Inspired by and drawn from just a fragment of the dynamic people in my life “Getting to Know A…” is my way of introducing you to a variety of professionals who are excelling in their various fields. Some follow a traditional path after finding their inspiration in unexpected places. Others carved out their own non-traditional careers. What they have in common is they are all incredibly passionate about what they do. My hope is something in these inspires you, the readers, as well.
Since the subjects of these pieces live far and wide, I had initially sent each of them a personalized questionnaire with the intention of drafting them into articles. Their answers were just so dang good there was no way I wanted to change them. I decided, with permission to leave them as is.
Tell me first what you do – the title and what you actually do.
The amount of teaching a Mathematician does varies somewhat depending on where they are, how much they want to teach, and the nature of their position. I personally teach 3 half-semester courses a year starting this fall. I get a lot of choice in what I teach, and once I get assigned a course I have to spend time preparing the material itself, and then ~3 hours a week lecturing. The amount of prep time for a course can be as little as 15 minutes a lecture for subjects I’m very familiar with (these include linear algebra and calculus, that most people take some form of in college) or as much as 6-8 hours a lecture, if the material is new and challenging to present.
Most of what I do, however, is research. This means I spend most days thinking about math problems and reading papers, trying to get ideas and find patterns, making guesses about patters that should exist and then proving that they actually happen. I spend a lot of time trying to prove my guesses, and this consists usually of me lazing around the couch for several hours trying to get an idea, and then maybe doing some (usually very simple, but too hard to do in my head) calculations to try to work out some simple cases. But very little writing actually occurs, the majority of my time is spent in silence or chatting with a friend/colleague.
What drew you to pursuing a career as a Mathematician?
I’ve wanted to do math for as long as I can remember. At the age of 3 or 4 I started doing math with my grandfather, and I always really enjoyed it. The first problem I remember hearing was this little gem: “You have a broken toaster. It can fit 2 pieces of bread, but only toasts them on 1 side. You have 3 pieces of bread that you want to toast on both sides. How many times do you have to use the toaster?” I immediately said 4, “Do the first two twice to get both sides, and then do the third one twice.” But in fact 3 suffices if one is more clever! I found this fact amazing and the solution so beautiful that I never looked back. Well, maybe a little at some low points in grad school.
Did you go to school for this?
I went to public school until grade 7, and then I went to a private school (University of Toronto Schools). In High school I was spending a lot of time doing math contests, and concentrated on that much more than the rest of my schoolwork. I did very well on them, which was encouraging, and I enjoyed them much more than the rest of my schoolwork, though I made a lot of good friends in school. At my mom’s suggestion, I left school at the end of grade 10 without a high school diploma and went to the University of Toronto to pursue an undergraduate degree in Mathematics.
Did you go to college? What did you go to college for?
I studied exclusively math in college, with the exception of a few electives I was required to take, an economics course and a philosophy course. I really wanted to focus exclusively on math. I worked really hard at college and enjoyed it a lot.
How did this help your career?
Well, I guess in the obvious way. I learned a lot of mathematics and how to think about it. Then I went to Princeton for Graduate school, and now here I am!
Who are your biggest mentors/influences in your career?
My grandfather was a mentor until I was about 12, at which point I started to know more than he did (he’s primarily a physicist). Also, Larry Rice worked with me in high school, and he was incredibly motivating and also fun to solve problems with. His encouragement helped a lot.
By far my biggest mentor was Peter Sarnak, my advisor in graduate school. Grad school was (for me and for many others) a time of real struggle. Before that it was all “learn this subject, do some problems sets, learn some more, you’re doing great!” but in Grad school there’s a need to produce original work, which I had never done or even considered really until that point. Peter is extraordinarily supportive, enthusiastic, and energetic. Every time I met with him I left feeling like a million bucks. This is pretty rare in an advisor and I really needed it.
