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Using ideas borrowed from graph theory, two mathematicians have shown that extremely complex surfaces are easy to traverse.

Art by Karen Lin. On a snowy February evening, thirty undergraduates gather inside a brightly lit classroom on the first floor of Leet Oliver Memorial Hall. At the front of the room is Hee Oh, the Abraham Robinson Professor of Mathematics at Yale, drawing crisp white circles on the board with a brand-new stick of Hagoromo chalk. By the time she turns around, she has traced out three perfect circles, each touching two others at a single point. Oh studies Apollonian circle packings, which are created by filling the space between three mutually tangent circles with successively smaller tangent c...