Interesting way to look at it. Your description of what physicists are experts at matches my math PhD pretty closely. I focused on mathematical modeling. I now work with a bunch of physicists, so I guess that checks out.
Yeah, if you work on the applied side of math it can be very similar to what people do in physics. But I was thinking more about pure math.
Edit: I think the main difference there is that in applied math they still prove that the models are mathematically correct. In physics they just show that the model align with experiments and skip math formalism.
I was with you on the generalities, but oh do theoretical physics suffer from math envy when it comes to formalism. Basically since the invention of quantum mechanics, has physics been dominated by “proofs” and “theorems” like the physical world is assumed to be axiomatically defined by Heisenberg’s and Pauli’s principles, and everything else is just maths.
No small part of the stagnation I sense in physics today stems from too deep a faith in the ultimate truth of the mathematical models we call theories. It doesn’t help the fact that we rely on Taylor expansions and perturbation methods for most experimental predictions.
The Higgs hunt and the passivity of the (experimental) physicists in challenging this stupid theory-driven search for new physics is emblematic of this era.
If only math was seen as a modeling language and not somehow truth/consistency itself, physics would be much better off.
Yeah, I saw that as well, met some professors in grad school that started talking about physics in terms of axioms and proofs instead of experimental results and models. At that point I lost interest and just went with math instead, if it is going to be math anyway why not go with the real thing.
