Hmm we may be talking of two different interpretations of intuition here. I agree that LLM weights contain representations of abstract concepts, as a lot of prior research has shown. This surely includes Mathematical concepts.
But to me that is analogous to what human brains do, and a bit different from intuition. I think of intuition as “heuristics”, typically developed through experience, that may link seemingly unrelated concepts via vague, hard-to-define associations, but which let us make mental leaps (or shortcuts) while reasoning. (Maybe analogous to System 1 / 2 thinking.)
On the other hand, LLMs can do both: build “intuition” from patterns in data AND brute force a huge amount of potentially unrelated concepts. This gets fuzzier when we realize that even these “concepts” themselves are gleaned from patterns in data! But my point is we necessarily have to take shortcuts to scale, whereas machines can scale with hardware.
This is of course a layman theory! But it could explain why these models are progressing so fast.
Yes, in my case "intuition" comes a lot from visualizing things spatially, manipulating them, and being able to capture their properties in equations/proofs, and it's that which is (currently) conspicuously missing when dealing with LLMs. (And may yet appear with world models).
With the alternate view of intuition that many of you are describing it is clear LLMs are somewhat either there or heading there now.
This is an intriguing observation! LLMs were famously bad at spatial reasoning, until Astra which apparently has a huge improvement. I wonder if that has any bearing on the recent jump in Mathematical performance?
One thing that struck me from Dario's last podcast with Dwarkesh was that he said training LLMs on a diverse set of tasks does not make them better just at those tasks, but they get better at unrelated and other tasks overall. What you described could be a concrete example of how that dynamic works!