Making clear the mathematically complex is priority number one for Andrew Casson

Students can count on one thing for sure in Andrew Casson’s classes: No matter how challenging and complicated the mathematical problems, he will do his best to be concise and clear.

Casson, the Philip Schuyler Beebe Professor of Mathematics, claims not to have been much of a mathematician during his youth, but is now known worldwide as an expert on geometric topology.

Honored with the Oswald Veblen Prize in Geometry by the American Mathematical Society in 1991, Casson’s newest accolade is the Dylan Hixon ’88 Prize for Teaching Excellence in the Natural Sciences (see “Six faculty members are honored with Yale College Teaching Prizes”). He recently spoke with YaleNews about his teaching. What follows is an edited version of that conversation.

What do you most enjoy about teaching at Yale?

I really love the small classes. Previously I taught at public universities and they generally were large classes and very impersonal. But this is really great. It allows the classes to be more interactive.

What have you learned from your students?

I’m very impressed with the amount of work they can do.  I grew up in England in a different system where students have focus mainly on their major. Here the students are roughly spending a third of the time doing their majors, and they are still reaching a high standard. I am very impressed by their capacity for work, particularly during reading week!

Is there a teacher who has particularly inspired you?

When I was at Cambridge, a couple of teachers really inspired me. I was particularly impressed with the ones who could lecture without notes. I think there was a time when I could literally go into the classroom without notes but now I do refer to them from time to time.

I also enjoyed teachers who thought through the material as they were teaching it. They worked on whatever they were teaching as they presented it.

If there is one thing you want your students to learn, what would that be?

The thing that I prize most about lectures — whether I’m listening to lectures or giving them — is clarity. So I guess I would like to communicate clarity of thought and that’s what I’d like them to learn. If anything, I do think I am reasonably clear.

Initially I wasn’t even very good at mathematics. Later it just seemed very attractive as systematic thinking. It was a different way of looking at the world, and I’d like my students to appreciate that.