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 ...

Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall. Summer Haag and Clyde ...

As he was brushing his teeth on the morning of July 17, 2014, Thomas Royen, a little-known retired German statistician, suddenly lit upon the proof of a famous conjecture at the intersection of ...