One of the oldest and simplest problems in geometry has caught mathematicians off guard—and not for the first time. Since antiquity, artists and geometers have wondered how shapes can tile the entire ...

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 ...

In September 2019, news broke regarding progress on this 82-year-old question, thanks to prolific mathematician Terence Tao. And while the story of Tao’s breakthrough is promising, the problem isn’t ...

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 ...

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 ...

The original version of this story appeared in Quanta Magazine. In 1917, the Japanese mathematician Sōichi Kakeya posed what at first seemed like nothing more than a fun exercise in geometry. Lay an ...

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 ...

The International Mathematical Olympiad (IMO) is a prestigious competition featuring talented high school students from around the world, in which competitors solve complicated mathematical problems.

For decades, temporal and inversion symmetry were taught as static geometric concepts, but 2026 has shattered that view with real-world demonstrations of symmetry in motion. From the first ...