On a more technical level a lot of my interests in mathematics were taken in one form or another from Peter. He was (and still is) very good at picking problems for me to work on and the directions he pushed me in have proven fruitful.
From a personal perspective, how does how does your work inform your life outside the office?
A great deal. Almost all of my friends are mathematicians, as well as my girlfriend. This is for two reasons. One is at Princeton the math grad students were very close and there was a really strong sense of community there. The other is that math is often on my mind, and a huge part of my life. It’s nice to be able to share that with the people I talk to. Even if we’re in different fields and can’t really speak about work directly, the culture persists which adds a level of familiarity and comfort to our interaction.
Not all my friends are mathematicians, and I realize by saying this I’m propagating a stereotype, so I just wanna mention that in my experience most mathematicians are NOT like me, and have most of their friends outside of academia. Me, though, I’m one minded I guess
What’s a pretty cool thing you get to do regularly that someone who ISN’T a Mathematician would get to do?
I get to travel basically anywhere for free if I agree to give a talk there, as grants pay for flights. It can get exhausting, but is also really fun.
What is a personal career highlight so far?
My highlights are results that I’ve proven and papers I’ve published. The best moments are when inspiration strikes and a problem I’ve been thinking about for a few years finally gets solved in my head. For instance, in my 2nd year I head a talk where the speaker was trying to prove some result but couldn’t quite get there. I was intrigued and had a vague idea, but then promptly forgot about it. Two years later, I was reading some other paper which I realized relates back to that talk, and a hot shower later it all came together. The euphoria lasts a few days, and that’s really as good as it gets for me.
Does your life outside the office inform your work? If so, how?
Well, the amount of work I do depends heavily on my mood, so in that sense yes. It’s hard to work when I’m annoyed, lethargic, or lonely, so I keep that in check. On the other hand, I’ve done some of my best work while depressed because math is a great escape – it’s all in your mind.
How is your life outside your office different from your work?
When not working I entertain myself as best I can. I like music and comedy so I go to a lot of shows, I play squash, etc.. Keep in mind that I’m interpreting the phrase “your office” to mean “work life”. I’m rarely ever at the office, I mostly work in my bed or on my couch.
Creatively and personally, what are the major benefits of your career?
My work is the most stimulating thing in my life by a mile, and most of the time it’s what I want to be doing. It’s all about thinking about beautiful patterns, reformulating them in my head, gaining clarity, trying out ideas, and talking them over with my friends. Another fantastic drawback is that I mostly get to set my own schedule, so I frequently wake up at 3PM If I feel like it, and I work whenever I want. Theres a lot of freedom you can’t really find in many places, both in terms of scheduling and what it is I choose to work on, which is entirely up to me. Also, I don’t have a boss, which I gather from talking to people who do have them is a plus.
What are the drawbacks, if any?
I’m really largely on my own, so if things aren’t going well and I’m in a creative slump it can be very demoralizing. Math is a field where success comes in the form of a good idea every 3-6 months, and the time in between can be difficult, and theres never a guarantee that the good idea is coming soon! It can be stressful, and it doesn’t help that the field is very competitive. I have to say though, that for me, I can’t think of any other job that even comes close to the one I have.
What advice would you give someone considering this as a career?
Studying math in undergrad opens so many doors that I can’t see much of a downside. People going to Grad school should really stop and think, however, if this is the life they want. There’s very little reward in math besides the work itself, so one should meditate on whether solving puzzles and finding patterns all day sounds like how you wanna spend the rest of your life. The hours may seem small at first but with the time spent doing research and writing up papers (which is all done on your own time!) it can be quite daunting.
Having said that, if you love math and wanna do it all day, I’d say the biggest problem most aspiring mathematicians face is the lack of problem-solving ability. When learning a subject, try to prove the theorems yourself. Ask questions, do exercises, and make sure you really grapple with the material instead of just quietly assimilating it. You’ll eventually need to solve problems for a living, so its best to get started now! A good source of advice can be found in Terry Tao’s blog.