Why Math is a Sport

Sunday, March 23, 2014 · 4 min read

I am not sure whether math has become more cool or less cool over the past few years; and I'm definitely not sure which one I prefer. Math used to be something people did because they loved math. Now… not so much.

The Rubik's started off as a cool puzzling toy that kids would fiddle with. The process of playing with this mechanism, finding patterns, and getting elated when you solve it was invaluable to your development as a person. But then people realized you could get better at it. Fast forward a few years, and people can solve them in 10 seconds flat. There are algorithms that people memorize, they oil their cubes regularly, and they even do hand excercises to warm up. It's crazy. How is being the #1 Cube-solver in the world going to help you in life?

The same thing's happening to math. A small set of people is emerging who are stretching competition math to its limit, and that's going to be a problem very soon.

Football for nerds.

People do competition math for the sake of doing competition math. Which is bad. As a high schooler into competition math, I routinely hear conversations like You got 98%? Sheesh, you're slipping… and …so I forgot to divide by two. I'm so dumb, I should move down a grade. I suppose that's as close as I will ever get to trash talk, but it's still rather depressing.

But being good at math isn't about acing tests or remembering to divide by two. Math is about taking ideas and exploring; and competition math has slowly shadowed that out. Now being good at math is like being good at solving problems.

To be good at competition math, you train all year long. You know the tricks that you should know—there are entire companies focused on collecting problem solving tips and tricks. You slowly learn heaps of techniques and formulae and theorems for all sorts of situations, and eventually you build up a mental index of all the major patterns of problems. You learn which situations merit Stewart's Theorem and when it is fruitful to try to apply the Pigeonhole Principle (answer: if the problem contains the phrase Prove that there exists…).

There are important seasons when the big tests come around: the AMC, AIME, and USAMO. You know the scoring systems for all these perfectly, and you think a lot about what your optimal strategy should be: how many questions you need to get right to make it to the next level, how many you should attempt, and how long you should spend on each problem. You need to do practice tests each day to keep yourself in shape. During the real test, you're nervous. You obsess over your answers, making sure you haven't made a calculation mistake anywhere. You spend far too long filling in the bubbles on the answer sheet. And when the test is over, the serious folk congregate in a circle and compare answers. If you've made a silly mistake somewhere, people look at you disapprovingly.

If you replace math with football and test with game, this describes a high-school athlete's life rather well. Weren't geeks supposed to hate sports?

What's wrong.

I mean, there's even the term 'mathlete'. Mathletes are their own unique culture, who take pride in doing math. You see them doing masochistic things like pi recitation competitions. But that's not what math is! Math is about taking an idea and thinking about it and deducing something surprising from it. Math is about spending days thinking about a problem, not just 30 minutes.

My favorite math competition is the USAMTS (USA Math Talent Search). It offers you five problems and 30 days to think about them and submit proofs for your solutions. USAMTS teaches you to think about problems persistently, to try fresh approaches, to research on a subject, and finally explain and justify your answer formally. Compare that to the AMC, which is 75 minutes for 25 multiple-choice problems, the first 18 of which are elementary and the last 7 of which are nontrivial. The AMC doesn't test your math skills, it tests your test-taking skills. And that is definitely bad.

Which is not to say that people who do well on these tests are not good at math. Many of them certainly are brilliant kids, and it is fascinating to watch them approach a problem. But I would imagine a substantial portion of AMC high-scorers consist of children who aren't sure they like math at all. They do it as a sport, perhaps because their parents want them to, or perhaps because all their friends are doing it. And the ulterior motivation often isn't even the competition itself. It's college. It's the fact that 'USAMO qualifier' looks stellar on an application that drives a large chunk of math students.

Why it's wrong.

In itself, this isn't horrible. We've invented a game which people compete in. Why do I care?

Because it's a disaster for anyone who can't bring themselves to be part of the game. For the math lovers who look at their mathlete friends 3 grades ahead and get discouraged. Your math class becomes like a badge, and mathletes try to take the hardest class they can possibly survive. And that hurts the rest of us, because the line between being good at math and being good at competition math fades, and even if you love math you aren't one of them.

Competition math is a wonderful thing if you do it for the right reasons. If you do it because you love math, patterns, and puzzles, then it's perfect for you. It gives you an opportunity to see where you stand in the world. You get dozens of beautiful problems every day. You meet smart people. It is probably one of the most fitting hobbies you could have.

If you do it because it will help your college application, because your friends are doing it, or for any reason that isn't for the love of math, then rethink it. It becomes an obsession. You worry about your scores far more than is reasonable. It bothers you, and it puts you off math for the sake of math. And that's tragic.

◊ ◊ ◊