A new theory proposes that the universe’s fundamental forces and particle properties may arise from the geometry of hidden extra dimensions. These dimensions could twist and evolve over time, forming ...

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 ...

DeepMind, the Google AI R&D lab, believes that the key to more capable AI systems might lie in uncovering new ways to solve challenging geometry problems. To that end, DeepMind today unveiled ...

Tiling a two-dimensional bathroom floor is a straightforward home renovation, but researchers have found that in higher dimensions it could blossom into a baffling mess of nonrepeating chaos. New ...

An AI from Google DeepMind can solve some International Mathematical Olympiad (IMO) questions on geometry almost as well as the best human contestants. How does ChatGPT work and do AI-powered chatbots ...