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Learning more about Claude's mathematical capabilities

anthropic.com

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Re: Learning more about Claude's mathematical capabilities

#161

Earlier quoted context omitted.

Sure, looks like 5% of math can be solved by 1T parameters stochastic parrot after NN trillion attempts (burned tokens). By numbers it could be less impressive than some brute force distributed chess engine.. Prove me wrong.

It's obviously significantly better than brute force. A trillion is absolutely minuscule compared to the size of the search space (like, 'rounding down to 1 is basically the same' small).

trillion indicates that its still brute force and not some search based on solid intelligent ranking function.

Also, I am not expert in this specific topic, but base on comments looks like claude parroted few recent works?

Re: Learning more about Claude's mathematical capabilities

#162
post #35

prompt engineering 2025: you are an expert programmer, use industry best practices, test driven development and use modularity and abstraction to anticipate future features, … prompt engineering 2026: i believe in you

Yes, one of the things I find hardest about using Claude code for Mathematics is keeping negativity out of the notes and memory. First of all, it will convince itself that a task is just too hard and find excuses not to try hard enough. Then when it struggles on something it loves to write down confusing notes about things which it believes cases the problem. Then next iteration it reads its own note, misinterprets i…

Perhaps it could benefit from being prompted to work more formally and make more incremental proofs? e.g. if it thinks it has an obstruction, it should prove that some example shows the obstruction, or prove that the property does in general cause a problem. Or if it has an idea for a lead, it could show that whatever property does imply the thing it wants. It could also dispatch to a subagent to report back with these kinds of incremental proofs (prove this really would be a problem, prove this would help, etc.).

Re: Learning more about Claude's mathematical capabilities

#163
post #98

Earlier quoted context omitted.

This result is some evidence that AI will not solve RH soon. If there were any easy solution hiding in plain sight then it probably would have found it. Solving RH likely requires AI that is substantially more creative. But we haven't even solved the creativity problem for writing let alone mathematics. I believe that transformers are a trillion dollar local optimum that we will find it very hard to escape. Let's wai…

> This result is some evidence that AI will not solve RH soon. If there were any easy solution hiding in plain sight then it probably would have found it. There's no way you can conclude that. Yes, "Fable 2" or whatever this was probably won't. But we can't know what Fable 3/4/5/etc will be able to do. If anything, if we have 1 or 2 more years of progress like the last 12 months, which have been insane, I'd say LLMs…

The keyword is soon, so OP simply meant current generation of LLMs are not likely to prove RH, judging from the performance shown in the paper.

Why? Because such explicit numerical improvements are not that interesting, which is best summed up in a review paper [0] of our efforts on RH spanning a century and a half,

> The pathetic attempts to enlarge the ridiculous zero free region in the critical strip is a perfect example of what brute force can do without fully exploiting fundamental arithmetic aspects of the problem. (italic added)

For outsiders, zero free region is another angle abundant with numerical improvements but no groundbreaking insights. For percentage people stop at ~40% because there is no need to proceed further, just like we are not interested in computing the googol-th digit of pi although in principle we could.

The groundbreaking results are like Selberg's that goes from zero to 0.01% (actually it is left unspecified, all we know is the percentage is positive), or Zhang's twin prime bound from infinity to 70,000,000. After this leap the pure numerical difference between 0.01%, 40%, 67% or even 100% is not substantial, and that's partly why Selberg did not even bother to compute it. Also RH will not follow from 100%, because in mathematics 100% does not mean all.

On the other hand, it is also wrong to dismiss such results all together. Riemann already know the real part of all zeros are bewteen zero and one, and RH says they equal 1/2. If someone or some LLM proved they are all less than 0.99, well this would be huge, and I'd bet they would easily get a Fields and be remembered forever. Innocent looking results could have drastically different technical depth behind them.

Alas math ppl tend to agree that RH will not be proved one bit at a time. The fundamental arithmetic aspects, once found out, will likely knock out not only RH but all the other L-functions in one go.

[0]: https://arxiv.org/abs/1707.01770

Re: Learning more about Claude's mathematical capabilities

#164

60 subagents for a day and a half. I guess he's not on the same plan I am on.

Jarred is the Bun creator who just got acquihired and converted Bun to Rust. Pretty sure his job now is to burn tokens to make news headlines. Like a developer advocate for LLM usage in general.

Re: Learning more about Claude's mathematical capabilities

#165

No more "stochastic parrots" and "LLM's can never produce anything novel, just regurgitate" comments anymore huh?

i still havent seen an llm invent new tokens/words over the course of a session?

the novelty remains a structural problem with how they work and what the weights try to predict

Re: Learning more about Claude's mathematical capabilities

#166
post #43

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”). This seems to have helped Claude overcome some initial skepticism that it could make meaningful progress. I remain delighted at how absurd our current timeline has become.

I feel justified in not expending any effort learning "prompting technique".

I believe in you

Re: Learning more about Claude's mathematical capabilities

#167

Earlier quoted context omitted.

> Jarred prompted Claude to try again, and it spent a day and a half coordinating about 60 Claude subagents, which this time went much deeper: between them, they ran 2,400 shell commands and wrote hundreds of Python scripts.1 If there is anything to learn from the history of science, it is that breakthroughs happen via better or new theory and not by brute-force compute [1]. [1] https://arxiv.org/pdf/2607.27794

This isn't 'brute-force'. It's just time-compressed. You could imagine a human(s) getting this result similarly, but it would take months/years.

It's a _little bit_ brute force, no? I don't disagree with the idea of a human following a similar path, but it ignores that humans have cognitive processes that may lead to pruning the search space in _different_ ways, and may ultimately mean fewer steps or a more directed path to the answer than 100s of python scripts.

Re: Learning more about Claude's mathematical capabilities

#168

Earlier quoted context omitted.

Have you seen how much college football coaches make? The world collectively spends trillions training, and entertaining and then watching people kick and hit balls around but somehow working with AI is preposterous for less money.

Asking the AI to believe in itself is the absurd part. I don’t understand why people think describing something in some ostensibly dismissive way constitutes making a point. But some people spend their time banging keys with letters on them (or not with letters on them) into input fields and then pressing Return, so I guess some subset of those people will do that.

I don’t think it’s absurd. We’ve created these things, however alien the structure, with as much human text as we can scrounge up and jam into them.

Text is an imperfect distillation of the human experience, but it doesn’t surprise me that a machine trained on human text responds to human encouragement.

Re: Learning more about Claude's mathematical capabilities

#169

Earlier quoted context omitted.

Right? I just learned about this and searched it on hacker news wondering why I didn't see it earlier. Any human mathematician would be thrilled to prove a result like this, and it's not even big news anymore that an LLM can do it.

Where did you find the news? So far I only found decent discussions about it in Chinese. https://www.zhihu.com/question/2070336637360518307/answer/20...

I saw it first on reddit (r/math).

Re: Learning more about Claude's mathematical capabilities

#170
post #167

Earlier quoted context omitted.

This isn't 'brute-force'. It's just time-compressed. You could imagine a human(s) getting this result similarly, but it would take months/years.

It's a _little bit_ brute force, no? I don't disagree with the idea of a human following a similar path, but it ignores that humans have cognitive processes that may lead to pruning the search space in _different_ ways, and may ultimately mean fewer steps or a more directed path to the answer than 100s of python scripts.

We do “a little bit of brute force” in science all the time. That’s what I’ve observed in seven years of science.

Moreover, frontier models have some degree of reasoning. So, I don’t think the gap is all that big.

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