A poset of math programs

There are a lot of different kinds of math enrichment activities now, ranging from olympiads to math circles to tons of summer programs and so on. I work in the competition sphere, and I used to spend a lot of time worrying about whether I took the right side.

Now that I’m a bit older, I came to the realization that maybe I don’t need to be so intent on comparing my work to others (even though I realize comparing yourself to others is human nature, haha). I eventually told myself: there are lots of people who don’t like olympiad exams; there are also lots of people who do, and it’s just okay for them to co-exist. We don’t need to decide which of the N systems is the best and kill the other N-1, because “best” is so different from person to person anyway.

Instead, we should see the diversity of these activities as a strength: each program brings whatever it can to the table, and we let each student pick whichever one they feel is the best fit for them. Something about free markets being good, y’know? Advanced math education isn’t exactly booming in the United States; it’s small enough I think the biggest leaders are usually both acting in good faith and at least semi-competent. So the quality of the programs seems to me like it should be embedded into a poset rather than a total order. (And improving your program from year N to year N+1 counts as moving up in the poset.)

Richard Rusczyk has a quote I like, where when asked how he’d run US educational policy, he replied:

I typically answer something along the lines of, “I would try to find ways that no one entity or person can run educational policy.” I think education as a whole, like foreign policy and domestic policy for a nation, is far too complex a problem for a single person or single centralized entity to solve. Moreover, the downside of inflicting mistakes on an entire generation are far too large. It’s much better to have the higher variance of allowing localized decisions.

I believe the same thing even in the smaller scope of gifted education.

So I’d like to suggest that everyone in the math enrichment spaces should be treated as teammates. It’s hard to remember this sometimes, especially in the face of serious philosophy disagreements, or when we programs have to compete for the attention of top students (summer is only so long, dates have a tendency to overlap). So that’s one reason I’m writing this post, to remind myself of this. And I’m really happy to see forums like the Summer Mathematics Program Consortium which bring together leaders from different initiatives together.