Traditional power system computations are based on either the Newtonian or Keplerian paradigm. The Newtonian paradigm struggles to manage the complexity and computational demands of large-scale systems in real time. The Keplerian paradigm faces challenges related to interpretability and generalization. This paper introduces the concept of Power System Intelligent Computing (PSIC), which integrates artificial intelligence to combine the strengths of both paradigms. A research framework is proposed to integrate the Newtonian and Keplerian paradigms for key applications, including power flow analysis, time-domain simulation, and optimal power flow computation. PSIC provides a novel perspective on addressing computational challenges in power systems while systematically outlining important future research directions.