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

This profound development is explained by analogy with non-Euclidean geometry In 1963 it was proved that a celebrated mathematical hypothesis put forward by Georg Cantor could not be proved.