The two-dimensional incompressible Euler equations is a PDE describing the evolution of an ideal incompressible fluid. In 1963, Yudovich proved global existence and uniqueness in the class of solutions with bounded vorticity. Since then, considerable effort has been devoted to understanding solutions with lower regularity. In this talk, we present an initiative to understand an AI-generated proof of a breakthrough result: non-uniqueness of physically realizable solutions to the two-dimensional Euler equations with vorticity in L^p, for any fixed finite p. Here, physical realizability means that the solutions arise as vanishing-viscosity limits of solutions to the two-dimensional Navier–Stokes equations.