6 ms·

Maybe, maybe not. The "proofs" may not have helped at all with finding a counterexample. Either way, it doesn't matter. A counterexample was found, no one found

by rowbin 2mo ago

Maybe, maybe not. The "proofs" may not have helped at all with finding a counterexample. Either way, it doesn't matter. A counterexample was found, no one found one before even though clearly a lot of people have tried who also had access to the prior "proofs".

ignoramous 2mo ago
This makes me wonder, what if anyone uses Fable-class LLM and passes of its novel results as their own work? There's no shortage of folks doing that in software, right now.
- semi-extrinsic 2mo ago
  Currently there seems to be very little anti-AI bias in maths, and more of a "huh, cool new toy, let's see what it can do" vibe.
  - IngoBlechschmid 2mo ago
    Strongly depends on the subbubble of mathematics. In some parts of type theory / formal proofs for instance, there is a rather strong rejection of LLMs (for moral reasons in addition to quality reasons). The proof assistant Agda was even forked for this reason: https://types.pl/@amy/116522250630340534 https://types.pl/@amy/116522250630340534
- aurareturn 2mo ago
  I think everyone assumes most, if not all of the code written in a piece of new software is done by AI.
cornholio 2mo ago
I think it's becoming harder and harder to argue that LLMs don't really reason and just mimicry human speech. This counterexample is clearly the result of a sequence of steps that build on previous knowledge in context and logically combine it to reach other true statements - to a degree and complexity that rivals the best human minds. For someone that use Claude Code every day, this is obvious, but for some reason many scientists refuse to accept that it's truly reasoning; perhaps not in the human sense, but in a very profound and real sense. These powerful results are devastating to their point of view. I can sympathize, because I too called LLMs "fancy Markov chains" in the GPT 3 era. But there comes a time where you have to update your world view to match reality, or be stranded in fantasy land.
- TeriyakiBomb 2mo ago
  I disagree. It's still extremely possible to "google whack" an LLM on a topic with little publicly available information. If you ask questions about APIs in desktop software, say something like Houdini, it'll produce a bunch of non-sequiturs. A lot of that knowledge lives offline in VFX studios, but it's just some fairly run of the mill python API stuff. You'd expect it to do better. Similarly I've run into several "you just gotta know" type problems where LLMs still just fail. My favourite was a quirk in how async relationships work inside emberjs. Three different models gave a variation of the same incorrect answer. When I searched myself, I initially came up with nothing and eventually found what I think might be the only example of the same issue on the internet, a single stack overflow question wth two responses. The first is what Claude, gemini and chatGPT said, the second response was the OP saying it was wrong. I asked in the Ember discord and a core team member responded instantly with the answer. There's a video I love on Youtube, where a guy uses ML to assemble a blank jigsaw. It performs amazingly, the jigsaw being blank is of no consequence and if it did have an image, it'd perform worse. That's all LLMs do. Just because the jigsaw pieces are smaller, they're still just getting assembled in whatever way fits, there's no mechanic for interpreting the image on the front.
- abernard1 2mo ago
  I think this is actually a perfect case of an impressive thing being done exactly by mimicry. Why do LLMs still have trouble on floating point math without forking out to a tool, but they can perform symbolic manipulation just fine? Because symbolic manipulation is just rote work and textual stepping through symbols. A side poster commented on the number of prior attempts on this problem which were close, but not quite. Starting from a known "close" solution (which this did), and using exploration to search around the space is exactly something an LLM would and could be good at (clearly). The "transformer LLMs are next-token predictors with some in-GPU processing of bounded complexity with respect to token count" remains undefeated. Both because that is mathematically what they are, and also because we don't have counterexamples to that effect that don't require some higher-order tooling wrapping the systems. Symbol manipulation is what LLMs are good at.
  - cornholio 2mo ago

by rowbin 2mo ago

ignoramous 2mo ago

This makes me wonder, what if anyone uses Fable-class LLM and passes of its novel results as their own work? There's no shortage of folks doing that in software, right now.

semi-extrinsic 2mo ago
Currently there seems to be very little anti-AI bias in maths, and more of a "huh, cool new toy, let's see what it can do" vibe.
- IngoBlechschmid 2mo ago
  Strongly depends on the subbubble of mathematics. In some parts of type theory / formal proofs for instance, there is a rather strong rejection of LLMs (for moral reasons in addition to quality reasons). The proof assistant Agda was even forked for this reason: https://types.pl/@amy/116522250630340534 https://types.pl/@amy/116522250630340534
aurareturn 2mo ago
I think everyone assumes most, if not all of the code written in a piece of new software is done by AI.

cornholio 2mo ago

I think it's becoming harder and harder to argue that LLMs don't really reason and just mimicry human speech. This counterexample is clearly the result of a sequence of steps that build on previous knowledge in context and logically combine it to reach other true statements - to a degree and complexity that rivals the best human minds. For someone that use Claude Code every day, this is obvious, but for some reason many scientists refuse to accept that it's truly reasoning; perhaps not in the human sense, but in a very profound and real sense. These powerful results are devastating to their point of view. I can sympathize, because I too called LLMs "fancy Markov chains" in the GPT 3 era. But there comes a time where you have to update your world view to match reality, or be stranded in fantasy land.

TeriyakiBomb 2mo ago
I disagree. It's still extremely possible to "google whack" an LLM on a topic with little publicly available information. If you ask questions about APIs in desktop software, say something like Houdini, it'll produce a bunch of non-sequiturs. A lot of that knowledge lives offline in VFX studios, but it's just some fairly run of the mill python API stuff. You'd expect it to do better. Similarly I've run into several "you just gotta know" type problems where LLMs still just fail. My favourite was a quirk in how async relationships work inside emberjs. Three different models gave a variation of the same incorrect answer. When I searched myself, I initially came up with nothing and eventually found what I think might be the only example of the same issue on the internet, a single stack overflow question wth two responses. The first is what Claude, gemini and chatGPT said, the second response was the OP saying it was wrong. I asked in the Ember discord and a core team member responded instantly with the answer. There's a video I love on Youtube, where a guy uses ML to assemble a blank jigsaw. It performs amazingly, the jigsaw being blank is of no consequence and if it did have an image, it'd perform worse. That's all LLMs do. Just because the jigsaw pieces are smaller, they're still just getting assembled in whatever way fits, there's no mechanic for interpreting the image on the front.
abernard1 2mo ago
I think this is actually a perfect case of an impressive thing being done exactly by mimicry. Why do LLMs still have trouble on floating point math without forking out to a tool, but they can perform symbolic manipulation just fine? Because symbolic manipulation is just rote work and textual stepping through symbols. A side poster commented on the number of prior attempts on this problem which were close, but not quite. Starting from a known "close" solution (which this did), and using exploration to search around the space is exactly something an LLM would and could be good at (clearly). The "transformer LLMs are next-token predictors with some in-GPU processing of bounded complexity with respect to token count" remains undefeated. Both because that is mathematically what they are, and also because we don't have counterexamples to that effect that don't require some higher-order tooling wrapping the systems. Symbol manipulation is what LLMs are good at.
- cornholio 2mo ago