> The fact is, LLMs are incapable of invention and synthesizing new ideas.

I don't think it's fully appreciated how much of the hard work of "synthesizing a new idea" is just combining existing ideas. LLMs have given me brand new algorithmic ideas with precious little in the way of a spark on my end to make that happen, and not just a few times either.

Mind you, that workflow is arduous and involves a huge amount of experimentation, screening through interesting but ultimately wrong ideas, screening through outright bad ideas the LLM can't help but spew out as well, and manually massaging the results into something useful. It exists though.