The caustic mathematician Roger Casals Gutiérrez saw on his kitchen wall in 2023. Caustics are a type of singularity, a mathematical phenomenon that occurs when an surface goes through a transition.

The original version of this story appeared in Quanta Magazine. Two blind spots torture physicists: the birth of the universe and the center of a black hole. The former may feel like a moment in time ...

A painless, non-invasive brain stimulation technique can significantly improve how young adults learn math, my colleagues and I found in a recent study. In a paper in PLOS Biology, we describe how ...