The agents here very likely used search. On top of that, they have boundless patience and can quickly process top K hits to find what they need. This is exactly the skill that is super useful for finding various niche sub-proofs that can help you build the final proof. A human mathematician is not going to digest 1000 papers from a different sub-field to find the needle they want, not knowing if it is actually there. AI can do it in few hours.

As Terry Tao said, LLMs are not outsmarting us, they are out remembering us.

I'm fairly sure your understanding is not fully accurate.

I did not mean to say that an LLM knows literally all the publications. But the abstract knowledge is probably encoded in the weights.

No but they have training data which teaches them certain amount of complex understandings and just not math but also physics. So this is one huge advantage.

And then they are for sure able to fill their context based on 'smart search on top' to actually progress further.