<p>In an exhibition of near-insanity (my own–it’s ok, I recognize it), I would like to respond to Pizzagirl, post #1260.</p>
<p>Also, I add the qualifier that I am not talking about the Ivies, for the most part, but rather about colleges with somewhat specialized missions.</p>
<p>The Ivies balance so many considerations in admitting classes that I think it’s fair to say that no one should expect to get in there–even though the experiences of students in earlier classes at the same HS may point to a reasonable probability of admission, which is higher than 5%.</p>
<p>When it comes to specialized institutions, though, I don’t buy Pizzagirl’s “special snowflake” argument. Suppose the HS student in question is a cellist, and suppose that a professional cellist who has a reasonable level of experience with young musicians in international competitions is assessing the level of promise shown by the student–at 16 or 17, not in the crib! If the professional cellist thinks the student “ought” to be admitted to Julliard, I would be inclined to give some credence to that judgment.</p>
<p>Now take mathematics. There are just not that many students in the country who are prepared to enroll in Math 55 at Harvard as freshmen, or in the corresponding course at MIT, Caltech, Princeton, and a few other schools, despite the improvements in math instruction at the high end. Perhaps there are 300 per year, coming from regions with a high concentration of interested students (i.e. regions with Math Circles) + those who are unusually talented auto-didacts (or near-auto-didacts). If Harvard caps the number of mathematicians in its entering class at 15 or 30, and thereby excludes someone who is ready for Math 55 in order to balance out the interests of the entering class, I don’t have any problem with that. </p>
<p>On the other hand, MIT is going to have a very heavy concentration of math/science/engineering types to begin with. That’s its nature–it’s an Institute of Technology. In this pool, I don’t think one is making a “special snowflake” argument, if a professional mathematician/scientist/engineer with some experience of very talented young students in that field thinks that the HS student “ought” to be admitted to MIT. </p>
<p>I’d guess that the exceptionally talented cellist would virtually always be admitted to Julliard, but that the exceptionally talented STEM student might or might not be admitted to MIT, as things now stand. </p>
<p>Let me add: I would not have been ready for Math 55. Over a long period, it is quite possible to catch up, if one has the basic capability and desire needed, and puts in a lot of effort. Four years (as an undergrad) might not be long enough, though.</p>
<p>So suppose a person is at the level of preparedness for Math 55, and is rejected by HYPSM. The next “logical” option would be Caltech, probably. But it has a particular atmosphere and ethos, and it really doesn’t suit every talented student. </p>
<p>Let me jump over universities such as Northwestern, Chicago, Duke, maybe Berkeley, and similar places for a moment. I am a strong advocate for large, public research universities, and the opportunities there for strong students. At a reasonably good state flagship (i.e., not Berkeley), a student who is ready for Harvard’s Math 55 would probably have preparation for an often non-existent course that lies somewhere between the undergraduate majors’ analysis course and the beginning graduate course in analysis. </p>
<p>I knew a student of this type (no relation) just a few years ago, who tried out the grad course. However, this meant that the undergrad, who was dealing with all of the adjustments of freshman year, and quite possibly learning how to do laundry for the first time, was in the same class with grad students. And often, an undergrad is taking 15 credits, while the grad students are taking 6 credits. This does not make for a good experience sometimes/often–I don’t really know which–the sample size is too small.</p>
<p>The top LAC’s might or might not be suitable for the person, depending on the specific one. At some, the student would exhaust all reasonable course choices other than independent study within 2 years.</p>
<p>So, now to return to Northwestern, Chicago, Duke, and schools in that category. I think that the student could find the right level of challenge there, with the right course choices–but they would probably be a little less challenging than Math 55, really. And the fact that these other universities could work out extremely well for the student would not negate my belief that MIT “ought” to have admitted the student.</p>