Rodrigo

If you want to major in math at an elite university, but all the knowledge you show up with is high school math and AP Calculus, and you’re not a genius, then you’re probably going to get your ass handed to you. High school math – even the “honors” track, even getting a 5 on the AP Calculus BC exam – often doesn’t accurately depict the level of background knowledge (especially proof-writing ability) that is assumed in serious math-major courses. It is not uncommon for elite university admits who are serious about majoring in math to graduate high school -- having already taken linear algebra & multivariable calculus and -- having already received plenty of exposure to proofs including inklings of real analysis (e.g., epsilon-delta limit proofs) and abstract algebra (e.g., structure of the additive & multiplicative groups of integers). These students make up such a tiny slice of the overall student population that you’re unlikely to encounter them as classmates in high school, but they do exist, and they’re going to be concentrated in the math-major classes at elite universities. Much of the content – or, at least, the overall way of thinking about it – will be familiar to them, and as a result, they'll have a far outsized ability to keep up with fast-paced, poorly-scaffolded instruction, even if they're not geniuses. If you’re not able to do the same, then the class is not going to slow down just for you. Not to mention, you’re going to feel dumb, which is going to severely impact your motivation.

Justin Skycak

@justinskycak

8 months ago

Last year I had a conversation with someone who majored in physics at UChicago. He initially started in math & thought he was prepared having taken AP Calculus BC, but he got smacked in the face by the level of abstraction and proof-writing ability that was assumed. He couldn't keep up with his classmates who had already done proofs while taking even MORE advanced courses in high school. So he switched to physics where proofs were less frequent & the playing field felt more level in terms of prior knowledge that classmates had coming in. He would have liked to study math if he had more time to catch up, or if he knew earlier how far behind he was – but he did great in his high school math classes & was recognized as one of the "smart kids," so he never suspected he was actually behind the curve. Zooming out, this case study is representative of a general phenomenon that can sneak up on you when you’re at, say, the 99th percentile of a skill. At first, you’re exceptional enough that you receive praise from virtually everyone, and you may never go head-to-head with someone who can beat you. That is, until you join some specialized program where everyone is at the 99.9th percentile – where, suddenly, you’re the worst one there. And here’s the real kicker: if it’s a time-sensitive program, you may be so far behind that it’s infeasible to catch up. If you knew the caliber of these people earlier, you could have spent time working harder to join their ranks in the 99.9th percentile… but that moment has passed, and now the door is closed on this opportunity.

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