An AI system developed by Google DeepMind, Google's premiere AI research lab, has surpassed the average gold medalist in ...

Google’s AlphaGeometry2 AI reaches the level of gold-medal students in the International Mathematical Olympiad ...

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in two-dimensional (2D) and three-dimensional (3D) settings. The rules of Euclidean ...

Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal.

THE philosopher Kant declared that Euclidean geometry was inherent in the human mind and expressed the truth about space. We now recognize that non-Euclidean geometry is equally valid as an ...

The ring of light surrounding the centre of the galaxy NGC 6505, captured by ESA’s Euclid telescope, is a stunning example of an Einstein ring. NGC 6505 is acting as a gravitational lens ...