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What sort of maths are LLMs good at?

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Re: What sort of maths are LLMs good at?

#151

Post by antonvs »

inigyou wrote: post #148
antonvs wrote: post #147

Earlier quoted context omitted.

Writing code and proving theories are flip sides of the same coin. See e.g. Phil Wadler’s “Proofs are Programs”: https://philarchive.org/rec/WADPAP The statement should probably really be “programs are proofs” since it’s difficult to make it a true bidirectional isomorphism, which is why the underlying principle is properly called the Curry-Howard(-Lambek) correspondence: https://en.wikipedia.org/wiki/Curry%E2%80%93H…

Not in any useful way, though. In the Curry-Howard correspondence, being able to write a function of type "int -> string" proves that there is at least one valid string or there are no valid ints. The code of the function is a proof of this statement. For example you might prove directly that there is a string, by writing return "hello"; or you might write return bool2string(int2bool(myInt)); thus chaining two implic…

> Not in any useful way, though.

Theorem provers and proof assistants like Lean, Coq/Rocq, Agda, Idris, NuPRL and Epigram all fundamentally depend on Curry-Howard.

And again, the point is not that there’s some magical isomorphism, but that if LLMs are good at coding, they’re also likely to be good at certain classes of proof.

Re: What sort of maths are LLMs good at?

#152

Post by famouswaffles »

thinkharderdev wrote: post #87
greenmoonx wrote: post #79

Earlier quoted context omitted.

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> You get better at modeling the trajectory because the neurons physically move closer together as you learn I think "modeling the trajectory" is not necessarily what we are doing either. It's more likely we are using much simpler heuristics. If you are trying to catch a ball flying through the air, you can just look at the ball and modulate your running speed to keep your eyes at a fixed angle until you catch the ba…

The brain doesn't process vision anywhere near fast enough for some of the stuff you see in fast sporting actions if it were purely reactive - batting in baseball/cricket, returning a table-tennis shot, etc. In some cases the time available for movement is extremely restricted and yet people can respond accurately. We may not know exactly how the brain implements it, but it clearly uses prediction to estimate where the object is going to be - i.e. it is, in some sense, modelling its trajectory.

Re: What sort of maths are LLMs good at?

#153

Post by nullsanity »

redox99 wrote: post #143
CamperBob2 wrote: post #132

Earlier quoted context omitted.

"ChatGPT" could mean anything from Instant to Pro. What was the prompt, and which model(s) did you try?

Almost surely the free model on the web ui. So a dumb model, no harness, and probably a bad prompt.

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Re: What sort of maths are LLMs good at?

#154

Post by energy123 »

root-parent wrote: post #44
scronkfinkle wrote: post #8

> A good sign that LLMs have reached human level for a much wider class of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. They should also be methods that are difficult to stumble on by accident. It is hard to say precisely what would count as such a proof, but I think…

>> To me, this is more or less what I would think "Artificial General Intelligence" is So then you need to explain ARC-AGI-3: https://arxiv.org/abs/2603.24621 "Our testing shows humans can solve 100% of the environments, in contrast to frontier AI systems which, as of March 2026, score below 1%." Back 1996, EQP automatically solved the Robbins conjecture. But nobody concluded EQP was generally intelligent. https://ww…

OpenAI claims that the harness that ARC used was unfairly handicapping the model: https://openai.com/index/how-two-settings-tripled-our-arc-ag...

Re: What sort of maths are LLMs good at?

#156

Post by KurSix »

scronkfinkle wrote: post #8

> A good sign that LLMs have reached human level for a much wider class of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. They should also be methods that are difficult to stumble on by accident. It is hard to say precisely what would count as such a proof, but I think…

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Re: What sort of maths are LLMs good at?

#157

Post by KurSix »

jerf wrote: post #75

Given coding agent's demonstrated difficulties with concurrent code, even relatively simple concurrent code, it would be interesting to see how they do with temporal logic. I don't know enough to throw AI at the problems in that space but I wonder if they wouldn't crash and burn on it. (I haven't had the opportunity to throw a current-gen frontier model at a concurrent problem because I haven't had one to try out lat…

The harder test would be whether they can come up with the right invariants and abstraction in the first place

Re: What sort of maths are LLMs good at?

#158

Post by woopsn »

fn-mote wrote: post #58
svantana wrote: post #29

Earlier quoted context omitted.

I would be extremely surprised if something as elegant, terse, and useful as the Fourier Transform had been missed by human mathematicians up until now. All expressible theorems are enumerable, after all (if we limit ourselves to a finite alphabet). It seems likely that any new theorems are long, highly complex and esoteric, regardless of human or machine origin.

1. The computer is going to struggle to recognize elegance. I’m not sure it’s relevant at this point (but who knows). 2. The statement about proofs is just way wrong. It doesn’t sound like you are familiar enough with them. This isn’t exactly what you implied, but witness the very short disproof of the Jacobean Conjecture.

Big leaps in insight I don't think are received as elegant, generally. Fourier's contemporaries actually thought he was wrong (which he was), about both the series and heat equations, and even with the whole thing worked out it's not really straightforward. It fits into integral transforms/linear operators but in a way more complicated than can explained in those terms alone. Plus truncation error is commonly unbounded! Complex numbers and "fluxions" were also objectionable on their face although now one can frame them more or less elegantly.

Re: What sort of maths are LLMs good at?

#160

Post by krackers »

root-parent wrote: post #44
scronkfinkle wrote: post #8

> A good sign that LLMs have reached human level for a much wider class of problems will be if they start proving theorems using methods that, like much of the very best human mathematics, are new and surprising but that with hindsight come to seem beautiful and natural. They should also be methods that are difficult to stumble on by accident. It is hard to say precisely what would count as such a proof, but I think…

>> To me, this is more or less what I would think "Artificial General Intelligence" is So then you need to explain ARC-AGI-3: https://arxiv.org/abs/2603.24621 "Our testing shows humans can solve 100% of the environments, in contrast to frontier AI systems which, as of March 2026, score below 1%." Back 1996, EQP automatically solved the Robbins conjecture. But nobody concluded EQP was generally intelligent. https://ww…

I think ARC-AGI-3 specifically forbids harnesses. This means that you're basically limited by the context window, so it's no wonder that LLMs can't do that well. Unofficial versions that use a harness seem to be doing fine on it.
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