Evan O'Dorney leaps from his seat and snatches the chalk from his teacher's hand. "I think it goes like this," the eighth-grader exclaims. He has come up with a formula for the number of ways to divide a set of objects into three subsets, and he explains it to the group.

"What do you think?" the teacher asks, turning to the group of teenagers. "Are you persuaded?"

"I am!" one student calls out. Others begin nodding their heads in agreement.