Two vectors close vectorA vector quantity has both direction and magnitude (size). are parallel if they have the same (or opposite) directions. Their magnitude can be different. In the image to the ...

Symplectic geometry is a relatively new field with implications for much of modern mathematics. Here’s what it’s all about. In the early 1800s, William Rowan Hamilton discovered a new kind of ...

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 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 ...

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

Researchers say the system not only outperforms American competitors in solving problems, it can tackle an even tougher challenge. — SCMP A Chinese AI system has outperformed its US competitors in ...

Watch out, nerdy high schoolers, AlphaGeometry is coming for your mathematical lunch. Credit...Christian Gralingen Supported by By Siobhan Roberts Reported from Stanford, Calif. For four years, 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 ...

A year ago AlphaGeometry, an artificial-intelligence (AI) problem solver created by Google DeepMind, surprised the world by performing at the level of silver medallists in the International ...