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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

#11

Post by EMIRELADERO »

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…

The former, because it's anthropomorphizing a model.

Anthropic is especially guilty of this. They have been using such language for a while, like when they analyze model weights for mechanistic interpretability and call it the model's "biology".

It's just distasteful.

Re: Learning more about Claude's mathematical capabilities

#13

Post by Philpax »

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…

For me, personally, it's that the Bun guy - specifically him, not a mathematician - indirectly progressed the Riemann hypothesis by repeatedly telling a model to ganbatte!

It's a ridiculous position we find ourselves in.

Re: Learning more about Claude's mathematical capabilities

#14

Post by bspammer »

rvz wrote: post #5

Although it took an unsuccessful attempt at it, the progress is as follows: "Claude found that combining the results from Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh with the work of Bombieri provides a way to surpass the previous state-of-the-art lower bound proportion of 41.6%, increasing it to 67.2%." The transcripts, papers, and Claude's explanation are an interesting and a better read than this article…

The acknowledgements section in the paper is so bizarre. We have an LLM thanking individual humans for their contributions.

Re: Learning more about Claude's mathematical capabilities

#15

Post by briansmith »

> 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?

Re: Learning more about Claude's mathematical capabilities

#16

Post by godwinson__4-8 »

EMIRELADERO wrote: post #11
astro1234 wrote: post #6

Earlier quoted context omitted.

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…

The former, because it's anthropomorphizing a model. Anthropic is especially guilty of this. They have been using such language for a while, like when they analyze model weights for mechanistic interpretability and call it the model's "biology". It's just distasteful.

> The former, because it's anthropomorphizing a model.

Not really. The input and output is already natural language. That is already "anthropomorphizing".

That is, if this is the bar for anthropomorphization its already happened.

Telling the model to "believe in itself" is just stochastic manipulation that has shown enough reliability to be a recipe to make it keep going.

It's only actually anthropomorphizing if you forget it's a trick and think it's a real person.

There is nothing distasteful about it. If people get confused that's on them. They wouldn't be very useful if you couldn't just talk to them. That's kind of the whole point. Otherwise you can just go back to coding by hand. Telling it to believe itself is just input that happens to work. This probably tells us more about human nature than you realize given the corpus on which it is trained. It obviously doesn't mean anyone actually thinks it's a person.

Re: Learning more about Claude's mathematical capabilities

#18

Post by math_dandy »

briansmith wrote: post #15

> 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?

> 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.

Re: Learning more about Claude's mathematical capabilities

#19

Post by brandall10 »

tristanj wrote: 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.

Re: Learning more about Claude's mathematical capabilities

#20

Post by briansmith »

math_dandy wrote: post #18
briansmith wrote: post #15

> 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?

> 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.

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