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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?

#91

Post by parhamn »

bwfan123 wrote: post #89
parhamn wrote: post #78

> If they were, then their big speed advantage over us would mean that there would be much more of a flood of results. Is this true right now? Just recently Jarred Sumner tweeted [1] that he managed to make some progress on the Riemann hypothesis while on a jog. Managed to get somewhere by encouraging the llm to “keep going” and “believe in yourself”. This raised a few questions for me. Had no one at Anthropic though…

From the tweet: > Still not sure what that means, but some analytic number theorists seem excited ie, I prompted AI and it put out a giant pile of tokens. I dont know what it means, but I hope someone gets excited. Mathematicians are now the priests and shamans chanting incantations and taking the holy blessings from the AI gods.

Thats the issue, they're going to get flooded soon with these holy blessings, then what?

Re: What sort of maths are LLMs good at?

#92

Post by justanotherjoe »

How i reason about this is that, there are two types of science works, exploitative and generative. Exploitative science is kinda like what ingen do in jurassic park, finding an use case based on available tensions in the literature.

Funnily enough, 'generative' ai is not good at generative science, of which requires unique human perception that is not purely symbollic manipulation, but requires a form of revelation. That I think is not here yet with ai...

Re: What sort of maths are LLMs good at?

#93

Post by redsocksfan45 »

suddenlybananas wrote: post #71
phantompeace wrote: post #49

Earlier quoted context omitted.

Nobody called anyone schizophrenic. They noted that the irrelevant link spam in a reply was reminiscent of schizophrenic posting. If you've spent any sort of time on places like 4chan, you'd understand. I don't think posting the HN guidelines is warranted here.

>Nobody called anyone schizophrenic. They noted that the irrelevant link spam in a reply was reminiscent of schizophrenic posting. Come on, that's being incredibly pedantic. If I say, your comment reminds me of someone being an asshole, I'm just using a circumlocution to call you an asshole. No?

[dead]

Re: What sort of maths are LLMs good at?

#94

Post by Smaug123 »

svantana wrote: post #29
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…

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.

Shannon was 1948, one-way crypto in 1978, univalence/HoTT something like 2007; I would be surprised if there weren’t simple new fundamental primitives out there! One problem is that some great advances are from viewing complex objects in a simple way, which take a lot of characters to define in formal logic but which are “simple” in platonic maths-space.

Re: What sort of maths are LLMs good at?

#95

Post by famouswaffles »

ozgung wrote: post #85
YeGoblynQueenne wrote: post #40

Disclaimer: I only scanned the article quickly; I might be re-stating something already in the article. We have just got some very strong evidence about the way in which LLM-based systems solve mathematical problems and this evidence supports what many have already suspected including myself. Here's what I'm talking about. On 10 August Anthropic released an article [1] claiming that: An unreleased research version of…

This is not "brute-force" though. It's an iterative search algorithm. You learn things at each iteration. You also don't search blindly. You use "something" (heuristics, experience, intuition) to come up with "ideas" at each iteration. You don't try 650 random programs. You try 650 different ideas each learning from the results of previous trials. Yes this is the "Universal Problem Solving Algorithm". It's actually t…

Thank you. I've never seen 'brute force' and 'type writing monkeys' abused so much than these LLM discussions.

Re: What sort of maths are LLMs good at?

#97

Post by retsibsi »

xnorswap wrote: post #50
xnorswap wrote: post #38

Earlier quoted context omitted.

That's cute, but it's driving me crazy, I guess I'll have to sit down and solve it to figure out how it's meant to be clued, assuming it's not just a red-herring entirely.

Right, this is based on pen-and-paper working, so I could be wrong, but I think it's a red-herring, the set of "clothing" seems to be: white, blue, yellow, and is otherwise undefined. But we know from [1], [2], [4], [5] and [11], that the order must be: A, B, C, D, E or A, B, E, D, C. Which makes C either the older 12 year old or the 35 year old. The key this is that D can't be a 12 year old without A being in slot 2…

I independently reached the same conclusion, and I think we must be right, because the thing I thought I might have missed was some way in which the shoes/clothes are actually relevant and rule out one of those orderings. But our answer matches the one in the paper, and I don't see a mistake we could have made to reach the right answer in the wrong way.

I guess they were not optimising for a satisfying solving experience! (I'm not sure what 'expansion' means in this context, but it sounds like maybe the 'expansion strategy' referred to in the paper involved padding out problems with red herring premises?)

Re: What sort of maths are LLMs good at?

#99

Post by lg5689 »

YeGoblynQueenne wrote: post #40

Disclaimer: I only scanned the article quickly; I might be re-stating something already in the article. We have just got some very strong evidence about the way in which LLM-based systems solve mathematical problems and this evidence supports what many have already suspected including myself. Here's what I'm talking about. On 10 August Anthropic released an article [1] claiming that: An unreleased research version of…

LLMs are indeed very special compared to past efforts at automated theorem proving. The search tree for proofs is enormous, even short textbook exercises (i.e. a few dozen lines of Lean) were difficult with GOFAI techniques. Adding a few orders of magnitude to your compute budget barely moves the needle, since the search space increases exponentially for every line of the proof.

Now LLMs have produced multi-thousand line Lean proofs. This is impossible by simply "try everything and see what sticks". LLMs are able to target their efforts to only promising proof strategies. Yes it helps that they work at superhuman speed, so they can try thousands of strategies where a human might try a dozen. But their results cannot be explained only by compute increases; they need genuine mathematical insight.

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