Alumni Newsletter: Spring '99

Steve Gonek - mathematician and teacher

Professor Steven Gonek, winner of a Goergen Award for undergraduate teaching, is an excellent researcher in the field of number theory, especially on the subject of the Riemann hypothesis and its connection to the distribution of prime numbers. With the proof of Fermat's Last Theorem, there is almost universal agreement that this is the hardest unsolved problem in mathematics. In the accompanying article "Reflections on the Meaning of Infinity," you will find a very basic introduction to the ways in which ideas in calculus can be used to prove theorems about prime numbers. Steve has a worldwide reputation as one of the best at this game.

But Goergen Awards are not given for excellence in research. They are given for excellence in teaching. Teaching involves two main activities, the design of curiculum and performance in the classroom. In both of these, Steve has excelled. He helped the whole department to win the Goergen Award by his contribution to the design of the Quest courses. But performance in the classroom is always more personal and satisfying. Here are Steve's own words about teaching:

I view teaching mathematics as I imagine music teachers view their work. I want my students to respond to the beauty of mathematics, which is one of the most powerful aesthetic experiences there is. I want them to understand the ideas behind the formulas and methods of the subject, and not just to manipulate symbols. Finally, I want my students to achieve the highest level of proficiency they can.

There is no one right path to these goals because , among other things, students have different levels of skill, ability, motivation, and intellectual maturity. However, what all the good ones have in common is that they engage the students. I always keep this in mind whether I am delivering a lecture or developing a new course.

Most of my teaching is in lectures, which are the least flexible and yet the most efficient format for explaining mathematics to a large number of students. I find that in lectures I consistently rely on several methods to engage students. One is to illustrate techniques and present ideas and proofs in the clearest possible way. This is an obvious point, but it has a benefit that may not be apparent: very clear explanations and chains of reasoning possess beauty even apart from their content. I think it is important to use this fact to attract and maintain my students' interest. However, it is never a good idea to fish with only one kind of lure. My others are to place a topic in historical context, to tell an anecdote about a mathematician associated with it, or to reveal a connection with something previously learned. Last, but most important is that students see my enthusiasm for the subject.