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 ...

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 ...

An artificial-intelligence (AI) tool can rigorously prove whether geometric facts — statements about two-dimensional shapes such as triangles or polygons — are true, just as well as competitors in the ...

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 ...

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.

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 ...

This video shows how to solve algebra problems using geometry, offering a visual approach that makes abstract equations easier to understand. By translating algebra into shapes and spatial ...