Careers

Mathematical Research

One career option in mathematics is research, which can be pure or applied. If you’re going to do this, you will probably be an academic, which means you will also spend your time teaching and applying for grants.¹ For the most part, this research just involves paper, pen, and a wastebasket full of failed proof attempts—no expensive laboratories needed.

Research of this kind requires a great deal of obstinacy. Often mathematicians will spend five to ten years on a single problem. And, as it works in mathematics, either you prove it or you don’t—so you may end up with nothing after all that time. The results may be beautiful, but you need a strong commitment to the much less glamorous process if you are going to make this career choice.

(One other tidbit of information about mathematical research: Unlike most other academic writing, the mathematics literature is written almost exclusively in the first person plural, even for works with a single author. If I say that “we will now solve Equation 2.6”, I mean that you, the reader, and I, the author, are partaking in this mathematical activity together. This inclusion of the reader is a really unique writing convention, that, as far as I am aware, is not present in any other discipline.)

Physics

Another career option in academia is the highly related field of theoretical physics. In fact, at some universities such as Cambridge, theoretical physics is literally part of the mathematics department.² As Bertrand Russell said: “Physics is mathematical not because we know so much about the physical world, but because we know so little”. No one understands why quantum mechanics works, but we do understand how it works very precisely using our mathematical models. So, for many theoretical physicists, there is surprisingly little “physics” that goes on trying to determine the mechanisms of reality—that knowledge is, at present, beyond our grasp. Instead, much of the work is prediction and mathematical modelling.

One difference of theoretical physics is that, although your process may be similar to that of the purely mathematical researcher, your work describes actual stuff in the universe. Some people don’t require this assurance, and they are happy to study abstract mathematics for its own sake. Others may find theoretical physics more comforting for this reason. In both types of research, the pay in academia is quite respectable at good universities, and of course you get summers off which is a nice perk.

Programming

Technology firms need people who are good at programming, and it happens that there is considerable overlap between programming skills and math skills. Both require a similar type of critical thinking to break a problem down into small steps, a willingness to experiment with a variety of methods to find a result, and the use of numbers and procedures. Both are also very precise: your code—or your proof—either works or it doesn’t. It would be misleading to say that a math degree automatically makes you a good applicant for a programming job. You still need to know how to program—but this is a skill, not a degree. Even computer science majors are not necessarily good programmers, no more than physics majors are necessarily good engineers; the degree mostly teaches you the theory, and you develop the practical skills through experience. As a result, it is very common for math students to learn programming as a hobby, so that when they graduate they are able to pass technical programming interviews (which are known to be quite challenging).

Unlike research, programming is a corporate job. Some tech companies let you work from home and others require you to show up in person. Either way, you will most likely be in an office most of the day. The salary tends to be much higher at “big tech” companies, and often it is higher at US offices than Canadian ones. The technology sector is also known to offer many unusual benefits; for example, Google is known for free food and bikes for employees, and Netflix is known not to track employee vacation days. On the other hand, technology jobs are less stable; companies tend to have mass layoffs every couple of years because they routinely hire too many people when the market is up.

Finance

Many people think of finance and jump straight to business majors. This is the correct reasoning for many banking jobs, but many finance jobs actually want scientists. In fact, two of the most successful funds of all time were founded by mathematics professors: Ed Thorp’s Princeton Newport Partners and Jim Simons’ Renaissance Technologies. These two men pioneered the idea of the quantitative hedge fund. Thorp devised the Black-Scholes model several years before its namesakes did and made a profit trading mispriced options contracts. Simons recruited scientists from universities and research labs to decipher patterns in the markets and predict short-term price movements.³ What both approaches had in common was the use of mathematics—mostly probability, statistics, and some calculus—to beat the market.

A job as a quantitative trader or analyst pays extremely well, but it usually requires long hours. Getting hired is extremely difficult because the number of applicants completely overwhelms the number of open positions for this very skilled and very specialised job. It is a rare example of a job in industry which requires advanced mathematics on a daily basis.

Conclusion

Of course, there are a great variety of other jobs involving mathematics. Many firms employ data scientists to analyse large volumes of information and look for patterns. Some mathematics students go on to write the actuaries’ exam and work for insurance companies. Others go on to write for The Simpsons. Even in careers that do not require any particular degree, mathematical thinking often proves itself an invaluable asset. While by no means exhaustive, I believe that this list provides an excellent synopsis of mathematical careers related to my current interests.