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, ...

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 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 ...

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 ...

On Thursday, Google DeepMind announced that AI systems called AlphaProof and AlphaGeometry 2 reportedly solved four out of six problems from this year’s International Mathematical Olympiad (IMO), ...

After cracking an unsolvable mathematics problem last year, AI is back to tackle geometry. Developed by Google DeepMind, a new algorithm, AlphaGeometry, can crush problems from past International ...

Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance ...

An AI system developed by Google DeepMind, Google’s leading AI research lab, appears to have surpassed the average gold medalist in solving geometry problems in an international mathematics ...