The modern theoretical physicist is a strange creature. Perhaps in every age the theoretical physicist has seemed so to his contemporaries who took the trouble to observe and think about him. There seems, for example, something almost too magical in the uncanny way in which he pulls a brand new atomic particle out of a theory, a way that reminds us of a rabbit being produced out of a hat. This is usually done in an off-hand manner with a considerable amount of patter of a highly abstract symbolic character but with a few words inserted in the right places for the benefit of the experimental physicist and a final prediction that if the experimenter does thus and so in the laboratory he will find a certain result. No wonder the observer marvels when the answer comes out right. But as he thinks further he is inclined to wonder whether it is necessary or desirable for the details of the process which led to the result to be so unintelligible. For unintelligible they seem to be to a great many people who are directly concerned with their understanding, to the people who for years have been laboring under the belief that they are engaged in the task of finding out how Nature works. What is this curious process whose whole task, according to one distinguished exponent of it, is merely to predict experimental results, and what is its future likely to be? These are the questions we are setting for ourselves in the present discussion. It is unlikely that the answers given here will satisfy everybody, but it is reasonably certain that nobody who aspires to an interest in science can fail to attach some meaning to them whether or not he agrees.