math.SG math.SG

Water can be ice, liquid, or steam. Physicists call these states phases. In theory, each phase has its own measure — a way to describe how likely it is. But not every measure you can imagine occurs in nature. Some phases are real, while others are just mathematical illusions. Scientists have found a simple criterion that separates reality from mirage.

An intricate carpet with a pattern that is invisible to the eye but strictly defined. Every thread in it follows rules that can be written as equations. In mathematics, the role of such a carpet is played by Calabi-Yau spaces — multidimensional shapes important for string theory. The curvature of spacetime in them resembles folds in fabric.