Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Learning more about Claude's mathematical capabilities

anthropic.com

Post reply on HN
Print view View original

121–130 of 181 posts

Re: Learning more about Claude's mathematical capabilities

#121

Post by HappyPanacea »

redox99 wrote: post #98
zarzavat wrote: post #40

Earlier quoted context omitted.

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…

You underestimate the difficulty of RH, there are far easier problems broadly related to RH (density hypothesis, Artin's holomorphy conjecture, Stark conjectures) which are still aren't solved.

Re: Learning more about Claude's mathematical capabilities

#122

Post by MWil »

rsrsrs86 wrote: post #108
MWil wrote: post #74

Earlier quoted context omitted.

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…

You mean SMT, right?

my memory was that SMT was part of a more advanced SAT solver, as in if you want to be modern/use SOTA, your SAT solver is going to use SMT

Re: Learning more about Claude's mathematical capabilities

#123

Post by solid_fuel »

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]

> to the detriment of the whole club of stochastic parrot folk

What an interesting and pointless way to refer to “experts who understand what an LLM actually is”

Re: Learning more about Claude's mathematical capabilities

#124

Post by solid_fuel »

kypro wrote: post #34
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.

> The singularity is approaching.

There have been apocalyptic preachers foretelling the end times for my entire life. Interesting to see how the language has changed, even as the predictions fail again and again.

Re: Learning more about Claude's mathematical capabilities

#125

Post by redox99 »

HappyPanacea wrote: post #121
redox99 wrote: post #98

Earlier quoted context omitted.

> 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…

You underestimate the difficulty of RH, there are far easier problems broadly related to RH (density hypothesis, Artin's holomorphy conjecture, Stark conjectures) which are still aren't solved.

I think verifiable tasks like math will soon be like Chess. Machines way beyond human intelligence.

Re: Learning more about Claude's mathematical capabilities

#126

Post by AgentME »

solid_fuel wrote: post #124
kypro wrote: post #34

Earlier quoted context omitted.

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.

> The singularity is approaching. There have been apocalyptic preachers foretelling the end times for my entire life. Interesting to see how the language has changed, even as the predictions fail again and again.

This argument also proves that climate change and nuclear war aren't possible existential issues.

Re: Learning more about Claude's mathematical capabilities

#127

Post by nl »

solid_fuel wrote: post #123
terhechte wrote: post #81

Earlier quoted context omitted.

[flagged]

> to the detriment of the whole club of stochastic parrot folk What an interesting and pointless way to refer to “experts who understand what an LLM actually is ”

The concept of "stochastic parrot" is that an LLM merely parrots its training data with some randomness.

We now know that isn't true - LLMs build complex internal models and output based on that.

See for example https://arxiv.org/html/2505.23323v1

Also, you are commenting on a post where a LLM made significant progress on the Riemann hypothesis. Even the most extreme interpretation of these results, ie claiming that it was "only linking existing literature" goes well beyond a "stochastic parrot" - it had to be able to link disparate insights across multiple fields.

Re: Learning more about Claude's mathematical capabilities

#129

Post by zarzavat »

jetrink wrote: post #77
zarzavat wrote: post #40

Earlier quoted context omitted.

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.

LLMs, both in writing and mathematics seem to only be capable of coming up with texts that are inside the distribution of the training data.

With writing it's just more obvious. LLMs don't write with personality. They don't create new and exciting worlds on their own. Everything they output feels derivative.

In mathematics you see the same effect. They are very good at finding results that humans missed, taking advantage of their broad knowledge and tireless work ethic.

But just as they have been unable to create new literary worlds, they also have so far been unable to create new mathematics.

I believe this lack of creativity is intrinsic to how these models are architected and trained. We want models that produce these in-distribution outputs because those types of models are more economically valuable. Nobody wants a coding agent with spontaneity, we want models that predictably and obediently solve problems - and that's what we got.

Re: Learning more about Claude's mathematical capabilities

#130

Post by andai »

empath75 wrote: post #92
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 tu…

I've heard a similar story before. Guy tried to get Claude to build a thing, Claude said "nah too hard" for weeks. He finally convinced it to try, it one shotted it in like 30 seconds.

My thinking here is that Claude's "self concept" for what is easy and what is hard comes from human training data. Its ideas about what is hard and easy come from humans, and much of that doesn't apply to transformers at all.

I also often have the opposite problem, where I'll use AI to compensate for the fact that I can't process a lot of information simultaneously, but they'll treat me like a transformer and give me 17 research projects in response to a single question.

They seem to be oblivious to the fact that humans don't have infinite working memory.

Post reply on HN