I am a baby here and just graduated from an elite private school as an engineer a few years ago myself. My husband just got his PhD in Physics a couple of years ago. So I have some thoughts. :)
The fact is, hardly any students are as advanced in coursework as he is, because you basically have to be homeschooled to get there. He's in an extremely small group of high school students who know so much math. There is simply not a school he could attend where there would be a large group of eighteen-year-olds who know multivariate calculus! So just get rid of that idea. He will either be retaking similar courses at a higher level with same-age peers or will be studying math with senior undergrads and beginning grad students. He may still be thrilled to find at a selective school that his peers are just as smart as he is, and he will enjoy making intellectual friendships. But they won't be in his math classes unless he's redoing classes.
Most American universities are narrowing the number of transfer credits possible, not increasing them. They don't want students coming in with years of credits and graduating in two years. Cuts into the bottom line...
Grad schools also will often not allow you to finish quickly because you already took most of the classes. So at some point in his career he will have to retake classes OR branch out and take more breadth of classes. There just aren't enough math classes to fill six years of higher education starting where he is. If he's going to do that anyway eventually, might as well do it in early undergrad, where the peer interaction is so valuable.
Is he just as advanced in Science? One possibility since he already knows so much of the undergrad math curriculum is to study either physics or computer engineering/programming/analysis type major, and fill in the rest of the math major too. If he wants to solve practical problems using math, math academia is probably not what he's looking for. He will probably end up somewhere in big computational supercomputer math stuff, because that's where the innovative problem-solving stuff is today. And as long as he's not advanced in computational methods already, he can start off on-level with peers. Even if he ends up in math grad school after the double-major, he won't regret the computing background.
Look for a school with high average SAT ACT scores. That will give him a whole school full of very smart people with different specialties.
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