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Should I Go To Graduate School … For Math?

2 Replies

Scott Baldridge asks

As I wrote in my reply, there are a lot of reasons why one wouldn’t apply to grad school for Mathematics.

I don’t like teaching

Somehow, there is a pervasive cultural belief that a math degree is not “practical”. That getting a degree (undergraduate or graduate) in Mathematics somehow relegates one to teaching jobs [insulting and dismissive of the teaching profession on the one hand (teaching isn’t practical?) and general obliviousness to what industry demands are for people with math degrees]. If you don’t get a PhD in Math, but either a Bachelor’s or Master’s, then your only prospects are to either teach math (usually high school) or to skulk around in the netherworld of the adjuncts, bouncing from one university to another teaching 101 math courses.

This is wrong. I have hired probably a dozen or so Math majors in the gaming / gambling industry. My first job was in commercial real estate finance in a newly formed structured finance group where the active requirement was that the candidate have a strong background in mathematics with a degree in one of the Engineering disciplines (Electrical, Chemical, Mechanical, Civil), or in Physics, Chemistry, Biology, or Mathematics. The hiring managers’ rationale was that “finance majors know the textbook finance, but can’t do anything beyond that. The hard science and math majors know math and we can teach them the finance.”

I have a BS in Electrical Engineering and an MS and PhD in Mathematics. When I was applying to colleges as a high school senior, it was a prevailing myth that if I wanted to secure good income-earning employment then I should pursue Engineering and not Mathematics. My high school had a very strong math program with math professors who fought to no avail against such propaganda. Then, while in college, some math professors encouraged me to pursue a graduate degree in mathematics, but I balked. Many of my friends and classmates couldn’t see the wisdom in going to graduate school for Mathematics for exactly the reason of “what the hell are you going to do with a math degree”? The only non-academic job prospect that we knew of was to become an actuary, which was unappealing.

Course sequence is screwed up

But let’s say that I were open-minded as an undergraduate about pursuing an advanced degree in Mathematics. What does my coursework look like? It looks like Abstract Algebra, Measure Theory, Topology, Number Theory, etc. All of this screams, to the unknowing student, more academia, which may not be the aspirations of many 18-21 year olds.

What’s missing or not well-advertised, perhaps, are the “applied” courses — Monte Carlo Methods, Applied Numerical PDEs, stuff like this. The problem is that if we want to really get into Monte Carlo Methods, for example, it’s probably best to have a solid theoretical foundation. Otherwise, we’ll get what we are witnessing in primary and secondary curriculum — a misguided approach to “practical” math. Monte Carlo Methods, conceptually, are easy to understand. But, there’s a theoretical framework that we probably oughtn’t ignore. That’s not to say that there isn’t a better ordering of topics, but somewhere in all this, a few courses in Probability Theory and Statistics are necessary.

To compound these woes, it’s likely the case that many math professors at certain universities have never worked outside of academia. They are research faculty. That is their job. That is their passion. They teach graduate courses and are busy publishing papers and overseeing PhD students. Other math professors may be professors during the day. But by night, they’re probably consulting for industry. And so, the prospects of full-time, non-academic employment look opaque at best, and almost surely bleak as it would appear that non-academic work is not enough to warrant a full-time position, but rather as an extension of an academic career.

This is a PR problem with most Math Departments. Some universities address this with different programs for non-PhD seeking graduate students and those pursuing a PhD. The latter focusing more heavily on theoretical coursework. This can help to alleviate some of the concerns about employment prospects. However, there exists a subtle bias in academic organization.

Bachelor’s degrees in the Engineering fields imply, at least at the outset, a career as an engineer; degrees in the hard sciences imply a non-academic career in that discipline — you can work for a pharmaceutical, an engineering firm, the aerospace industry, etc. But there aren’t prominent, large employers of math degrees or a “math industry”, per se. Sure we have software companies that specialize in mathematical software (Maple, Matlab, Wolfram Alpha, etc), but students’ exposure to those technologies are in an academic setting. So it would seem that the math degree just comes full circle back to academia.

