Lessons on Teaching Differential Equations

Gian-Carlo Rota

One of many mistakes of my youth was writing a textbook in ordinary differential equations. It set me back several years in my career in mathematics. However, it had a redeeming feature: it led me to realize that I had no idea what a differential equation is. The more I teach differential equations, the less I understand the mystery of differential equations.

One of several unpleasant consequences of writing such a textbook is my being called upon to teach the sophomore differential equations course at MIT. This course is justly viewed as the most unpleasant undergraduate course in mathematics, by both teachers and students. Some of my colleagues have publicly announced that they would rather resign from MIT than lecture in sophomore differential equations. No such threat is available to me, since I am incorrectly labeled as the one member of the department who is supposed to have some expertise in the subject, guilty of writing an elementary textbook still in print.

The Administrative Director of the MIT mathematics department, who exercises supreme au- thority upon the faculty’s teaching, has only to wave a copy of my book at me, while staring at me in silence. At her prompting, I bow and fall into line; I will be the lecturer in the dreaded course for one more year, and I will repeat the mistakes I have been making every year since I first taught differential equations in 1958.