These essays examine the work of Gilles Deleuze, in particular his practice of enlisting mathematical resources to underpin and inform a wide variety of philosophical positions. Deleuze's work serves as a focus in these pieces for alternative conceptual lineages and as a rich source for fashioning mathematical concepts as tools for understanding a world seen in terms of becoming and difference.With contributions from Alain Badiou, Manuel DeLanda, Gilles Châtelet, and Daniel Smith, this analytic review challenges the self-imposed limits of philosophy while it elucidates a host of connections between mathematics and philosophy.