Students gain experience across the core fields of theoretical physics, from classical mechanics and electromagnetism through statistical and quantum mechanics to general relativity and quantum field theory. Solving problems is certainly one part of it. More important is learning to see the beauty in these subjects, enough to conjure up interesting problems of one's own, which ties directly into our methodology of asking the right questions. These can be as simple as wondering what happens when you attach a pendulum to a pendulum, and then another, forming an n-pendulum, or why the laws of motion involve only the second derivative of position and whether they could be more general. They reach all the way to the forefront of research, where toy models built out of matrices offer genuine insight into quantum gravity and the interactions of fundamental particles, to name only one idea among many.
There is also an art, largely forgotten, in reading the original papers, in following James Clerk Maxwell's own formulation of electrodynamics or working through Steven Weinberg's papers on quantum field theory and QCD. The great texts belong to this tradition too. Landau and Lifshitz sparked a revolution in the Russian school of physics with their celebrated Course of Theoretical Physics. Our students learn to draw from such wells directly rather than only through second-hand accounts, and in time to add to those wells themselves, bringing novel insights that enrich the understanding of the larger community.
Mathematics itself has been quietly reshaping the understanding of physics, yet very few venture into those depths to become equipped with its tools, and there are hardly any programs built around doing so. This is something we pioneer. Students journey into differential geometry, topology, and algebraic geometry among other fields, gaining deeper insight through abstraction and then tying it back to grounded situations, completing the loop of understanding.