Teaching and Research: The History of a Pseudoconflict

I have chosen this topic for its appropriateness both to the theme of the conference—new directions in applied and computational mathematics—and to the occasion on which we honor Gail Young. For the new directions, with which other speakers will be dealing more directly in their contributions, carry strong implications for the teaching of mathematics at graduate and undergraduate levels—indeed, at all levels—so that it is fitting that we pay attention now to those implications. The organizers have, of course, taken note of this aspect of the conference theme, in placing on our agenda, as its final item, a panel discussion on the general issue of the shape of a new mathematics curriculum. I will confine myself to one aspect of the implications for us as teachers of these new directions; and I promise that my remarks today will be neither repeated nor contradicted when I reappear before you as a panelist tomorrow.