Modern machine learning has had an outsized impact on many scientific fields, and particle physics is no exception. What is special about particle physics, though, is the vast amount of theoretical knowledge that we already have about many problems in the field, as well as the daunting deluge of data coming from flagship experiments like the Large Hadron Collider (LHC). In this talk, I will explain how one can teach a machine to "think like a physicist" by embedding theoretical principles into advanced machine learning architectures. At the same time, I will advocate that physicists must learn how to "think like a machine" to maximize the physics reach of the LHC. These joint developments are leading to a new kind of "centaur science" that, analogously to the mythical centaur, draws half from particle physics and half from machine learning.