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Some folks in Silicon Valley and elsewhere say a conventional education can't possibly give kids with outsize talents what they need. Others, like Vivek Wadhwa, a fellow at Stanford Law School who teaches and advises startup companies, say dropping out to pursue a dream is like "buying a lottery ticket — that's how good your odds are here. More likely than not, you will become unemployed. For every success, there are 100,000 failures."

"I loved math. I loved algebra. I really loved geometry, [but] I hit the wall at pre-cal," said Rocca. "That's the problem," said Whitney, "because you were only given one road to go through mathematics. You got the impression that once you hit the wall, that's it. There's nothing more for you. In fact, math is this extremely, very beautiful landscape. And we're showing people just one road cut right through the center of it." Whitney says our math curriculum is designed for rocket scientists. Literally! Fifty years ago America was in a space race against the Soviet Union, and beefing up on our math program was seen as a winning solution.

At Exeter, I learned that what you said was more important than what you knew. I learned that the louder you are, the better you are. I learned that there's only one way to learn anything, and that's to talk in circles until someone takes notice.