Mathematics

## Jacob A. Rasmussen ’98

### Reader in Pure Mathematics, University of Cambridge

I knew I was interested in math and physics before I came to Princeton, but I didn’t know much about either subject or what I might do with them. My freshman year was a real eye-opener. I loved the PHY 105–106 sequence, and thought about majoring in physics, to the extent that I spent the summer after freshman year working for an experimentalist in the physics department. Eventually, however, I decided that math was what I really wanted to do.

Looking back, two points along this path stand out in my mind. The first is a yearlong course in topology that I took from William (Bill) Browder. This was the first “real” math course I ever had, and I’ve loved topology ever since. I can still remember every question on the first semester’s take-home final. (I should—I spent the whole Christmas break thinking about it!)

**Fighting off doubt**

In my junior year, I had something of a crisis of confidence. I had learned lots of topology from the 1950s and 1960s, but very little after that. I began to worry that all the interesting problems in the subject had been solved, and the field was dead. It took me a while to work up the nerve to do it, but eventually I settled on the following plan. I would look up all the junior faculty members who listed topology as a research interest, knock on their doors, and ask them what they did. I decided I’d work my way from the bottom of Fine Hall to the top.

My first stop was an office on the fifth floor belonging to someone named Zoltan Szabo. I knocked (completely unannounced!) and explained my problem. The hour that followed is very clear in my memory. Szabo reassured me that there were plenty of interesting questions about topology left, especially in the geometry of three and four dimensions. Then he explained some things related to his own research in four-manifolds. I didn’t understand everything, but I still remember his description of the rational elliptic surface and the K3 surface. Even before I left, I knew I didn’t need to bother with any of the doors on the upper floors.

I’ve always been profoundly grateful to Szabo for taking the time to talk to me that day. Everything I’ve done in mathematics started with my walking through his door. I wrote a junior paper with him, then my senior thesis. I could not have asked for a better adviser.

**A rewarding outcome**

After graduation, I went to Harvard University, where I studied the topology of three- and four-dimensional manifolds. Midway through my time there, Szabo and his collaborator Peter Ozsvath made some remarkable advances in three-dimensional topology. These wound up playing a major role in my thesis. Once I had my Ph.D., I came back to Princeton to work with Szabo, who was now on the permanent faculty. I spent five years as a postdoc and assistant professor here before leaving to take a permanent job at the University of Cambridge. Teaching in the same classrooms where you’ve been a student can be a bit surreal at times but is also very rewarding. I know two students in the junior seminar I taught my first year at Princeton who have recently finished a Ph.D. in mathematics—one was in the office next to mine in Cambridge last year.

On the subject of how Princeton prepared me for what I do today, I probably have it easier than most. I have the luxury of doing mathematics every day, and the opportunity to teach it to others. I’ve been around enough math departments to appreciate the quality of the education I got here. The level of personal attention and the emphasis on independent thinking (all those take-homes) are hard to duplicate anywhere else.

I’ll end with a simple piece of advice for students of all stripes (not just math majors): Don’t be afraid to knock on some doors!