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 ...

Overview Math AI tools use advanced algorithms to instantly recognize equations, generate accurate solutions, and explain each step clearly for better understan ...

The following is an excerpt from The Gravity of Math: How Geometry Rules the Universe by Steve Nadis and Shing-Tung Yau. Copyright 2024. Available from Basic Books ...

Arithmetic geometry, at its core, investigates the rich interplay between number theory and geometry. In the context of unitary groups—algebraic groups defined as the symmetries of Hermitian forms—the ...

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 ...

Noncommutative geometry offers a radical reformulation of traditional geometrical concepts by replacing the classical notion of a manifold with a noncommutative algebra of coordinates. This approach ...