Picking Teams With the Math of Imbalance

Combinatorial discrepancy theory is a branch of mathematics concerned with balance. If you’re making two teams — sports, trivia, you name it — how can you make sure that they’re perfectly balanced and fair, skill-wise? You start with vectors. On this episode of The Quanta Podcast, host Samir Patel speaks with award-winning science journalist and regular contributor Max Levy on an “absurd,” “holy grail” conjecture, and the major breakthrough made in fall 2025 by two theoretical computer scientists. This topic was covered in a recent story for Quanta Magazine. Each week on The Quanta Podcast, Quanta Magazine editor in chief Samir Patel and Senior Editor Hannah Waters speak with the people behind the award-winning publication to navigate through some of the most important and mind-expanding questions in science and math.