This, too, is all wrong. Math departments, for their part, often aggressively promote the non-academic options that exist to math majors that are beyond actuarial work. For whatever reason, that message runs into a sound dampening field outside of the Math Department.

Intimidation

Some students are intimidated — not necessarily intimidated by Math, but by the culture. As sad as it is, I’ve heard enough stories about females and ex-athletes being given a very hard time about their math ability. This is an ugly side of math education that doesn’t get talked about much. But this is a reason. Many graduate school programs are overwhelmingly male dominated and hence skewed in a variety of ways in the favor of males; this can be a deterrent. The intimidation, however, comes from a handful of professors. Usually, the intimidation isn’t overt like, “you can’t do math”, but more of the tone “maybe math education would be better for you” — simultaneously calling the student’s ability into question and creating a discipline “hierarchy”. It takes just one professor to push a student out. If you are a student, keep this in mind. I’m not female, so I can’t know first hand what the experiences are, but I am certain that this type of intimidation does occur.

A similar thing happens with ex-athletes. These stories I know first-hand. The ex-athletes are viewed, by some, as “dumb jocks” and thus, their math work is put under greater scrutiny than the (stereo-) “typical” student. Nitpicking of syntax, proofs. Slightly harsher grading.

If you do find yourself being put down or otherwise intimidated, work past it. Ignore that professor. Seek out other professors who are encouraging. Talk to me, if you want. There are always going to be people who try to put you down. Ignore them and barrel forward. Come to your own conclusion if you can’t do it or don’t want to it.

There are other interests

I’ve done my fair share of classroom soliciting. When I see a student who shows strong aptitude for mathematics, I encourage them to pursue mathematics more fully. Some consider it. Others dismiss it for the above reasons. And still others, while they recognize that they have some talent, are more interested in what they are pursuing and view mathematics as a part of their training. One of my students wanted to pursue Psychology and she understood that it would be good to have a good background in Statistics. But she was uninterested in spending more time on topics that weren’t directly related to Psychology. This is reasonable.

So what kind of work can I do with a Math degree?

I’ve hired BS, MS, and PhD holders in Mathematics. I work in the gaming and gambling field. There is work in those fields and requires people who have an understanding of Probability and Statistics. It also helps that they know how to program. Paper-and-pencil math, while good, isn’t how math is done in a lot of industry work. Math is done through programming.

There are LOTS of jobs out there for math degree holders. However, a key requirement today is that students need to know how to program if they want to be employable. And by “know how to program”, I mean “write software”, not the hack job programming done to solve the problem at hand. The latter is a typical approach of scientists who are not versed in software development [I’ve seen a lot of ugly code]. This leads to unscalable and untransferable code and is not optimal in an industry setting — though the practice does still exist, but more as a resignation to the lack of ability than an acceptance of the practice.

Major League Baseball is hiring Data Scientists. Facebook, IBM, Microsoft employ several baseball teams’ worth of math degree holders of all levels. I work as a mathematical consultant.

But the undergraduate math major doesn’t want to go further

I’ve had several students who had no desire to pursue Mathematics beyond the undergraduate curriculum. Some students’ reasons revolved, somewhat contrary to this entire article, on getting employment and earning a real salary. They understood that they did have job prospects and that was their aim. Graduate school doesn’t have to be an immediate succession to a completion of an undergraduate degree. In fact, it may be better if delayed, provided that the student (now working) can manage this logistically, financially. But some students have financial matters to address immediately and graduate school is an unaffordable luxury — the stipend often does not compare to a full-time salary at a company. This is reasonable.

Still other students have simply been burnt out. They were good at math in high school, but somehow, some way, their vision of a math major and the coursework that ensued didn’t match reality. And so, after a few years into the degree, it becomes cost prohibitive to switch majors. As such, they limp through and finish the degree.

In any case, I’m sure there are other reasons for why otherwise good students of mathematics don’t pursue further math education, but I think this covers the majority of cases. I don’t think there is much that a professor can say or do other than to show the many realities that can exist and to dispel cultural myth about the limited realities.

For more reading, see Should I Get A PhD … In Math?