Descartes
Early Life and Education
René Descartes was born on March 31, 1596, in La Haye en Touraine, a small town in central France. He was the youngest of three children and was sent to the Jesuit college at La Flèche at the age of eight. Here, he studied a wide range of subjects, including mathematics, philosophy, and theology, and was introduced to the works of ancient philosophers such as Aristotle.
Philosophical Contributions
Descartes is often referred to as the "father of modern philosophy," a title that signifies his break with the traditional Scholastic-Aristotelian philosophy prevalent at his time. He is best known for his philosophical statement, "Cogito, ergo sum" (I think, therefore I am), found in part IV of his Discourse on the Method (1637) and §7 of part I of his Principles of Philosophy (1644).
Descartes' philosophy generated much contemporary and subsequent controversy. He was accused of harboring secret Deist or Atheist beliefs, largely because he developed a metaphysical framework that does not necessarily reference God. Descartes' philosophy must be understood in the context of his times; he was a product of the Scientific Revolution, a time of radical change in the sciences.
Mathematical Contributions
Descartes' work in mathematics is perhaps his most lasting legacy. He is credited with the development of Cartesian coordinate system, which is fundamental to modern analytical geometry. Descartes' work provided the basis for the calculus developed by Newton and Leibniz, who applied infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. His rule of signs is also a commonly used method in mathematics to determine the number of positive and negative roots of a polynomial.
Legacy and Influence
Descartes' influence in mathematics is apparent; the Cartesian coordinate system — allowing reference to a point in space as a set of numbers, and allowing algebraic equations to be expressed as geometric shapes in a two- or three-dimensional coordinate system (and conversely, shapes to be described as equations) — was named after him. He is also credited as the father of analytical geometry, the bridge between algebra and geometry—used in the discovery of infinitesimal calculus and analysis.
His philosophical ideas have also had a profound impact on subsequent Western philosophy. Generally regarded as the first of the modern school of mathematics, Descartes' approach to the subject — based on abstractions rather than concrete realities — made it possible for the development of modern theoretical physics and technology.