> Formalizing those intuitions is real work, but it's not the same as generating something with no prior basis.
> The fact that Euclid existed doesn't tell us much about what the other billions of humans are doing cognitively on a Tuesday afternoon.
Birds can fly - so, there is some flying intelligence built into their dna. But, are they aware of their skill to be able to create a theory of flight, and then use that to build a plane ? I am just pointing out that intuitions are not enough - the awareness of the intuitions in a manner that can symbolize and operationalize it is important.
> The whole point, drawing on Kahneman, is that most of what we call reasoning is fast associative pattern-matching, and that the slow deliberate stuff is rarer and more error-prone than people assume
David Bessis, in his wonderful book [1] argues that the cognitive actions done by you and I on a tuesday afternoon is the same that mathematicians do - just that we are unaware of it. Also, since you brought up Kahneman, Bessis proposes a System 3 wherein inaccurate intuitions is corrected by precise communication.
[1] Mathematica: A Secret World of Intuition and Curiosity
The bird analogy is actually a really good one, but I think it supports a narrower claim than you're making. You're right that the capacity to symbolize and formalize intuitions is a distinct and important thing, separate from just having the intuitions. No argument there. But my point wasn't that symbolization doesn't matter. It was about how often humans actually exercise that capacity in a strong sense versus doing something more like recombination within familiar frameworks. The bird can't theorize flight, agreed. But most humans who can in principle theorize about their intuitions also don't, most of the time. The capacity exists. The base rate of its deployment is the question.
On Bessis, I actually think his argument is more compatible with what I was saying than it might seem. If the cognitive process underlying mathematical reasoning is the same one operating on a Tuesday afternoon, that's an argument against treating Euclid-level formalization as categorically different from everyday cognition. It suggests a continuum rather than a bright line between "pattern matching" and "genuine reasoning." Which is interesting and probably right. But it also means you can't point to Euclid as evidence that humans routinely do something qualitatively beyond what LLMs do. If Bessis is right, then the extraordinary cases and the mundane cases share the same underlying machinery, and the question becomes quantitative (how far along the continuum, how often, under what conditions) rather than categorical.
I'll check out the book though, it sounds like it's making a more careful version of the point than usually gets made in these threads.