There is also something else horizontally to this that occurs.

There are numerous scientific discoveries that have been made because one human looked at all available data and turned off the assumptions other people in the field have been using for years, maybe hundreds of years. Once you delete the assumption and make a new one the answer is obvious any anyone from that point wonders how so many humans could have missed it for so much time.

This can occur readily with LLMs as it can with people. It's very likely we will see this a lot as the causal connection in the available data will connected differently in their minds.

Escaping from a local maximum can be very difficult as you have to climb uphill with a nearly infinite amount of freedom but no ability to see the horizon. Psychics, LLMs, or some guy name Bob walking in an providing a workable analogy for you to escape the local maxima and move closer to a global maxima are all the same. Moreso, if LLMs are AGI we should expect these "psychic" behaviors just as much as actual discovery because both continuums exist in the same problem space as human minds.