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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

#31

Post by lithobraking »

This area seems to be moving so quickly. I wonder if it'll be worthwhile to start building a list of formal math problems whose solutions, or partial solutions, would help my subfield. (Though I work in the physical sciences, mostly with the messy, real world implementation problems which are likely difficult to formalize or directly connect).

Then, whenever a new SOTA model drops, throw it at the list to see if we get "free" research progress.

Re: Learning more about Claude's mathematical capabilities

#32

Post by mahogany »

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…

Taking Anthropic’s whole AI framing to its obvious logical end: if this is true as written, why was Jarred needed at all in this loop? It seems like an utter waste of time for a highly paid Anthropic employee. Can’t Anthropic have a top level agent that is looking at all interesting unsolved problems and orchestrating subagents via the same process?

Re: Learning more about Claude's mathematical capabilities

#33

Post by MWil »

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 actually implemented non-implemented but published SOTA).

And that was just the first time I really tried out Claude's mathematical prowess. I've been working with boolean circuits, FHE, and lean proofs ever since.

So none of this suprises me.

Re: Learning more about Claude's mathematical capabilities

#34

Post by kypro »

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.

Re: Learning more about Claude's mathematical capabilities

#36

Post by MelonArmiger »

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…

[dead]

Re: Learning more about Claude's mathematical capabilities

#37

Post by atleastoptimal »

It seems like everything will follow this pattern:

1. AI is dismissed because an expert in a particular field finds an outdated model's outputs sub-par

2. New model, released or unreleased, makes a major stride in that field

3. Expert either recants and becomes AI-pilled, or claims it is just an artifact of the broad search space available to AI, and "no new knowledge was created".

Re: Learning more about Claude's mathematical capabilities

#39

Post by arjie »

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?

The full paragraph quoted for other readers is:

> Two mathematicians at Anthropic studied and validated Claude’s paper, and produced an informal note for experts stating Claude’s proof concisely. Claude also produced a formally verifiable proof of its result. We are grateful to Brian Conrey and Dan Goldston, two experts in this area, who generously examined the paper on short notice.

They may wish to know that an archive of the page on 2026-08-10 at 17:47:33 is available with this paragraph here: https://web.archive.org/web/20260810174733/https://www.anthr...

Re: Learning more about Claude's mathematical capabilities

#40

Post by zarzavat »

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 wait for the models to produce a good novel first.

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