A fascinating aspect of physics is the appearance of unexpected violent change in seemingly smooth contexts. Catastrophe theory explores such phenomenons, albeit from a mathematical standpoint. Through the study of critical points of a certain function with a physical meaning, one can derive scenarios where a continuous perturbation leads to sudden changes.
René Thom has come up with a theorem known as Thom's classification theorem which allows us, in dimensions up to five, to classify these critical points. This allows for qualitative predictions concerning the behaviour of the function at or around these points.