[glial]

I think LLMs will need to do what humans do: invent symbolic representations of systems and then "reason" by manipulating those systems according to rules.

Here's a paper working along those lines: https://arxiv.org/abs/2402.03620

[dunefox]

Is this what humans do?

[ezrast]

Think of all the algebra problems you got in school where the solution started with "get all the x's on the same side of the equation." You then applied a bunch of rules like "you can do anything to one side of the equals sign if you also do it to the other side" to reiterate the same abstract concept over and over, gradually altering the symbology until you wound up at something that looked like the quadratic formula or whatever. Then you were done, because you had transformed the representation (not the value) of x into something you knew how to work with.

[monadINtop]

People don't uncover new mathematics with formal rules and symbols pushing, at least not for the most part. They do so first with intuition and vague belief. Formalisation and rigour is the final stage of constructing a proof or argument.

[glial]

Perhaps, but then what's the point of symbolic systems at all?

[vatsadev]

Yeah, the AI in question can turn intuition into statements, then turn that to symbolic intuition, then work with that until something breaks it, then revise the system, etc, quite like a human?

[monadINtop]

No. Not in my experience. Anyone with experience in research mathematics will tell you that making progress at the research level is driven by intuition - intuition honed from years of training with formal rules and rigor but intuition nonetheless - with the final step being to reframe the argument in formal/rigorous language and ensure consitency and so forth.

Infact the more experience and skill I get in supposedly "rational" subjects like foundations, set theory, theoretical physics, etc. the more sure I am that intuition / belief first - justification later is a fundamental tenant of how human brains operate, and the key feature of rationalism and science during the enlightenment was producing a framework so that one may have some way to sort beliefs, theories, and assertion so that we can recover - at the end - some kind of gesture towards objectivity

[glial]

Arithmetic

[auggierose]

That's what I am doing. I follow my intuition, but check it with logic.