<p>Hi. I'm a Caltech student, a math major, and am also on the admissions committee. I've thought about this precise question a lot and advised a lot of people about it, so I'll try to offer what help I can.</p>
<p>Especially if your interests are math/CS, I don't think there's a enough of a difficulty disparity between Caltech and MIT (or insert Ivy here) to justify choosing based on that. Quite a few people have said that already, but maybe I can provide another reason from firsthand experience: namely that the disparity depends on who you are. Biologists at Caltech tend to find the math core a little overwhelming sometimes (this is the sense in which Caltech is "harder" -- the minimal core requirements for EVERYONE are harder). At MIT, you don't have to take as many math courses if you don't want to. But mathematicians (especially on the theoretical track) would basically be taking the same things in both places to fulfill the math major requirements. And while I've argued before that Caltech might still be in some ways somewhat more demanding, there are also compensating factors. You can do your hard sets in January in the California sun, which is, for some, less hard/sad than doing them in the bleak Boston winter. I like snow, by the way, so this doesn't apply to me :-).</p>
<p>As far as social life goes, I can't do better on this question than advising you to come to prefrosh weekend and see for yourself. Some people immediately fall in love with how personal and tight-knit the houses are, even taking into account the "nerdiness" of their inhabitants. Others would prefer to feel like part of a much larger university, even if some of its parts are more impersonal (obviously there are very close-knit groups at MIT, too, though).</p>
<p>A pretty typical reason that people don't like it here after visiting, if they don't, especially those who are of the more quiet and reserved type, is how crazy Caltech students act sometimes to let off steam. We have silly dinner rituals, absurd pranks, etc. Some would definitely like a more usual and "respectable" environment, in a more typical dorm. When I came for prefrosh weekend, I expected to find people to be very bookish and withdrawn, but was a little jarred by how much the opposite were true -- they were a little <em>too</em> much fun for me, at least then. It sounds like your son might enjoy the non-academic side though. To be honest, I personally have never heard a person decide not to come to Caltech because it's too reserved or quiet or bookish upon inspection. (No promises that it's never happened.) As I said, whether you enjoy it or not, whether you would be active in your house, depends on your personality.</p>
<p>That's true of almost all the other "social" issues. Some people adore a given situation, others hate it, and there's no way to predict what will happen to you. The only way to guage whether Caltech "fits" well with you non-academically is to come and immerse yourself in it for a while. And you're certainly planning to do that, which is great.</p>
<p>But I will give you one piece of honest advice. You should go with your gut. Don't let the money make the decision if you visit here and your heart's just not in it. You'll be thinking "what if" forever. On the other hand, don't let a fear of the work pull you back if you come here and enjoy it. Otherwise, you might realize later that your worries were unjustified and you'll be sad about not making the choice that would have made you happy.</p>
<p>One more thing. If you come, as a scholarship recipient, you'll be part of a small, academically distinguished group. Whether that's fair or not, it carries weight with professors, etc., so Axlines have tended to have access to their pick of top labs to start research experiences in. Since MIT doesn't offer merit scholarships as far as I know, you won't have that initial leg up, though obviously you can earn it by being extraordinary.</p>
<p>More generally, especially in theoretical work (and even more especially in math), Caltech students have unmatched access to undergraduate research. It's rare and hard to be able to do a non-experimental project at other places, even the very top places. Labs have deficits of undergraduate workers, not theorists, since at this age almost nobody is capable of being more useful as a theorist than as a coder / experimentalist. It's just the truth. Getting a theoretical project is essentially a gift, an opportunity to play mathematician for a summer on the university's tab. I've done so and it's great fun. Caltech, being more overfunded per student than other places, can afford to give out more such gifts than other places.</p>
<p>So, as I mentioned, my advice is be aware of the actual distinctions between the places, then come and try to have an open-minded look and listen to your gut. Then do what feels right.</p>
<p>(Oh, by the way. Caltech/MIT is a dilemma. {MIT or Caltech} /WashU is not. My unqualified advice is to remove WashU from consideration, since it doesn't hold a candle in essentially and respect to either of the other schools in the areas your son is interested in.)</p>