After 80 years of fruitless struggle by human mathematicians, a major geometry conjecture has at last been solved—via a straightforward query to a chatbot. “No previous AI-generated proof has come ...

A long-standing problem in discrete geometry involving how many pairs of points can be exactly one unit apart has been addressed using an artificial intelligence system developed by OpenAI, according ...

OpenAI said one of its internal models had made a breakthrough with a challenge first posed by Hungarian mathematician Paul Erdős in 1946. Experts say this result could indicate that AI is capable of ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...