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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

#151

Post by jcfrei »

bryan0 wrote: post #120

I'm not sure what's crazier: AI improving a lower bound on RH, or AI improving a lower bound on RH and it not even making the front page of HN.

That's how quickly your perception shifts when you are inside of a real, fundamental technological shift. If some similar computer program figured out the same improved bound just 6 years ago there would have been numerous blog posts, experts interviews and NYTimes, WaPo op-eds about some computer working on the Riemann hypothesis. Now that we are in the middle of it it's going to be a footnote at best.

Re: Learning more about Claude's mathematical capabilities

#152

Post by dosinga »

bwfan123 wrote: post #56
simonw wrote: 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.

> 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

> 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

that might just be an illusion. humanity as a whole applies brute force by just trying all the reasonable new theories until one of us discovers something that works and declares it a breakthrough

Re: Learning more about Claude's mathematical capabilities

#153

Post by 5555watch »

astro1234 wrote: post #6
Philpax wrote: post #2

> Jarred Sumner, an Anthropic staff member (and non-mathematician) prompted Claude to “take a real stab” at the hypothesis itself, leaving the mathematical choices from there up to the model. Initially, Claude generated and tried 650 ideas, none of which worked. 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, th…

Im curious if you find this to be a parody in a bad way or simply a “the state of the art in math research right now is telling a machine to believe in itself”. I am in the latter camp…

But the words don't really matter, do they? The model thought "user said believe in yourself, it means they want me to continue"..

AI did a fixed amount of guesses, didn't yield anything. It probably documented the tries, outcome, and some numbers hinting at why they failed. So the user could have prompted "continue", or "try again with previous outcome in mind, generate new ideas and test them" and it would probably yield the same result.

Re: Learning more about Claude's mathematical capabilities

#154

Post by not_a9 »

TacticalCoder wrote: post #55
geodel wrote: post #41

Earlier quoted context omitted.

Jarred Sumner is the Bun (javascript build tool, packager) guy who recently converted Bun code from Zig to Rust via Claude of course! It lead to thousands of comments discussion here on HN just a few weeks back. It is great to see his claude skills are suitably put to use.

> ... who recently converted Bun code from Zig to Rust via Claude ... The project that is full of bugs and not really working? I probably missed something but I was under the impression that even a "simple" translation like that couldn't be properly done and that the result was, well, buggy? Where's that thing at?

To the best of my knowledge: doesn’t the current build of Claude Code use the Rust port of Bun?

Re: Learning more about Claude's mathematical capabilities

#155

Post by jdub »

nl wrote: post #127
solid_fuel wrote: post #123

Earlier quoted context omitted.

> to the detriment of the whole club of stochastic parrot folk What an interesting and pointless way to refer to “experts who understand what an LLM actually is ”

The concept of "stochastic parrot" is that an LLM merely parrots its training data with some randomness. We now know that isn't true - LLMs build complex internal models and output based on that. See for example https://arxiv.org/html/2505.23323v1 Also, you are commenting on a post where a LLM made significant progress on the Riemann hypothesis . Even the most extreme interpretation of these results, ie claiming that…

only if you don't understand the difference between metaphor and analogy

Re: Learning more about Claude's mathematical capabilities

#156

Post by sscaryterry »

samrus wrote: post #76
simonw wrote: 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.

Broke: the AI is sycophantic to me Woke: im sycophantic to the AI

100%. I've disliked people because people lie, and loved computers because they didn't. Now they do too. :(

Re: Learning more about Claude's mathematical capabilities

#157

Post by llelouch »

MWil wrote: post #33

Several released versions and months ago, I asked Claude to figure out the MC (multiplicative complexity) of Conway's Game of Life and it pretty quickly arrived at k=7, despite no previous literature on the topic. Let it run it through SAT solvers for a week and sure enough. It claimed, in the process, to have made great headway in improving boolean circuits beyond the implemented SOTA (in large part no doubt by actu…

Claude is underrated in math. The 10 problems that openai solved? They needed an internal version. Fable 5 solved 5 of those.

Re: Learning more about Claude's mathematical capabilities

#158

Post by imko_ »

bwfan123 wrote: post #56
simonw wrote: 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.

> 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

I think that mathematics is a uniquely positioned space because this type of progress is possible for AI models exactly because they do not have to necessarily come up with new theories.

Re: Learning more about Claude's mathematical capabilities

#159

Post by mkl »

simonw wrote: post #63
bwfan123 wrote: post #56

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

Brute-force compute hasn't been an option for most of the history of science.

It still isn't an option for most problems, either because it would take far more computing power than is available or because the number of things to compute is infinite. In both cases, new theory is what can succeed instead. Developing new theory by brute force can be attempted, but will almost always run into the same problems. Using AI to develop new theory is using heuristics rather than brute force.

Re: Learning more about Claude's mathematical capabilities

#160

Post by mkl »

johnnienaked wrote: post #134
Philpax wrote: post #2

> Jarred Sumner, an Anthropic staff member (and non-mathematician) prompted Claude to “take a real stab” at the hypothesis itself, leaving the mathematical choices from there up to the model. Initially, Claude generated and tried 650 ideas, none of which worked. 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, th…

It's literally just brute forcing lol

Definitely not. Brute forcing this would be exhaustively searching the space of possible proofs until succeeding. This is heuristically remixing and extending existing work.
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