Abstract: Details Descartes's relationship with Beeckman, and their collaboration on three projects in mathematics, dealing with music, falling bodies, and hydrostatics. Presents Beeckman's version of corpuscularianism, its differences from traditional atomism, and its relevance to their collaboration. Letters to Beeckman give details of Descartes's mathematical discoveries on the subject of longitude, compasses, and his attempt to revive a traditional mathematical art, mathesis universalis.

Keywords: atomism, Beeckman, corpuscularianism, falling bodies, hydrostatics, mathematics, mathesis universalis, music,