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 ...

New research has found ChatGPT-5.2 can generate original mathematical proofs, introducing “vibe-proving” as a new AI ...

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 ...

The new framework replaces approximations, accurately modeling current crowding and spreading resistance in 2D materials to ...

After some serious number crunching, a researcher says that he has come up with a mathematical model for a viable time machine: a Traversable Acausal Retrograde Domain in Space-time (TARDIS). He ...