In this talk I will discuss a general framework for unifying multiple problems in scientific machine learning (ML), in particular equation learning, PDE solvers, and operator learning. I will discuss how equation learning sits at the center of scientific ML and how it relates to classic ideas in control, inverse problems, and data assimilation. Then I will present an efficient kernel method that can learn equations and their solution maps implicitly. I will present some interesting numerical benchmarks as well as theoretical support in the form of convergence rates.