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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

#101

Post by MWil »

empath75 wrote: post #94
MWil wrote: post #88

Earlier quoted context omitted.

Claude was persistent that I post there at the time, and even drafted an eprint brief for me, but I think it's defensible why I did not, never came forward or spoke of it in any way (except for a private DM discussion on Discord if I ever needed timestamp proof) until now. As amazing as Claude is to seemingly make unprecedented progress, it is even more likely to blow the most insane levels of smoke up your ass befor…

Literally nobody is interested in reading "claude proved this" claims right now about anything. There's such a huge volume of proofs being made right now and nobody has time to look at them. There's probably an opportunity here to build some kind of system to filter and categorize LLM generated formal proofs produced by non-academics.

i think that opportunity optimally exists separately in each niche community impacted, if only to break up the number needed to be reviewed.

someone who loves Game of Life and is also technically capable if they were so inclined, is more likely to want to collect stuff like this for GoL specifically and build a system for that niche.

the combined GoL/technical community can vouch for things - the greater populace can see what the technical GoL community has vouched for/identified as serious work.

just my two cents on top of your thoughtful comment.

Re: Learning more about Claude's mathematical capabilities

#102

Post by applicative »

delightgull wrote: post #99
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.

[flagged]

OpenAI and Anthropic don't own any datacenters or order anyone to build them. It's easy to find out who does; you won't like the answer.

Re: Learning more about Claude's mathematical capabilities

#103

Post by nonethewiser »

behnamoh wrote: post #9

Since they say that this is from an unreleased research version of Claude: I wonder if at some point Anthropic and OpenAI will start delaying the release of their models intentionally so they can reap the benefits from the models in, for example, mathematics, medicine, physics, and other fields. Just as an example, imagine if your model were capable of proving P = NP, or if your model could cure diseases. Would you r…

It seems like theyd have incentive to

Re: Learning more about Claude's mathematical capabilities

#104

Post by jsnell »

fph wrote: post #86
briansmith wrote: post #20

Earlier quoted context omitted.

Are they the authors of the “informal note” or not? I’ve never seen a math paper of any formality written without the authors’ names on it before.

Anthropic seems to be challenging the traditional way math gets published. As far as I understand, these results did not get submitted to journals, and did not get Arxiv preprints; they are released only as self-hosted pdfs, and we don't even know the names of their authors. The canonical reference for the counterexample to the Jacobian conjecture is a tweet with no puntuations nor capitals.

As far as I can tell, Arxiv does not allow an AI to be listed as the author, so publishing there would not have been an option.

https://blog.arxiv.org/2023/01/31/arxiv-announces-new-policy...

Re: Learning more about Claude's mathematical capabilities

#105

Post by evilfred »

kypro wrote: post #34
kingstnap wrote: post #12

Lets play over/under on an AI model proving (or counter exampling) the Riemann hypothesis? I'm not sure what a good mark would be, but considering this result lets put it at 2027-08-10 (One year from today).

Let's extend this by asking: If an AI model can solve an extremely well known Math problem which has been open for centuries but hasn't be solved by a human mathematicians, why wouldn't that same model be able to find ways to improve it's own algorithms beyond that of the capabilities of human mathematicians / ML researchers? The singularity is approaching.

the AI model has NOT solved Riemann

Re: Learning more about Claude's mathematical capabilities

#106

Post by laukhin »

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.

it's pretty much a marketing attempt to humanize the LLM (it seems successful from the reaction I see)

Re: Learning more about Claude's mathematical capabilities

#107

Post by modeless »

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.

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

Re: Learning more about Claude's mathematical capabilities

#108

Post by rsrsrs86 »

MWil wrote: post #74
bauldursdev wrote: post #59

Earlier quoted context omitted.

Sounds really cool, were you able to verify the correctness of the results?

SAT solvers run until they reach the "SAT" status, meaning "satisfied" or UNSAT. The harder the problem the longer you might be running the program - days, weeks even. Ideally, what you want is a single SAT value among a remainder universe of UNSATs. Sometimes the best you can achieve at any given point is a lower bound and an upper bound range, like "greater than 3 but less than 9." Of course I simplified in my post…

You mean SMT, right?

Re: Learning more about Claude's mathematical capabilities

#109

Post by benswift »

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

Nah, the main lesson is that fundamentally new ways of doing things are only accepted once the old guard are all dead [1].

[1] https://en.wikipedia.org/wiki/The_Structure_of_Scientific_Re...

Re: Learning more about Claude's mathematical capabilities

#110

Post by black_knight »

tosh wrote: 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 it and completely messes up by trying to avoid some imaginary problem.

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