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 ...

Imagine the tap of a card that bought you a cup of coffee this morning also let a hacker halfway across the world access your bank account and buy themselves whatever they liked. Now imagine it wasn’t ...