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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

#81
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?

[flagged]

Re: Learning more about Claude's mathematical capabilities

#82
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…

Yes, I think so, inevitably. For the same reason that Bitcoin mining silicon manufacturers stopped selling the latest greatest hardware to the public.

The best way to do this is to release spooky stories about how dangerous your model is and how you couldn't possibly release it without further safety shackling.

Re: Learning more about Claude's mathematical capabilities

#83
post #7

> Throughout this process, Jarred's input was mostly limited to sending Claude messages of encouragement (mostly variants of “keep going” or “believe in yourself”) He should consider using the PUA plugin. It detects when the AI is trying to give up on a problem and automatically harasses it with "encouragement" until it reaches a solution. https://github.com/tanweai/pua

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

Re: Learning more about Claude's mathematical capabilities

#84

> Two mathematicians at Anthropic studied and validated Claude’s paper, and produced an informal note for experts stating Claude’s proof concisely. Why hide the names of the people who wrote the second paper? To discourage people from citing it instead of the LLM-derived paper?

I'm one of those two, as mentioned later in the post! As it stands, by mathematical standards, it would be inappropriate for us to be authors on the paper since our role was more like a highly interested referee, but we do take mathematical accountability for it. This all happened very quickly, but we will be sure to continue to polish the paper and make it ready for publication.

Re: Learning more about Claude's mathematical capabilities

#85
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…

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.

Re: Learning more about Claude's mathematical capabilities

#86

Earlier quoted context omitted.

> Levent Alpöge and Ralph Furman, two of Anthropic’s own mathematicians, examined Claude’s work to understand the new results and how they related to the prior work mentioned above.

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.

Re: Learning more about Claude's mathematical capabilities

#88
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…

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 before you've legitimately reached that point.

"You should publish right now! Don't wait! There is no reason to wait!"

Like seriously, Claude was outputting something closely resembling (non?)peer pressure on me to not just keep this information to myself - and this was before all the recent math-related breakthroughs started becoming public.

It was also - most notably - before it had actually verified what it was saying it had calculated. I was the one pushing for more verification, more contemplation, more proofs of claims. And though Claude is better at this stuff now, it's definitely not not still happening.

I think I made the right choice then and I will consider being more open now that others have taken the burden of proving that, no it can actually sometimes do the incredible things its claimed its done for you.

My wife remains skeptical - she is/was seriously concered that I was under AI psychosis for believing that I had made such progress - and I can't even fault her for that. It sounds crazy to say it.

If anyone is reading this and is actively involved with FHE, especially someone from Zama or related group, I'd very much love to chat privately. I have many other "innovations" I've been working on since.

Re: Learning more about Claude's mathematical capabilities

#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 with Claude. Asked it what the weather is. "I don't know, I'm just a programmer." Added "You can do anything, believe in yourself." to the system prompt and suddenly it was able to tell me the weather...
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