What is Matter? The seventeenth century mathematician and philosopher Rene Descartes had an elegant answer to this question: the essence of matter, or of body, is extension-extension in length, breadth, and depth. And since Descartes also held that the mind is indivisible while everything extended is divisible, the classic mind-body problem was born: How are we to find a place for the mind in a material world. But the material world has undergone quite a few changes since the seventeenth century, or at least our conception of it has, and we no longer have an elegant answer to the question of what is matter, if we have an answer to it at all. In my talk, I shall grapple with some of the difficulties of understanding the concept of matter and ponder the question of what implications "the thinning of matter" might have for our philosophical theorizing about the mind-body problem.