This paper extends grid-free Monte Carlo methods like walk on spheres and walk on stars to solve time-dependent diffusion problems with initial and boundary conditions, eliminating the need for volumetric meshing and sequential time stepping. The method uses random walks with finite time budgets and kernel sampling techniques to directly estimate solutions at any requested time while maintaining parallel and progressive evaluation properties.
Twenty-five Fields medalists argue that AI companies' goals are misaligned with mathematics' goal of conceptual understanding, but the letter's authors acknowledge the mathematics community itself has failed to nurture students and ideas with care. The article illustrates this historical failure through examples of mathematicians like Schauder, Ladyzhenskaya, and Uhlenbeck who faced antisemitism, gender discrimination, and systemic barriers despite foundational contributions to mathematics.