I wrote my diploma thesis 10 years ago and had to do a lot of pen and paper calculations. Actually it was kind of standard stuff (Lagrangians of Standard model, calculating parametrized decay widths) At that time I really hoped I could automatize the error-prone steps of plugging in and simplifying equations but I found nothing, except for isolated steps. Maybe this is also due to the fact that the most powerful tools for manipulating symbolic expressions are closed source. Not sure how it is now but as long as these tools are not expressive enough to work "end-to-end" with SM Lagrange densities, I doubt anything innovative could be done by automatizing that with AI.
That problem of pen-and-paper calculations featuring unintended errors is what I try addressing in a project I work on [1]. My approach is to use Sympy (which has a lot of Physics support) to validate expressions entered by a human. Not quite the AI-focus of this thread, but still a machine augmenting the work of researchers. To your point about the complexity of the math, the Physics Derivation Graph is able to handle simple inference rules but there's nothing preventing more advanced use.
