We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. In this paper, we propose using the ...

Google DeepMind's AlphaGeometry AI system impresses at the International Mathematical Olympiad, outperforming human gold medallists in geometry problems.

“I imagine it won’t be long before computers are getting full marks on the IMO,” says Kevin Buzzard, a mathematician at Imperial College London. Solving problems in Euclidean geometry is one ...

An AI system developed by Google DeepMind, Google’s leading AI research lab, appears to have surpassed the average gold medalist in solving geometry problems in an international mathematics ...

Solving problems in Euclidean geometry is one of four topics covered by IMO problems — the others cover the branches of number theory, algebra and combinatorics.

A flat universe has Euclidean geometry, and the simplest shape it can adopt is that of a sheet. There are also other, more complex shapes that a flat universe could have, such as a "3-torus." ...

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in ...

Exploring the ‘wonderful world’ of symplectic geometry to solve problems in mechanics Wolf Prize laureate Yakov Eliashberg delivers the new TNQ Distinguished Lecture in Mathematics ...

Detecting targets in dynamically changing clutter environments has always been challenging for radar techniques. The innovative matrix information geometry-based (MIG) detector, which equips with ...

Finally, they only require small training samples. Consequently, Riemannian geometry-based methods are a promising group of approaches for brain signal decoding (Congedo et al., 2013). However, ...