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

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 ...

Mathematicians use “large cardinal axioms” to describe these layers, defining specific types of infinite numbers with unique and powerful properties. At the base of the ladder is the infinity ...

The general idea is that there are some truths that can never formally be proved, as long as these truths are within a formal system, such as basic arithmetic or Euclidean geometry. In a way ...