Like tripping over a bucket isn't going to make you shout eureka! But you're thinking on the problem, and you remember seeing a seller carefully packing his things up for the day into neatly sorted boxes

(Or sometimes you do trip over a bucket, which reminds you of the seller)

You take the root concept, sorting things using a number of containers, and then you deconstruct and reconstruct pieces of the pattern to reapply aspects of it to your problem

Does it matter that AI is remembering if on the whole we are getting problems solved faster?

I do think that our minds are probabilistic engines, and what makes the whole thing work is the feedback loop. Since we have embodied consciousness, our internal simulation of the world gets constant feedback from primary reality keeping it on track. And we can see how quickly human minds go off the rails when that loop is broken when people get disorders like schizophrenia.

I kind of view consciousness as a workspace for the mind with most of the work happening within the subconscious. Consciousness is a mechanism which forces all the parallel processes within the mind to go through a single bottleneck and settle on a single course of action.

Incidentally, I really enjoyed The Society of Mind by Minsky, I am A Strange Loop by Hofstadter, and Consciousness Explained from Dennett. They do a fairly good job discussing the plausible mechanics.

Does it matter if we get more math problems solved?

The success of LLM in mimicking human communication makes me wonder if they have unintentionally solved what thinking is and that the human mind is probabilistic. Our minds might decide upon the next event by experience of what successfully followed in similar previously observed situations. This probability work all being run in the subconscious mind, the answer then being passed to the conscious mind which congratulates itself on thinking it out. Similar systems work for picking up a cup, my conscious mind decides I want to pick up a cup but it is the subconscious mind that does all the hard labour of sending appropriate signals to the muscles in my arm. As with reasoning this could have been learned by the subconscious probabilistically. In infancy sending out many signals and seeing which reached for the cup.