Chudnovsky, 27, yearns to understand the world completely. Why do storm clouds appear before it rains? Why do we catch cold? What was really wrong with her car? Most of the time, she ends up frustrated. So she takes comfort in the abstract realm of mathematics, where all facts derive from provable universal laws. "I have to understand things all the way," she says. And when she says "all the way," she means it. Her single-mindedness helped prove a hypothesis that stumped generations of her predecessors. "Young mathematicians are called promising if they are expected to become at least half as good in 10 years as Maria is now," says Rutgers mathematician Vasek Chvtal.