LLM does not know math as well as a professor, judging from the large number of false functional analysis proofs I have had it generate will trying to learn functional analysis. In fact the thing it seems to lack is what makes a proof true vs. fallacious, as well as a tendency to answer false questions. “How would you prove this incorrectly transcribed problem” will get fourteen steps with 8 and 12 obviously (to a student) wrong, while the professor will step back and ask what am I trying to prove.