Descartes' Discourse marks a breakpoint in European thought: in it, he sets out a radical new philosophy, which begins with a proof of the existence of the self (the famous "cogito ergo sum").
Next he deduces from it the existence and nature of God, and ends by offering a radical new account of the physical world and of human and animal nature.
Written in language accessible to all, it swept away all previous philosophical traditions.
Descartes' influence in mathematics is equally 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-dimensional coordinate system (and conversely, shapes to be described as equations), was named after him.
He is likewise credited as the father of analytical geometry: the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis.