So you want to be a mathematician?

Dedicated to my incoming doctoral students Daniel and Erin.


A few years back, I volunteered for the Ontario Universities Fair and spoke to a high school student who loved mathematics and wanted to study it in university. I told him about our programs and we chatted about math.  He returned a few minutes after our discussion, this time with his mother.

“What good is studying mathematics? I want my son to be a CEO,” she said, arms crossed and brows knit.

Image result for ontario universities fair crowds ryerson
The Ontario Universities Fair is held each Fall in Toronto. Thousands of high school students and their parents chat with university professors, staff, and students about post-secondary program options.

I pointed out how studying math can make you a great problem solver in any career. The analytic skills honed studying advanced mathematics would even benefit you as a CEO. Math is also fun and is universal in the sciences and engineering.

I don’t think she was impressed with my answer, as I never saw the student again.

If the title of this blog appeals to you, then it is likely that you have ignored the advice of parents, loved ones, and friends to pursue a career as a mathematician. Good for you. The world needs more bright, young minds to join our profession (especially women and POC, of course, but all are welcome). To become a mathematician, you have to dream big.

Pursuing a career in mathematics is not for everyone, however. I give advice to students entering a doctorate about the slim chances of becoming a working mathematician. A Conference Board of Canada report tells us that about 18% of graduating doctoral students become full-time university professors. I don’t have stats specific to math, but that number jives with what I’ve seen.

Would be mathematicians may burn out as a post-doc. Others may try, but fail to land a permanent academic position. Others may get a tenure-track position only to realize that academia is not for them. The good news is, however, there are many, many people who have accomplished their goal of becoming a professional mathematician. Most are in academia, but many mathematicians work in industry, government positions, or work freelance as consultants or authors.

What we do

Mathematicians teach. We teach courses to either graduates or undergraduates, or both. Teaching loads typically vary from three to five or more one-term courses in an academic year.  Often, we teach courses that are outside our main interests owing to demands in our Department and institution. For example, I use Calculus in my research, but I have never used trigonometric substitution in my papers. I have taught that particular topic, however, many times. It’s all good as I find Calculus relaxing!

Image result for professor teaching math auditorium
Mathematicians often teach large classes such as first-year Calculus. You might look like this to the hundreds of students attending your lectures.

Mathematicians make new math. People outside academics may not understand this part. “Hasn’t all math been discovered?” is a question I’ve heard before. If we were talking to sentient quantum computers while orbiting Jupiter in our Tardis, the answer would be “yes”. The truth is we’ve just really scratched the surface of what mathematics is about. Mathematicians prove new results often with only pen and paper, but can use computers or other aids.

Mathematicians supervise graduate students. This is a hybrid of service, teaching, and research that supports the next generation of mathematicians. I’ve done so at the Masters and doctoral level. The challenge with supervising is giving direction but also letting students realize their passion and ask their own questions.

The road is long

My undergraduate degree was in Honours Mathematics and that took four years. I did a two-year Masters after that and then completed a four-year doctorate. I had a limited term teaching position for a year and then landed a tenure-track position after that. It took me eleven years to realize my dream of becoming a mathematician working in an academic department.  You should expect similar timelines if you share that goal.

Image result for long road
The inspiring cliché of the long road.

Almost twenty years since I graduated with my doctorate, I’m still teaching, supervising, and publishing and I wouldn’t trade it for anything.

People won’t get you

Let’s face it: most people either don’t like mathematics or don’t understand why it is important. It’s hard to convince someone to the contrary—believe me when I say I have tried, often in this blog with limited success.

That’s why it’s imperative that you love mathematics. You have to love mathematics to endure your Jedi training and become a master. You also have to love it when you are mid-career and thinking about your next research topic or how to inspire your graduate students in their thesis. If you don’t love it, then don’t pursue it.

You will work as a mathematician not for the recognition or glory. If you get those, then more power to you. But the majority of mathematicians toil in relative isolation. Why? Because we love math.

Why being a mathematician is the best job in the universe

After all this, it might seem like an awful bother to become a mathematician. The years of study lead to challenges teaching and navigating administrative tasks and research culture. And many people won’t understand or appreciate what you do. Most people don’t even know there are mathematicians out there creating new math.

However, your hard work will pay off if you stick with it.

Mathematicians have the envious job of creating new patterns from nothingness. We get to see the nuts and bolts of how the universe of patterns works. Make that: the multiverse of every possible universe of patterns. When you make a discovery, there is nothing like it. When you prove a theorem it as if you’ve bypassed all the noise of everyday life and peeked into a locked treasure box.

Mathematicians don’t need big expensive particle colliders to do our work, or labs full of petri dishes and machines that go bing. All we need is a pen and paper to make new math and teach others about its riches.

The mathematical world is out there waiting for you to explore it. Go dive in.

Anthony Bonato



One thought on “So you want to be a mathematician?

  1. Great advice and insight in this inspiring article. As a future mathematician, I must say that all of what you said here was not in the slightest a turn off from mathematics. It is my dream to achieve what you have achieved.


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