Grandparent was talking specifically about Caltech. I don’t see how anyone can go to Caltech without knowing calculus, possibly even linear algebra. This school has tougher admission standards than MIT.

I was rejected by MIT, Hahvahd, and Stanford :-)

The calculus requirement was not listed as an admissions requirement. The other students were astonished that I didn't simply assume it was required.

Fortunately, physics prof Ricardo Gomez invited me to his office for some impromptu calculus tutoring, which saved my bacon. I owe him.

Frankly, a major thing that Caltech admissions looked for is a very strong interest in engineering and science. It's gotta be in your bones, or you ain't going to thrive there. With their limited resources (it's small) it's just not pragmatic to accept those with a more casual interest. And really, why would you want to go there if you weren't? After all, 9 out of 10 classes were 90% math, math, more math, and math.

There should exist places designed to provide maximum learning opportunity to those who come in already knowing a fair bit. It is a loss to society if such places start disappearing, or perhaps a sign of such loss if the reason is less demand.

This does not in any way imply that those should be the only kind of places to exist.

This does not in any way imply that there's anything wrong with people who started to recently to have relevant background.