I think how math is taught at the early stages (rote, focus on finding a simple answer which is already clearly known, focus on mechanical arithmetic and calcul

I think how math is taught at the early stages (rote, focus on finding a simple answer which is already clearly known, focus on mechanical arithmetic and calculation) filters out many of those who would enjoy the more advanced stuff. There are some clear filters (basic arithmetic probably is 80-90 IQ, algebra 95, probability and statistics 100, calculus 100-105, differential equations, analysis, and linear algebra maybe 110, algebraic topology a bit higher), but those are really lower bounds for raw intelligence required. I’d rather have basic arithmetic treated as a separate subject, and then some form of “problem solving math” which can incorporate concepts from calculus, algebra, and especially probability and statistics. The best three math classes I’ve ever taken were a combination of physics and calculus in a small group taught by two teachers who worked closely together, a weird MIT ESG seminar with a postdoc and 3 students covering the broad expanse of everything post 18.03, and number theory and crypto at the same time (a grad class I snuck into without prereqs and spent the first month essentially 30h/wk catching up on those.). What was consistent with two of these was having a clear problem to solve; with the third it was just high interactivity with an expert for an extended period. Providing students with exposure to the problem space addressed by a certain form of math, then letting them discover some of the truths and techniques on their own in the same way they were originally discovered, is going to take more time and far more skilled instructors than just repeating facts, but will be more engaging and produce better understanding.