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 ...

Mathematicians have finally solved a geometry problem that has puzzled the field for decades. By wiggling a needle around while spinning it, you can minimize the amount of space it moves through, ...

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.

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 ...

Its performance matches the smartest high school mathematicians and is much stronger than the previous state-of-the-art system. Google DeepMind has created an AI system that can solve complex geometry ...

A year ago, AlphaGeometry, an AI problem solver created by Google DeepMind, surprised the world by performing at the level of silver medallists in the International Mathematical Olympiad (IMO), a ...

Mathematicians have finally solved a geometry problem that has puzzled the field for decades. The question was proposed by Japanese mathematician Sōichi Kakeya in 1917. It sounds simple: How can you ...