DeepMind's AI has made remarkable progress in mathematical reasoning within a span of just one year.  After earning a silver ...

One of the biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last ...

Greek geometry wasn’t just math—it was an attempt to decode the universe. Its logic still powers rockets, bridges, and every GPS route today.

Intelligence—natural or artificial—may be a matter of geometric structure, not temporal sequence, challenging how we understand thought itself.

A 125-page proof posted to arXiv may represent a huge breakthrough in geometric measure theory. This problem has implications in fields like encryption, computer science, and number theory.

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

An AI system developed by Google DeepMind, Google's premiere AI research lab, has surpassed the average gold medalist in solving geometry problems in an international mathematics competition.

Hodge operators and groups of isometries of diagonalizable symmetric bilinear forms in characteristic two. arXiv:2208.11326 Kramer, Linus. Locally compact groups. Manuscript in preparation. Kramer, ...

Unlike Euclidean geometry where space is continuous, any shape in finite geometry must fit on a limited set of points on a discrete grid. These and other characteristics provide axioms mathematicians ...

Following the principles of representation theory, mathematicians take abstract shapes that exist in Euclidean geometry – some of them extremely complex – and transform them into arrays of numbers.

We have in mind the deductive method and the axiomatic foundation of geometry on the one hand, and geometric transformations and the group-theoretic foundation of geometry on the other. These ideas ...