Occasionally, it appears as if the dominant question is whether mathematical problems should be solved. For mathematical teaching and research in many sectors are caught between the Scylla and Charybdis of those who condemn the subject because of applications that make it a potential conveyor of human destruction and those who wish to strip it of anything but its applications so as to tender it more socially useful, whether for medicine or war. Yet, history appears to support the reflection of André Weil that "the great mathematician of the future, as of the past, will flee the well-trodden path. It is by unexpected approchements, which our imagination would not have known how to arrive at, that he will solve, in giving them another twist, the great problems which we shall bequeath to him." Looking ahead, Weil was also confident of one further thing: "In the future, as in the past, the great ideas must be simplifying ideas."