In a talk he delivered at Google's Zeitgeist conference, Malcolm Gladwell gave this advice to rising high school seniors: "If you want to get a science and math degree, don't go to Harvard."
Why? Because "persistence in science and math is not simply a function of your cognitive ability; it's a function of your relative standing in your class." Regardless of an individual institution's selectivity or prestige, Gladwell says, the students majoring in STEM fields are in the top of their class while those as the bottom of the academic heap earn STEM degrees relatively rarely.
As a rule of thumb, your odds of successfully getting a math degree fall by two percentage points for every ten point increase in the average SAT score of your peers.
Watch the talk.