The path from a mathematical model of a physical system to an executable simulation passes through a surprising number of layers of mathematics, numerical methods, algorithms, and software abstractions. Each layer admits its own design choices and notions of correctness, making formalization challenging both within individual abstraction layers and at the boundaries between them. This talk is a perspective on this formalization stack, from continuous mathematical models through discretization, numerical solvers, parallel algorithms, and ultimately high-performance simulation software. While rapid progress has been made recently in formalization of pure mathematics and software verification with the acceleration due to modern AI-augmented methods, substantial gaps remain if the goal is to build trustworthy simulations of complex physical systems on the world's most capable computing systems.