The mythical centaur (half human, half horse) has become a metaphor for human-AI collaboration.  In this talk, I explore what centaur science looks like at the intersection of artificial intelligence and fundamental physics.  I share adventures from both directions of this exchange: teaching machines to "think like a physicist" by incorporating physics principles into machine learning frameworks, and teaching physicists to "think like a machine" to maximize discovery opportunities in both experimental and theoretical physics.