If you can remember the content of any scientific publication and any book in the world, you are able to make use of this knowledge in every step of you proof.
However, this does now answer how the model came up with the specific route it has taken for the proof.
I'm fairly sure your understanding is not fully accurate.
And then they are for sure able to fill their context based on 'smart search on top' to actually progress further.
But obviously, it adds up to something greater than went in; in aggregate, our contributions are something to awe.
But my point is, if you zoom in at the marginal, incremental contributions of any individual human in this process, it's really hard for me to say LLMs are not at the same level already.
On this topic, people like to compare LLMs to Einstein, but as far as I know, Einstein did not zero-shot special relativity in an afternoon. He built it up incrementally over time, it took him three times longer than the time between first ChatGPT release and today, and it depended on centuries of prior art, culminating in the right observation and right notation being available to him in his moment of greatness.
At what level LLMs are is then an entirely separate discussion, I think.
Name three.
So your view is that everything was there at the creation of the universe (it's a possible view, of course)? Or are there any "things" that can create ideas from scratch?
I think it's not impossible that words evolved as adaptations of the environmental sounds with which our ancestors lived. The human creativity producing DNA is also a remix of preexisting molecules formed under evolutionary pressure, so the view that it's turtles all the way down, unintuitive as it is, may not be so indefensible after all.
They combine things, verify it and if it works and progresses the problem, they created something new.