Mathematics professor Rekha Santhanam began her love affair with math in high school and has since gone on to do extensive research in algebraic topology both here in the United States and in her native city of Mumbai.
Here, Professor Santhanam takes a moment to explain her work in homotopy theory in layman’s terms, and sheds some light on the career possibilities of a potential mathematician.
News-Letter (N-L):How did you get interested in mathematics?
Rehka Santhanam (RS): I guess I got interested in math in high school. Basically, calculus was fun for me.
And it turned out well, luckily, since I made this decision to major in math before I started my undergraduate degree.
But I actually enjoyed the theoretical side of math too – we learned a lot of analysis when we started off, and it was very different from what we did in high school, but I found that was also very interesting for me, and it just took off from there.
N-L: What specifically within the realm of mathematics are you interested in?
RS: I work algebraic topology, in particular, homotopy theory. Sometimes people confuse topology with topography – both have something to do with shapes, but algebraic topology is the study of mathematical spaces, which have a notion of open sets, continuity, etc. You can think of spaces as circles, spheres, tori… but when studying topology, you don’t really care so much about the geometry of the spaces.
The usual example that I give everyone is that you are only looking at things up to continuous transformations. For instance, if you have a disk, you can contract the disk radially until it becomes a single point. Whereas if you took my ring, there’s no way you can turn the ring into a point without breaking it.
So in homotopy theory, which is the specific area of algebraic topology that I work in, the ring and the disc are two different things, whereas the disc and the point are the same thing.
You’re studying objects in terms of continuity – not caring about the geometry.
The algebraic part comes in when you’re trying to compare the two spaces. It’s very difficult to show geometrically when two things are the same. But what you can do is attach certain algebraic structures, for instance, homotopy groups, to the objects. If the attachments are different, then the objects have to be different, and vice versa.
N-L: What were you doing before coming to Johns Hopkins?
RS: I got my doctorate degree at the University of Illinois at Urbana-Champaign. In math, obviously. I did my dissertation on homotopy theory.
Before that, I was in Mumbai, India, where I received my undergraduate degrees and my master’s degree.
N-L: So how did you find the move from Mumbai to the United States?
RS: I didn’t really think about how I would feel about moving to the States until I got here. Living in the States did take some adjusting because obviously India and the States are two very different countries. But there were a lot of friends around, and ultimately I did really enjoy graduate school.
I found that Urbana-Champaign was pretty good in the sense that it was a campus town. You get to meet a lot of different people from diverse cultures, so it was a nice mix.
UIUC has a very academic culture, so in that sense it was also very familiar. My father used to be a professor, and I grew up living on a university campus in India, so I was very used to that kind of lifestyle. That made the transition much easier.
N-L: Academically speaking, what are your plans for the future? Are you continuing to do research here in addition to teaching?
RS: I do enjoy teaching; it’s a good part of what I want to do here. But I am still doing research. I’m not a permanent faculty member here, and my plan is to move back to India in the future and get a tenured position there.
Long-term, I would like to stay in research and do more work with homotopy theory.
N-L: Any last words of wisdom for wannabe math students?
RS: I guess math is one of those subjects that you know very quickly if you like it or not. And if you know that you like it, it’s not very difficult to pursue. There are a lot of options after you get a Ph.D. Nowadays, it’s not as if a Ph.D in mathematics means that you have to be an academician, which is a common misconception. Industries such as finance and information technology also have avenues for mathematicians.
Or you can be like Charlie Eppes in NUMB3RS.
So you can also be very glamorous. It definitely is a good career, but only if you genuinely enjoy it. Otherwise it can get very frustrating. You have to be careful not to confuse aptitude with interest because the two are very different things. Aptitude is always relative, and doesn’t necessarily remain constant – interest does. If you are genuinely interested in math, then chances are you’ll stick with it, and you will do well.
