Rene Descartes was a great philosopher and thinker, many overlook his contribution to math because of his overwhelming addtions to the field of philosophy, however we would like to point out this mans work on mathematics so that he gets even more credit to his name. By the way he passed away from a cold, away from him native France, and could have probably made an even bigger impact on modern science if he had not passed away in a reletivley early age.

This from the Wikipedia page on Descartes:

Descartes’ theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics.[13] This appears even more astounding considering that the work was just intended as an example to his Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences (Discourse on the Method of Rightly Conducting the Reason, and Searching for Truth in the Sciences, better known under the shortened title Discours de la méthode; English, Discourse on the Method).

Descartes’ rule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.

Rene Descartes created analytic geometry, and discovered an early form of the law of conservation of momentum (the term momentum refers to the momentum of a force). He outlined his views on the universe in his Principles of Philosophy.

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, who discovered it 16 years earlier) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow’s centre is 42°).[14] He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.[15]

One of Descartes most enduring legacies was his development of Cartesian geometry which uses algebra to describe geometry. He also “invented”, the notation which uses superscripts to show the powers or exponents, for example the 4 used in x4 to indicate squaring of squaring. The first notations of exponents were given by Franciscus Vieta in 1591, after whom the scottish mathematician James Hume, wrote A{iv} and the french one Herigone : A4.