For Most Students, Competition Math is a Waste of Time

by Justin Skycak on

Competition math problems generally don't require students to learn new fields of math. Rather, the difficulty comes from students needing to find clever tricks and insights to arrive at solutions using the mathematical tools that they have already learned. But if you look at the kinds of math that most quantitative professionals use on a daily basis, competition math tricks don't show up anywhere. But what does show up everywhere is university-level math subjects.

When a middle or high school teacher has a bright math student, and the teacher directs them towards competition math, it’s not because that’s the best option for the student. Rather, it’s the best option for the teacher. It gives the student something to do while creating minimal additional work for the teacher.

Competition math problems generally don’t require students to learn new fields of math. Rather, the difficulty comes from students needing to find clever tricks and insights to arrive at solutions using the mathematical tools that they have already learned.

A student can wrestle with a competition problem for long periods of time, and all the teacher needs to do is give a hint once in a while and check the student’s work once they claim to have solved the problem.

But if you look at the kinds of math that most quantitative professionals (like rocket scientists and AI developers) use on a daily basis, those competition math tricks don’t show up anywhere. But what does show up everywhere is university-level math subjects like multivariable calculus, linear algebra, differential equations, and (calculus-based) probability and statistics.

So, given that most students who enjoy math are going to end up applying math in some other field (as opposed to becoming mathematicians) – wouldn’t it be more efficient for them to get a broad view of math as early as possible so that they can sooner apply it to projects in their field(s) of interest?

The countering view is that “students should go ‘deep’ with the math that they’ve already learned – they’ll learn the other math subjects when they’re ready.” But, in practice, this is not true.

If students “learn the other math subjects when they’re ready,” then when is that? Is it when they complete a quantitative major during college? No – even most math majors only learn a tiny slice of all the math that’s out there.

(If you know someone who majored in a quantitative field, ask them if they took algebraic geometry, convex optimization, and control theory. Chances are, they haven’t taken any. On rare occasions, they may have taken one. These are just three out of hundreds of university-level math subjects.)

Do students “learn the other math subjects when they’re ready” after college, on the job? No – if you’re trying to solve cutting-edge problems that nobody has solved before, then there is no “known path” that can tell you what additional math you need. And to even realize that a field of math can help you solve your problem, you generally need to have learned a substantial amount of that field in the first place.

In practice, the only way for students to “learn the other math subjects when they’re ready” is to learn as much math as possible during school.