This paper reconstructs Gilles Deleuze’s interpretation of Epicurean atomism, and explicates his claim that it represents a problematic idea, similar to the idea exemplified in early, “barbaric” accounts of the differential calculus. Deleuzian problematic ideas are characterized by a mechanism through whose activity the components of the idea become determinate in relating reciprocally to one another, rather than in being determined exclusively in relation to an extrinsic paradigm or framework. In Epicurean atomism, as Deleuze reads it, such a mechanism of (...) determination can be found in the famous atomic “swerve”. It is necessary to bear this interpretation of Epicurean atomism in mind when understanding Deleuze and Guattari’s promulgation of a new image of thought in What is Philosophy? , which has an explicitly Epicurean inspiration. The paper argues that this inspiration is particularly evident to the extent that Deleuze and Guattari identify the sub-representative feature that lies at the heart of their new image of thought with “chaos”, defined as “infinite speed”. I claim that infinite speed, this otherwise puzzling feature of What is Philosophy? , ought to be understood in the light of Deleuze’s interpretation of Epicurus. Moreover, the Epicurean distinctions between different speeds must be read together with Deleuze’s appropriation of the metaphysics of the ancient Stoics, who, although widely recognized as Deleuze’s Hellenistic counterparts, lack important theoretical resources that the Epicureans provide for Deleuze. (shrink)