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 ...

For all of the recent strides we’ve made in the math world—like a supercomputer finally solving the Sum of Three Cubes problem that puzzled mathematicians for 65 years—we’re forever crunching ...

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 ...

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 ...

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 ...

But now, two mathematician friends have used their quarantine time to crack a variation of the age-old geometry problem. They analyzed a set of loopy shapes called smooth, continuous curves to prove ...

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 ...

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 ...

These student-constructed problems foster collaboration, communication, and a sense of ownership over learning.