Web search isn't desirable or even an option in a lot of use cases that involve GenAI.

It seems people have turned GenAI into coding assistants only and forget that they can actually be used for other projects too.

That's because between the two approaches "explain me this thing" or "write code to demonstrate this thing" the LLMs are much more useful on the second path. I can ask it to calculate some third derivatives, or I can ask it to write Mathematica notebook to calculate the same derivatives, and the latter is generally correct and extremely useful as is - the former requires me to scrutinize each line of logic and calculation very carefully.

It's like https://www.youtube.com/watch?v=zZr54G7ec7A where Prof. Tao uses claude to generate Lean4 proofs (which are then verifiable by machine). Great progress, very useful. While the LLM only approachs are still lacking utility for the top minds: https://mathstodon.xyz/@tao/113132502735585408