Noncommutative geometry offers a radical reformulation of traditional geometrical concepts by replacing the classical notion of a manifold with a noncommutative algebra of coordinates. This approach ...

The original version of this story appeared in Quanta Magazine. In the fall of 2022, a Princeton University graduate student named Carolina Figueiredo stumbled onto a massive coincidence. She ...

In October 2015, a young mathematician named Clemens Sämann was flying home to Austria from a conference in Turin, Italy, when he had a chance encounter. He found himself seated beside Michael ...

The geometry of space, where physical laws unfold, may also hold answers to some of the deepest questions in fundamental physics. The very structure of spacetime might underlie every interaction in ...