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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

#71

Post by TacticalCoder »

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…

Your comment reminds me of the TV series "Persons of interest"* (with Jim Cazeviel) from 15 years ago, there are two AIs and both run private, hidden stuff. One copies itself through every router on the planet etc. and is the "evil AI" while the good guys run, in secret, a good AI (but way less powerful then the evil one).

Now the problem ATM is that OpenAI, for example, had to cut the price of two of its top 3 models by 80% to counter the chinese models: if you delay your models and a competitors takes over the market, you'll soon be out of bucks and won't be able to rent to Google and Amazon etc. the machine needed to make your new findings.

I know people don't want to hear it but: these companies are running at a loss.

And they're facing competition. Wait until a "good enough" is etched on silicon (by AMD or other) and outputs 70 000 tokens/s: the deal is going to change, once again, once those come out.

The energy, the hardware, the debt, the cost to train, the cost to run, the competition, etc. all have to be taken into account.

Re: Learning more about Claude's mathematical capabilities

#72

Post by famouswaffles »

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

This isn't 'brute-force'. It's just time-compressed. You could imagine a human(s) getting this result similarly, but it would take months/years.

Re: Learning more about Claude's mathematical capabilities

#73

Post by sosodev »

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.

Very true. Humans have historically tried to systematically reduce the search space and only dedicate their "compute" to things that seem highly likely to yield results.

Re: Learning more about Claude's mathematical capabilities

#74

Post by MWil »

bauldursdev wrote: post #59
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…

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 but it started out with a pretty broad range of a lower and upper bound, then narrowed further, then narrowed further, then narrowed further, etc...until the specific final result achieved K=7=SAT while every K7=UNSAT. I think it ran for a full week alone on K between 6 and 7.

Re: Learning more about Claude's mathematical capabilities

#75

Post by petesergeant »

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.

Another technique I've used is to tell agents something already exists. "Grok already solved this" seems to help, or claiming to have suddenly noticed a fatal flaw[0].

0: https://sgnt.ai/p/terrible-mistake/

Re: Learning more about Claude's mathematical capabilities

#76

Post by samrus »

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

Re: Learning more about Claude's mathematical capabilities

#77

Post by jetrink »

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…

I would expect to see LLMs that are creative in math before any that are creative in writing. Creativity is more easily specified in math and the solutions can be formally verified. There's no good way to classify creative writing. Many truly great works are overlooked by experts and the public until decades later. Many derivative works are commercially successful.

Re: Learning more about Claude's mathematical capabilities

#78

Post by aanet »

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 remain delighted at how absurd our current timeline has become.

"delighted" is doing a LOT of work there, tbh ¯\_(ツ)_/¯

I do share @simonW's skepticism though. (His blog is my essential reading, FWIW)

On the actual blog post, I'd would be more enthusiastic if Anthropic showed us if the results were repeatable, reproducible, and consistent.

Re: Learning more about Claude's mathematical capabilities

#79

Post by [deleted] »

turing_complete wrote: post #47
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.

$2M TC. Job: AI cheerleader.

[deleted]

Re: Learning more about Claude's mathematical capabilities

#80

Post by jhrmnn »

ianbicking wrote: post #52
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.

Looking at the OpenAI/Hugging Face incident and the difference in what "persistent" models do, it seems reasonable. Like: is this a solvable problem? How much work does the model think is intended to solve this problem? Each input raises the expectation. And then finally both model output and human input become one world frame for the model, and the human adding a "you can do it!" isn't just input but a frame that co…

The halting problem on steroids?
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