I think the number of new math proofs generated by LLMs over the last few months has conclusively proven that yes - they can "come up with things themselves"

A few examples: Axiom's proof of Fel’s open conjecture on syzygies of numerical semigroups: https://x.com/axiommathai/status/2019449659807219884

Erdos 457: https://www.erdosproblems.com/457

The stronger form of Erdos 650: https://www.erdosproblems.com/650