Yes, when you use a standard theoretical physics textbook / course sequence, it is 100% correct.
More broadly, LLMs or anything at all, needs a verifier. If the task can be automatically verified, great, then anyone can use them. If you can't automate the verification, then you need to be able to verify it using your knowledge. Knowledge required to verify is lower than the knowledge required to create in very few cases. This is why you still need a fully trained human verifier. We are yet to reorganise the overall "tasks" in the economy such that verification can be done with much lesser knowledge, for no reason other than that there was never demand for this until creation became automatic few years ago. It is possible and is slowly being done, there are many many startups working on automating verification in different fields and in many cases we will see fields reorganise themselves to be more amenable to automatic verification. Note that _effort_ required to verify is much lower than what is required to create, for almost anybody, and LLMs have economic use just due to that alone, albeit in the hands of a knowledgeable human.
Math professors are remarkably good at answering math questions or solving ad hoc math puzzles correctly. Also at stepping back and asking, why are you trying to show this result, what do you think it has to do with the thing we are trying to prove. Much better at knowing when the student has gone off the path in some subtle way than the LLM (without a Prof Tao in the chat).
Professor Tao also put out some YouTubes of him working with an older LLM to do Lean proofs, and his intelligence matters - things where I would be stuck for hours trying to understand what was failing in the model proof were just instantly clear to him and fixed in thirty seconds.
And I am an ok coder (rather than a bad maths grad student), but the LLM will happily thrash around the edges of a problem with me with no clear convergence when I don’t have that clear insight and the problem is weirdly presented enough; I still find the trick to walk around the block and disengage and then return knowing exactly what to do (now prompting it to the right thing) to be a super power for getting what I want out of the coding system.
More broadly, LLMs or anything at all, needs a verifier. If the task can be automatically verified, great, then anyone can use them. If you can't automate the verification, then you need to be able to verify it using your knowledge. Knowledge required to verify is lower than the knowledge required to create in very few cases. This is why you still need a fully trained human verifier. We are yet to reorganise the overall "tasks" in the economy such that verification can be done with much lesser knowledge, for no reason other than that there was never demand for this until creation became automatic few years ago. It is possible and is slowly being done, there are many many startups working on automating verification in different fields and in many cases we will see fields reorganise themselves to be more amenable to automatic verification. Note that _effort_ required to verify is much lower than what is required to create, for almost anybody, and LLMs have economic use just due to that alone, albeit in the hands of a knowledgeable human.