Counterexample to Grad’s Conjecture (Ideal MHD and Incompressible Euler Flow)

arxiv link: arxiv.org/abs/2609.26742 This conjecture is probably not well known in mathematics broadly. In plasma physics, we often seek to find equilibrium solutions to the ideal MHD equations (the Grad-Shrafranov equation). Harold Grad conjectured that if a solution possesses nested flux surfaces that it must possess a strong symmetry such as axial symmetries. This question is of interest in the stellarator community, who aim to construct fusion devices where the 3D equilibrium configuration does not possess strong symmetry. So, it was feared that nice stellarator equilibria don’t actually exist. This paper is notable in that families of solutions use only elementary functions. The solutions were found using GPT-6 Astra.