Kepler was the greatest mathematical astronomer of his generation and, with Galileo, the strongest advocate of the Copernican system in the first third of the seventeenth century. His determination of the elliptical orbit of Mars and his three laws of planetary motion, taken together with his attempt to delineate the forces that cause planetary motion, effectively instituted the new discipline of celestial mechanics (Kepler 1992 [1609]). Kepler also made major advances in optics. In his Ad vitellionem paralipomena (Kepler 2000 [1604]), he established the modern theory of vision and of the functioning of the eye as an optical device. Then, in his Dioptrice (1611), he significantly advanced the theory of the telescope. Descartes’ intellectual debt to Kepler is deep and complex and has often been misunderstood or oversimplified.

In a rare display of candor, Descartes confessed to Mersenne in 1638 that Kepler had been “his first master in optics” (AT II 86). This refers, first of all, to Descartes’ successful demonstration of the anaclastic properties of planohyperbolic lenses, following his discovery of the law of refraction of light in 1626–27. Descartes was stimulated by Kepler's surmise along these lines in the Dioptrice, where he had to employ an approximate version of the law. Equally importantly, in his Dioptrics (1637), Descartes transposed into mechanistic terms Kepler's revolutionary theory of vision.

However, the intellectual links between Descartes and Kepler extend further, to their overall natural philosophical agendas and results: just as Kepler was not simply an astronomer, so Descartes was not simply a mathematician or metaphysician. Descartes, like Kepler, was a bold, pro-Copernican and anti-Aristotelian natural philosopher. Both also envisioned the mathematization of natural philosophy, pursuing that aim in the form of what Descartes explicitly called “physico-mathematics.” The goal was to revise the Aristotelian view of the mixed mathematical sciences – such as astronomy, optics, and mechanics – as merely descriptive or instrumental. These disciplines were to become more intimately related to natural philosophical issues of matter and cause, the details depending upon the brand of natural philosophy an aspiring physico-mathematician endorsed. This is the deeper lesson that Kepler's novel, more physicalized optics taught to the young Descartes, and what he pursued in optics and theory of light throughout his career, employing corpuscular-mechanical rather than Keplerian Neoplatonic conceptions of matter and cause (Schuster 2012, Dupré 2012).