We’re not talking about only taking Calc I though, these kids are literally acing Multivariable Calculus at their State Universities before they could drive. I actually have seen a kid like that who basically had the highest grade in my college’s Diff Eq and Physics III course that semester. My friend was like “Man, that kid is still in high school and I see his mother drop him off. I don’t think he drives.” I would not be surprised if they were going to one of those high-tier colleges and that was just an extracurricular on their transcript.
That’s just not normal and if so is more along the lines of their parents knowing those subjects very well and teaching it to their kids night after night, which isn’t common and the kid would still have to be smart.
All of that is why I didn’t bother to pretend I was/am anything special in school because these professors have either been in a class with or taught some kids who aced all this shyt when they were 18. They probably are amused when they see some mid-level A-student who thinks their Einstein. While I’m somebody who found this stuff easy (usually constantly finish top 3-5 in my classes without too much effort) and am interested in it, I know I’m not an ultra genius like the people who go to those schools.
Was teaching at a two-year feeder to Berkeley, UCLA, Stanford, and the occasional prestige out-of-state.
Kids start at Calc. I (in California its a, b, c, d. C/D = multivariable calc) and obviously progress through to linear and maybe diff.
Here are some paths I've seen.
Parents throw their kids in Kumon programs at a young age. The kids cry and fight but eventually acquiesce. Eventually gain maturity through the years. The parents who know enough to have their kids in Kumon programs, know enough to mature them for the next decade.
Kids who grew up in a place serious about academics. They come over here and are more mature than peers.
Kids learn proof work in their teens due to exposure.
Kids taking Calc a/b at 14 and c/d at 15. Now they have the maturity to take basic linear and maybe diff.
More importantly, if they've already been exposed to the basic sequence and proofs, they might open Axler's treatment (Linear Done Right) or an advanced calculus book. They can start number theory work and so on.
They run circles around people who are in even AP computational math classes. They have been exposed to way more than even the teachers of such classes.
He/she ran circles around you due to mathematical maturity and exposure to concepts at an earlier age.
Most people are not exposed to abstract concepts until undergrad. They have to learn and process the vernacular, change their model of thinking, and so on while handling the workload.
If some guy has a 2-4 year head start, yea, he looks like a genius because he no longer has to worry about vernacular and nailing down basic concepts.
They're thinking beyond 'em.