The Red Queen race or parable describes how, “Species have to ‘run’ or evolve in order to stay in the same place, or else go extinct as the Red Queen said to Alice in Lewis Carroll’s Through the Looking-Glass in her explanation of the nature of Looking-Glass Land: Now, here, you see, it takes all the running you can do, to keep in the same place.'”
A similar social phenomenon has been observed with elite college admissions and high-stakes math competitions.
As contest prep/practice becomes more common and math competition performance more important for getting into high-ranked schools and good jobs, then everyone is made worse off except for the winners. Even the winners are arguably worse-off by having to study more, but this is negated by higher salaries, prestige, and other benefits of good math placings.
The winner-take-all nature of math competitions tracks the rest of American society overall. Those who place well reap outsized social and economic benefits, whereas a poor/mediocre placing confers nothing.
This means more practice, harder problems, and more work. But because math ability at the highest levels of competition has a genetic or otherwise innate component, everyone is still at the same place than had they not studied at all. Studying/prep has the effect of shifting everyone’s score higher, yet everyone is still in the same relative place.
The AOPS (Art of Problem Solving) books are often recommended for math competition practice. But if everyone’s rich Bay Area or NYC kid is using these books, then everyone is still in the same place. The kid who is innately talented or smarter will still score higher. These books are a waste of time unless you enjoy learning math for the sake of learning. Otherwise, you will lose to the kids who are also reading those books but are smarter.
The rising importance of math competitions is part of the broader trend towards the bifurcation of American society. On one extreme, college students are underqualified due to dumbing-down. And on other extreme, more qualified than ever, such as for elite schools. This means lots of extra curriculars, good placings on aforementioned math competitions, AP exams, top SAT scores, and 4.0+ GPAs.
So the best option is to find some way to have math competitions in which the effect of studying is minimized, or that no one studies. This is how it used to be decades ago. But given how high the stakes have become in recent years–especially post-’08 crisis (and even more so post-Covid), when tech and quant compensation really surged and admission rates plunged for top schools–I don’t see this happening.