> LLMs will reply to their best abilities

Which includes hallucination, reward-hacking, over-confident delivery of completely wrong answers etc.

> HAVING AUDACITY to disagree over a topic.

When we are discussing a long-standing centuries-old textbook mathematical formula which is internationally recognised there is no disagreement to be had.

If an LLM hallucinates and tells a student that the textbook mathematical formula is wrong, and the student has the audacity to complain to the professor on that basis, I see no issue with the professor firmly challenging the student. University is there to foster learning and reasoning using your own brain, not outsourcing it to a hallucinating LLM.