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 ...

The telescope conjecture gave mathematicians a handle on ways to map one sphere to another. Now that it has been disproved, the universe of shapes has exploded. In early June, buzz built as ...

Experienced mathematicians warn up-and-comers to stay away from the Collatz conjecture. It’s a siren song, they say: Fall under its trance and you may never do meaningful work again. The Collatz ...

An artificial intelligence has disproved five mathematical conjectures – unproven theorems – despite not being equipped with any information about the problems. Adam Zsolt Wagner at Tel Aviv ...