In July of 2001, 473 high schoolers from around the globe came to Fairfax, Va., for the 42nd International Mathematical Olympiad. Steve Olson followed the six extraordinarily gifted teens who represented the U.S. that year, and emerged with an up-close look at a world little seen and, more to the point, little understood by outsiders. Don't mistake this contest as Spellbound with numbers. The problem solving at Olympiads doesn't involve the perfunctory wrestling of huge figures. Instead, it's more akin to gymnastics, with routines that begin, ''Consider nine points in space, no four of which are coplanar...'' and require a level of creative and analytical insight that would challenge most college professors. Olson, a math-team coach himself, has painted an engaging, accessible portrait of some beautiful (and startlingly young) minds.