<p>You are completely missing the point, though. Math 55 is just one pathway into high-level math. It’s not the only pathway, or even necessarily the best one. Relatively few colleges offer anything like it, and not always because they wouldn’t have anyone to place into it. Princeton’s math faculty is not outshone by Harvard’s, and Princeton deliberately does not offer a stunt class like Math 55. Nor, I believe, does MIT. Chicago has a similar course, but unlike Harvard it fills half of the class with second-year students who performed really well in Honors Calculus their first year (and Honors Calculus there, if I understand things correctly, is equivalent to Math 23 at Harvard). And I know of at least one student who placed into Chicago’s version of Math 55 as a first-year and, after talking about it with the faculty, decided with their full support to give it a pass and to take other advanced math courses.</p>
<p>Harvard does NOT have some kind of a monopoly on high-level math education, and even at Harvard there are more ways than one to skin a cat. Have you read what the Harvard math department says about Math 25?:</p>
<p>
</p>
<p>Doesn’t that sound like you? Do you think they are lying when they say you can catch up? </p>
<p>In fact, maybe you can’t completely catch up to the Math 55 guys (and they are overwhelmingly guys), at least while you are an undergraduate. But do you really think the 10-15 people who complete Math 55 each year grab all of the desirable math grad school slots in the world? Some of them drop out of college and start companies (like You-Know-Who). Some of them make it through Math 55, but barely, hardly covered with glory (I know one of those). Some of them burn out on math and get interested in other things. Some, like many of their classmates, go for the big bucks in financial industry jobs (I know one of those, too). And the handful that are left? By the time you and they are 25, barely into your adult careers, no one will be able to tell you apart based on what you know, and whether any of you have the stuff for a brilliant math career will just be beginning to be shown.</p>
<p>Look at the people who have faculty positions in math departments you respect. How many took Math 55, or anything like it, when they were 18? A few, sure, but certainly not all of them. Certainly not most of them. Some of them may well have started college in the equivalent of Math 1a, or not even that. Where people start in college reflects their past, not their potential.</p>
<p>And, anyway, if you love math and want to learn more of it, and to do it well, what other choices do you have? Go to a university with good mathematicians. Take as much math as you can. Get to know the faculty, and follow the advice of the ones you respect and trust. Work like a dog. What you achieve, ultimately, will likely be everything you are capable of achieving, and which freshman math course you took at which university will have absolutely nothing to do with anything.</p>