Here’s a simple-sounding problem: Imagine a circular fence that encloses one acre of grass. If you tie a goat to the inside of the fence, how long a rope do you need to allow the animal access to ...

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 ...

Google's second generation of its AI mathematics system combines a language model with a symbolic engine to solve complex geometry problems better than International Mathematical Olympiad (IMO) gold ...

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 ...

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 ...

Sam Raskin has wrapped his head around a math problem so complex it took five academic studies — and more than 900 pages — to solve. The results are a sweeping, game-changing math proof that was ...

The Greek philosopher Plato wrote about Socrates challenging a student with the "doubling the square" problem in about 385 B.C.E. When asked to double the area of a square, the student doubled the ...

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us? A mathematician may have just proved the impossible possible. For 30 years, ...

Mathematicians have long pondered the reach of a grazing goat tied to a fence, only finding approximate answers until now. Here’s a simple-sounding problem: Imagine a circular fence that encloses one ...