By the way, does anyone know what it takes to get into maths at an elite institution? Is it based purely on merit? Or do you, as some have suggested on this forum, have to fluff your CV with extracurricular activities like volunteering at the homeless cat shelter and playing polo?
It will surely depend on which elite institution, but I can say for sure that neither Oxford nor Cambridge could care less about anything but academic merit, because they're both on record saying this clearly. I sort of doubt that someone who had IMO medals and/or papers in reputable journals to their name, and didn't have two heads, would in practice get turned down even at US elite institutions - but it would be good to hear from someone who knows.
I came across the following, which makes me pessimistic. This guy was twice a USAMO winner, meaning he was in the top 12 meaning he could compete to get into the USA IMO team, but he didn't make the final 6. He was rejected from both Princeton and Harvard. (He was accepted by MIT.)
http://blog.tanyakhovanova.com/?p=150http://www.maa.org/news/051209usamo.htmlIt's not clear why, but it's clear the selecting is not being done by the mathematicians, but instead by bureaucrats (admissions officers).
There's a financial issue here. Places like Princeton and Harvard (supposedly) select on merit, but charge fees based on financial means, as determined by the FAFSA formula. So a family earning say $75k/yr would pay $10k/yr instead of the sticker price of $60k/yr paid by people earning >$200k/yr. MIT (like most private and public universities) doesn't do this, so it is much more expensive.
Paradoxically the financially feasible options for us are Princeton/Harvard type places that "meet full financial need" or else the local state university (or delayed retirement). This forces us to set our sights that high, even though we really don't know that that's realistic.
