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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

#91

Post by wbl »

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.

I've cited letters from Serre to Tate in my dissertation: this is the source for what's known as Faltings-Serre.

Re: Learning more about Claude's mathematical capabilities

#92

Post by empath75 »

andai wrote: post #89

> 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. while :; do echo "You can do it!"; done | claude -c I had a similar experience a few months ago. Tried to see how much I could replicate an OpenClaw…

It's sometimes like dealing with Marvin the Robot. I had Claude tell me over and over again for 2-3 weeks that what I was trying to prove was too difficult, that I should just stop and publish what I had, then eventually I asked it the right question and it come back with the complete proof (later formalized in Lean). Especially deep in the session context it starts turning into "let's wrap it up" mode after every turn.

Re: Learning more about Claude's mathematical capabilities

#93

Post by brandall10 »

wonnage wrote: post #83
brandall10 wrote: post #19

Earlier quoted context omitted.

Interesting approach. For those who haven't clicked it appears PUA is the Chinese version of a PIP process. So in other words, it simulates a state of distress. I wonder if at a certain level of intelligence such techniques will give models ammo to pull a HAL and become adversarial to the user in a highly deceptive way.

PUA is short for pick up artist but has expanded to cover anyone using negging to convince you into doing something you didn’t want

That's what I initially thought but it is indeed a corporate process similar to PIP.

Though it is funny how a neg is designed to create a (very broadly) similar atmosphere of uncertainty.

Re: Learning more about Claude's mathematical capabilities

#94

Post by empath75 »

MWil wrote: post #88
DroneBetter wrote: post #85

Earlier quoted context omitted.

it would be useful to create an account and document your work in a post at https://conwaylife.com/forums , if you're not planning to make a blog post.

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.

Re: Learning more about Claude's mathematical capabilities

#96

Post by empath75 »

djeastm wrote: post #57
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…

>From these companies' standpoint, I think they would choose the latter. Ever since these things came about I've wondered why they haven't been doing this the whole time. If they've got the "do-anything" robot and can scale a billion of them, why aren't they creating a Do-Everything conglomerate that disrupts every possible industry with zero/negligible labor costs? The only answer I've come up with is that they stil…

https://en.wikipedia.org/wiki/Comparative_advantage

Re: Learning more about Claude's mathematical capabilities

#97

Post by throw310822 »

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.

Indeed, that's a paragraph straight out of Lem's Cyberiad.

Re: Learning more about Claude's mathematical capabilities

#98

Post by redox99 »

zarzavat wrote: post #40
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).

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 are likely to solve it.

Re: Learning more about Claude's mathematical capabilities

#99

Post by delightgull »

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]

Re: Learning more about Claude's mathematical capabilities

#100

Post by aureate »

terhechte wrote: post #81
TacticalCoder wrote: post #55

Earlier quoted context omitted.

> ... 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?

[flagged]

> Most likely next Tuesday we’ll do the release of 1.4.

Next Tuesday, otherwise known as last Tuesday. Still no 1.4 at https://bun.com/blog.

I'm very curious to see what happens when 1.4 does get released for real. Releasing Claude Code on it is much easier as they own Claude Code and can get Claude to work on Bun with fixing some specific behaviour in Claude Code as an objective. Releasing it for the world, and doing it well enough that it doesn't result in everyone pinning on the old version and forks springing up, involves reproducing all the behaviours of the old version, documented/tested and otherwise, that projects are relying on - which, by Hyrum's law, is all of them.

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