René Descartes

René Descartes

Born: 31^st March, 1596, Descartes, Indre-et-Loire, France

Died: 11^th February, 1650, Stockholm, Sweden
Influenced: Noam Chomsky, Baruch Spinoza, Slavoj Žižek
Influenced by: Aristotle, Plato, Thomas Aquinas, Archimedes

It is considered that René Descartes was the inventor of both analytic geometry and symbolic algebraic notation. His use of equations to partially solve the geometric Problem of Pappus revolutionized mathematics.

René Descartes refused to accept the authority of previous philosophers. He frequently set his views apart from the philosophers who preceded him.

He also pioneered the standard notation that uses superscripts to show the powers or exponents, for example, the 2 used in x² to indicate x squared.

He was first to assign a fundamental place for algebra in our system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities.  

European mathematicians had previously viewed geometry as a more fundamental form of mathematics, serving as the foundation of algebra.

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 to determine the number of positive and negative roots of a polynomial.

Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction (also known as Descartes' law or more commonly Snell's law) that the angular radius of a rainbow is 42 degrees. It means that the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's center is 42°. He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.