For 10 points, identify this dude who notably said "I think, therefore I am."
A theorem named for him solves a special case of the Apollonius problem and gives the curvature of two Soddy circles which are tangent to three mutually tangent circles. For a given curve, a method named for this man to find the tangent line at any point relies on introducing a circle with its center on the x axis, and the change of signs in a polynomial equation can be used to find the number of real positive zeros of that polynomial according to this man's rule of signs. This French thinker lends his name to the coordinate system using the coordinates x and y. For 10 points, identify this dude who notably said "I think, therefore I am."
A theorem named for him solves a special case of the Apollonius problem and gives the curvature of two Soddy circles which are tangent to three mutually tangent circles.
Rene Descartes