[davesque]

Without any more context, "keep going" seems to be doing a lot of work. The user is placing a lot of faith in the LLM to not make subtle logic mistakes and to take good approaches to each problem. In my experience, even frontier models (such as Fable) are quite capable of getting confused during even simple technical work I've done in the dev ops world. For example:

LLM: This package hasn't made it to production.

ME: are you sure? i see it right here!

LLM: You're right to push back. I inferred that based on weak data. I see now that the package has been deployed!

If the above conversation is typical for me, how could one expect to achieve a sound result by repeatedly prompting an LLM to simply "keep going" in dense mathematical proofs? Perhaps the user in this case had actually checked the LLM's work before issuing the prompt, but I think you see my point anyway.

[blargey]

There may be something(s) about mathematics (proofs) that makes it particularly amenable to LLM reasoning - highly inductive from facts that are explicitly within-context/associative space? Being an unusually well documented discipline in general, with less influence from tacit knowledge or idiosyncratic “it works however the opinionated human made it work +- bugs” processes? Something about simulating even the smallest non-pure-inductive leaps necessarily risking simulating mistakes due to the nature of context “perception”?

[appplication]

There’s also probably a lot less noise from casual internet conversations. I imagine a nontrivial amount of what LLMs know about certain technologies comes directly from forums like reddit where quality of response isn’t guaranteed.

[SOLAR_FIELDS]

I mean, just the way Tao phrases these inqueries seems to imply a weighting towards an extremely abstract and high level rigorous corpus. In a way, prompt engineering really is the big unlock here.

[eru]

Maybe! But I suspect you can write a little LLM assisted helper to at least make your prompts sound more like Tao's. (Your ideas won't necessarily be better, but you can probably 'imply a weighting towards an extremely abstract and high level rigorous corpus'.)

[lanstin]

Not likely. You run the risk of bleeding into the crank mathematics language pool which is well represented in the training. I mean the prompts may sound good to you and me, but they will have low probability words in respect to the Tao level maths.

[davesque]

I disagree. In fact, I think the field of dev ops gives a clean analogy with mathematical proofs. My point was that my work often requires that I figure out a consistent way to prove to myself what the condition of a system is by asking the right probing questions about it. What I've seen is that even the best LLMs lack a good intuition about what questions they should be asking and instead reach for the quickest and most obvious checks that leave edge cases uncovered. Maybe it is something about the domain of the problem; I don't know. But it makes it hard for me to imagine that an LLM wouldn't make similar errors in other cases, especially when generating mathematical proofs that will soon be too dense for humans to review.

[hgoel]

Agreed, often you have to step in and stop it from reasoning itself into dumb directions, but occasionally it goes just like the transcript in question.