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 ...

In Chasing (a) Conjecture, Khare has done more than narrate a personal triumph. He has rendered the abstract palpably human, ...

When the mathematicians Jeff Kahn and Gil Kalai first posed their “expectation threshold” conjecture in 2006, they didn’t believe it themselves. Their claim — a broad assertion about mathematical ...

After German mathematician Gerd Faltings proved the Mordell conjecture in 1983, he was awarded the Fields Medal, often described as the “Nobel Prize of Mathematics.” The conjecture describes the set ...