<p>^^ I don’t go to Caltech either, but have done a relatively good bit of homework on different schools’ math programs. I think while I wouldn’t say that one can beat MIT or Caltech, depending on one’s likes, there are schools easily as good for math. This may not necessarily be true for engineering – there may be fewer such terrific ones. But the main thing is that some Ivy League schools like Harvard and Princeton suddenly are on the the radar when you’re talking about math, and they’re really awesome. </p>
<p>So calling the department the best in the world is more than a little strange way to put it. </p>
<p>Realistically I would say that for a student coming in to major in math, the least of your concern should be whether Caltech will have enough for you to do in math, and rather the focus should be on what kind of school it is, and how it fits you. The comment about a rigorous core is for instance key. </p>
<p>For math, honestly I don’t even think HYPSM is any longer close to a canonical list. Yale for instance is a great school, but my personal view is that there would be schools where there is simply more math going on in the various different subfields. MIT, while with a strong math program, has a student body with plenty of applied interests, as friends of mine have confirmed. UChicago and UMichigan will enter the list for sure. UChicago is quite hardcore from what I hear. But might I add, each of these math programs are very different. There is something more to seeing if a school fits you than just visiting and seeing how you like the general feel – the academics can be structured incredibly differently, and this is mainly what I think shouldn’t be underestimated when making a decision. </p>
<p>One little tidbit. If I take a look at where some of the best mathematicians in the world even got their undergraduate degrees, the list is hugely varied. Whereas somehow in a given subfield, they all tend to have obtained graduate degrees from roughly 3 suspect schools. </p>
<p>I’m not sure how much of this you did and didn’t know, but I think it’s worth saying for anyone considering coming in as a math major.</p>