I always loved Math (still do). I started in applied Electrical Engineering (telecommunications), then moved to Applied Math (for BS) with Statistics focus and chose Industrial Engineer for MS with Economic Decision Analysis.
I did not like pure Operations Reseach, theoretical Math, or programming (that one is a necessary evil).
I worked as Industrial Engineer, Data Analyst, Statistician, Operations Research Analyst etc.
A word of caution. If you have an Engineering degree you can move anywhere. If you have a science degree, some schools would not take you for graduate Engineering degree. I had to jump thorough a lot of hoops to get accepted to school of Engineering for MS with BS in Math.
In terms of admission, I believe schools of Engineering are hardest. I would also try to choose a college where he would have an opportunity to switch majors and stay away from very restrictive schools with limited enrollment.
The issue is getting into the school that he might want to stay in. If he really, really wants engineering, then you’ve got to check how easy it is to transfer from arts and sciences into engineering. School-specific. But at this point, all he’s doing is putting down a major for application purposes. At most schools, it is possible to switch after he’s begun.
Pure math is about studying the structure of different kinds of mathematical objects (sets, real numbers, integers, functions, vectors, etc.) and their properties and relationships, irrespective of whether the results will ever be used. Each area of pure math starts with a minimal set of “indisputable facts” called axioms, and from there a bunch of theorems are proven, often in the form of one theorem building on top of other known theorems, like a tree growing from a root (the axioms).
Some say pure math is a quest of knowledge in its purest form, and this romanticized notion and underlying challenges can be attractive (addictive?) to a very small number of very smart people, driving them to work tirelessly to come up with new results. It is often a lonely pursuit, because it’s hard to explain to families and friends what they are doing, and why it’s exciting. It’s like a drug they can’t pass around. When they are at the forefront of their areas, even their colleagues can have difficulties fully grasping every detail of their work.
The general public rarely ever hear about pure mathematicians, except perhaps when they succeeded in proving a longstanding conjecture such as Fermat’s Last Theorem (Andrew Weil) or a result that made a dent into the elusive Twin Prime conjecture (Yitang Zhang). Or when they were child prodigies who became extremely productive pure mathematicians (Terence Tao). Movies like A Beautiful Mind (John Nash, which some may argue isn’t pure math) help, but not by much. They are often underappreciated by society, and most are okay with that.
At the undergraduate level, students pursuing a track in pure math is trained to acquire the background and knowledge to do the aforementioned things. Given the lack of demand for pure mathematicians and given their rigorous training in abstract thinking, a lot of graduates are forced/able to transition into related careers such as becoming applied mathematicians, engineers, computer scientists, and quant traders. A tiny fraction of graduates go on to pursue a Ph.D. in pure math followed by one or more stints as a postdoc, keeping their hopes of becoming a pure math professor at a research university alive.
The degree requirements (particularly the upper level course work) for the majors and (upper level) course offerings within the departments may be more useful in helping him determine which colleges’ math and math-adjacent departments are more likely to have majors and courses that appeal to him.
Any major he feels like he’s interested in should be ok to put in the application right now. I know several students who changed their major between applying and matriculating.
Most Math majors I have seen basically just have a set of required courses and then some advanced electives maybe with a distributional requirement (like you have to take at least 1-2 advanced courses in each of a few areas).
Undergraduate math is interesting in that you can more or less fill up four years just continuing to study what are considered core areas.
But for people who are really serious about doing things like Math PhDs, they will likely start going beyond that in one or more subfields even as an undergrad. Some Math departments may have a lot of such options as undergrad courses, but some Math people like that start taking grad classes as undergrads–could be at that college, could be an affiliated one.
But if you are not interested in the PhD route, you can maybe do different things. Maybe you take some math-heavy sciences. Maybe you do the prereqs for a health profession. Maybe you do businessy stuff like econ or maybe finance. Maybe you just take whatever else you like and start gearing up for law school. And so on.
My point is I think in many cases, the core of a Math major is a fine start, and then in your last 2-3 years you can chart a path with additional courses that are a little more tailored to whatever you want to do next.
I agree with entering math as a major of interest. But in case he’s not aware of what it is, actuarial science is also a very math-heavy field, should he come across it when looking at lists of majors. From my (limited) knowledge it’s common in the insurance industry for calculating the risk of something happening, what the costs would be, and how to price something out (say, what the chances were of someone needing to use insurance, what the costs would be if they used it, what the premiums should be priced at including possible inflation effects or stock market gains/losses, etc).
But…
However, actuarial science is rather adjacent to statistics, finance, and economics, so if he is interested in those areas, perhaps he may want to reconsider whether actuary is a possible career path.
Actuarial science majors are not required to go into actuary work, but (when offered) can be convenient checklists of courses to take for those who do want to go into actuary work.
Interesting comment. In my industry and in my role - I’ve helped set vehicle pricing, determine monthly incentives, set lease terms and the like. A host of people are involved.
We’ve got MBAs and my focus is marketing (not a quant person), geology, stats, urban studies, management, and all sorts of majors involved.
That’s why I think no matter what OP ultimately chooses to major in, the being good quantitatively and analytically is always a positive and because careers are so long and unknown, the skill sets will probably be put to good use no matter the career they are in and no matter what they’ve studied.
Apparently, I’m not reading carefully enough today. Thanks for bringing that to my attention!
I was suggesting it too, but than read in the very first post - no Actuarial…
My college junior son had thought he wanted to major in physics or even applied math when he was applying to college. But, when he was selected to participate in a guided reading program on knot theory his first year, he became hooked on theoretical/pure math which he never knew existed as a high school student. He has powered through the math program finishing the math major requirements by the end of his sophomore year and is now taking graduate math courses and working one on one with a professor on an advanced theoretical math topic they both share an interest in.
His plan right now is to go for the PhD and look to be a professor, but I am also trying to get him to look at Quantum Computing which kind of links math with his other majors of physics and computer science. From IBM’s website - “ Quantum computing is a rapidly-emerging technology that harnesses the laws of quantum mechanics to solve problems too complex for classical computers.”
Check out Tufts University–it has a Quantitative Economics major. My D was one of those lopsided kids–nearly perfect SAT math score and less than perfect in other areas. She went to Tufts, majored in quantitative economics (in the Econ Department), and got a job offer shortly after she graduated.
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