By most measures, Will Manidis is like many other American high school students. He plays lacrosse for Westtown, his Quaker boarding school outside Philadelphia. He’s captain of Westtown’s robotics team, which has deepened his interest in math and computer science. Last fall, in the heat of the election, he helped organize debate nights.

Such activities are great material for college applications. When he enrolled at Westtown, Manidis figured he’d wind up at Harvard or Princeton, maybe go on to earn a Ph.D. and do cutting-edge research.