This course is primarily a course in mathematical physics. Its central themes are stability, differential equations, mode decompositions, perturbative reasoning, and the mathematical structure behind classical physical theories. Artificial intelligence is used throughout the course, but as a supporting tool: not to replace understanding, but to help reconstruct derivations, expand missing intermediate steps, and make difficult arguments more accessible and explicit.
A major inspiration for the course comes from classical scientific works such as Maxwell’s study of Saturn’s rings. These articles are not treated merely as historical curiosities, nor simply as examples of how to use AI. Instead, they serve as rich entry points into substantial mathematics and physics. By reformulating such material in a more modern and explicit style, we try to uncover the deeper content hidden behind the compact notation and omitted steps. The omission of steps is often done in scientific articles, but nowadays we can use AI at our own advantage to bridge that gap.
Along the way through the course, students encounter stability theory, partial differential equations, Fourier and mode-based reasoning, linear algebraic structures, perturbations, asymptotic thinking, and elements of fluid-mechanical and mechanical intuition. The course therefore offers much more than a methodology for studying: it is also a genuine path through important areas of mathematical physics.
