I don't know. I have talked to a few math professors, and they think LLMs are as good as a lot of their peers when it comes hallucinations and being able to discuss ideas on very niche topics, as long as the context is fed in. If Tao is calling some models "a mediocre, but not completely incompetent [...] graduate student", then they seem to understand math to some degree to me.
Tao said that about a model brainstorming ideas that might be useful, not explaining complex ideas or generating new ideas or selecting a correct idea from a list of brainstormed ideas. Not replacing a human.
Obviously not, but that is tangential to this discussion, I think. A hammer might be a useful tool in certain situations, and surely it does not replace a human (but it might make a human in those situations more productive, compared to a human without a hammer).
> generating new ideas
Is brainstorming not an instance of generating new ideas? I would strongly argue so. And whether the LLM does "understand" (or whatever ill-defined, ill-measurable concept one wants to use here) anything about the ideas if produces, and how they might be novel - that is not important either.
If we assume that Tao is adequately assessing the situation and truthfully reporting his findings, then LLMs can, at the current state, at least occasionally be useful in generating new ideas, at least in mathematics.
