytic Geometry.” Recall that Alhazen, Islamic mathematician in the 10th and 11th centuries, had developed analytic geometry ideas centuries prior. The work of Descartes and Fermat established a foundation for the calculus of Isaac Newton and Gottfried Leibniz to come later in the century. In particular, Descartes found a method for finding tangents to curves, a basic idea behind the derivative in calculus.

Descartes' mother died when he was only 1 year old. At 8 years old, Descartes attended a Jesuit school. In addition to his formal education, Descartes traveled much during his youth and he believed this advanced his education. His father wanted him to study law, which he did at the University of Poitiers, but Descartes was motivated by a dream he had in which he decided to pursue science as a young man.

Descartes applied the scientific method to philosophical thought. He abandoned any philosophical notions that could be doubted, and worked his way up through theories based on an axiomatic system. However, despite accusations of the like, he did not abandon his faith in God because he felt that God's existence could be proven ontologically through a priori reasoning. In his famous 1637 philosophical work that greatly influenced modern philosophy, the Discourse on the Method, Descartes stated his famous line: “Cogito ergo sum.

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