The title of this paper was chosen before I had put my thoughts together, and even before I had considered thoroughly whether it were possible to make any general conclusions at all. I hope I shall not be accused afterwards of making something out of nothing, or of seeing connections where none exist. Perhaps it will be that, instead of having a vague notion that mathematics and morals are strangers or opposites, we may arrive at the end of the evening with a reasoned conviction that they are indeed so. But that the subject is not unprofitable to discuss I am strengthened in believing by noticing that Henri Poincaré, perhaps the greatest mathematician of the last fifty years, in the closing years of his life wrote an essay on the “Relations of Morals to Science,” which is included in the volume of his last thoughts.