5 Conclusion In Villani's work, we have seen not only rigorous mathematical analysis providing deep insights into physical behavior, but also important new mathematics emerging from the study of natural phenomena, in the spirit of Maxwell and Boltzmann. Besides his research articles, Villani has written extensive surveys and books [48, 50, 49, 51], and, through these, as well as the insights of his work, he has inspired a generation of young mathematicians with deep, rich, physically motivated mathematical questions. We are witnessing the beginning of Villani's spectacular career and in uence in shaping the directions of analysis and mathematics.
