Equiangular lines are lines in space that pass through a single point, and whose pairwise angles are all equal. Mathematicians are not limited to three dimensions, however. "In high dimensions, things really get interesting, and the possibilities can seem limitless," says Yufei Zhao, assistant professor of mathematics. But they aren't limitless, according to Zhao and his team of MIT mathematicians, who sought to solve this problem on the geometry of lines in high-dimensional space. It's a problem that researchers have been puzzling over for at least 70 years. Their breakthrough determines the maximum possible number of lines that can be placed so that the lines are pairwise separated by the same given angle.