**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 x

^{2}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.