In science and engineering, it's unusual for innovation to come in one fell swoop. It's more often a painstaking plod through which the extraordinary gradually becomes ordinary. But we may be at an ...

Invariant distances lie at the heart of complex geometry, providing intrinsic measures of separation between points in complex manifolds that remain unchanged under biholomorphic mappings. Chief ...

Whether it’s a 3D printed robot chassis or a stained glass window, looking at a completed object and trying to understand how it was designed and put together can be intimidating. But upon closer ...

A study published in Nature Communications and directed by Professor Carlo Vittorio Cannistraci, Director of the Center for Complex Network Intelligence (CCNI) at the Tsinghua Laboratory of Brain and ...

Complex geometry studies spaces that locally resemble complex coordinate systems and examines their intrinsic curvature and topological properties. Central to this field is Kähler geometry, where a ...

DeepMind said its AlphaGeometry AI model was able to solve complex geometry problems at a level comparable to an Olympiad gold-medalist, showcasing the ability of AI models to use reasoning skills ...

Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...

Researchers at DeepMind, the artificial intelligence research division of Alphabet Inc., have created software that’s able to solve difficult geometry proofs that are often used to test the brightest ...