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 ...

Fermat’s last theorem is just one of many examples of innocent-looking problems that can long stymie even the most astute mathematicians. It took about 350 years to prove Fermat’s scribbled conjecture ...

Two young mathematicians are illuminating a frontier in the study of rational solutions to polynomial equations: the cubics. According to one version of the story, Hippasus made this discovery at sea, ...