Combinatorial geometry and density problems form a dynamic field at the intersection of discrete mathematics and geometric analysis. Research in this area explores the intricate arrangements of points ...

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 ...

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 ...

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 ...