4 ms·

I doubt Anthropic will share the details (or at least the full true details). The mystery of the magic makes for much better marketing. I think a reasonable as

by castedo 2mo ago

I doubt Anthropic will share the details (or at least the full true details). The mystery of the magic makes for much better marketing. I think a reasonable assumption is that there is an interaction between an LLM, a https://en.wikipedia.org/wiki/Computer_algebra_system https://en.wikipedia.org/wiki/Computer_algebra_system tool, a human prompting with deep math expertise, and lots of compute that explains hitting upon the remarkable cancellation.

p-e-w 2mo ago
> a human prompting with deep math expertise The original tweet implied that the whole thing was done while the author was watching the World Cup final. I know it’s tempting to hope that a human did the “real” work here, but if some special insight was put into prompting, the author kept it to himself, and there is no reason why they would hide this since it would elevate their own status.
- monster_truck 2mo ago
  I don't think it is as much about 'real' work or a special insight as it is being willing to push back multiple times, or simply asking in a way that steers it towards actually 'giving enough of a fuck' to even bother. We tend to be ~blind to how differently we would ask about something we know compared to a novice, this is what makes some better teachers than others. Have encountered a similar flavor in programming, wrote it off until I saw someone point out how garbage in garbage out they tend to be. If you hand any frontier model dogshit and ask it to do something simply, the result is often not great. But! If you spend 20 minutes having it comb through and clean up with something like jscpd, then tell it to step through with a debugger, gather profiling traces, etc... very likely it will yield meaningful improvements or catch some corner cases. If it doesn't, anyone with experience is going to tell it to try something else, or that it isn't good enough, as opposed to accepting the first result. You can recreate this by disabling web search and asking a model about the conjecture and then giving it his post. I've tried a few and their initial responses range from "this is a meme I'm not even going to verify it" to vaguely insulting chains of thought, concerns about the need to be careful because you're clearly nuts or stupid, then falling back on remedial explanations. After a few nudges they all eventually work through it, accept it, and apologize. IMO its reasonable to imagine a situation where someone is having a beer or two watching The Big Game, asking an LLM to do something stupid for fun and landing somewhere like this on the magic jump to conclusions mat.
- castedo 2mo ago
  I know it's temping to hope there is a single simple factor that does the "real" work, but this feat of mathematics is likely best explained by multiple interacting factors, one of them being the mathematical insights of the human mathematician that tweeted the counterexample. I don't doubt that an LLM is also one of the multiple factors. It is premature to assume the author is not going to share more information in the future about the mathematical insights to narrow down the search space for this counterexample.
jasonfarnon 2mo ago
Not just an assumption, I saw the LLM saying it used sympy.
- deleted 2mo ago
  [deleted]
tptacek 2mo ago
I think you can reasonably assume that frontier models are using SymPy or something like it any time interesting math gets into the picture, and the person driving Fable here is an accomplished mathematician, but I don't think we can reasonably assume either extensive prompting or brute-force compute in any sense other than what it normally takes Fable to, say, whip up a calculator app.
- somenameforme 2mo ago
  The two big discoveries both came from the negligible handful of mathematicians working at OpenAI/Anthropic in spite of many orders of magnitude more mathematicians using them outside of the companies. I don't see any way to explain this without assuming that the limiting factor is the ability to burn a few rainforests worth of tokens in pursuit of something publishable. I think it would also explain their opacity towards the process. Being able to solve such well known problems in a nice replicable 1-2-3 way would be far more effective marketing than their complete opacity outside of the result, which suggests that they feel transparency is not in their best interest for some reason.
  - tptacek 2mo ago
    Would you ordinarily be able to "explain this", if a mathematician had come up with this on their own? How would that story go?
    - somenameforme 2mo ago
      Bayesian probability. Were outcomes being driven by 'normal' usage of LLMs then it's extremely improbable that both big discoveries would come from the small number of people working at the companies. That suggests working at the companies is more the decisive factor than the LLMs in and of themselves. And what do you get from working at the company? Likely a rather massive token/processing budget. The companies opacity towards the path to these discoveries also makes this further probable as 'spend millions of dollars in tokens' is a somewhat less attractive narrative than the implied narrative of 'just use Fable.'
  - 2mo ago
impendia 2mo ago
I have no idea what actually happened behind the scenes, but the human prompter, Levent Alpöge, indeed has deep math expertise. Princeton PhD, Harvard postdoc, and some excellent research (prior to this) to his name. https://alpo.ge/ https://alpo.ge/
vatsachak 2mo ago
Yeah more or less. I proved a SOTA result using Gemini 3.1 Pro a year ago and it was a lot of back and forth. We're definitely still in the computer chess phase.

by castedo 2mo ago

p-e-w 2mo ago

> a human prompting with deep math expertise The original tweet implied that the whole thing was done while the author was watching the World Cup final. I know it’s tempting to hope that a human did the “real” work here, but if some special insight was put into prompting, the author kept it to himself, and there is no reason why they would hide this since it would elevate their own status.

monster_truck 2mo ago
I don't think it is as much about 'real' work or a special insight as it is being willing to push back multiple times, or simply asking in a way that steers it towards actually 'giving enough of a fuck' to even bother. We tend to be ~blind to how differently we would ask about something we know compared to a novice, this is what makes some better teachers than others. Have encountered a similar flavor in programming, wrote it off until I saw someone point out how garbage in garbage out they tend to be. If you hand any frontier model dogshit and ask it to do something simply, the result is often not great. But! If you spend 20 minutes having it comb through and clean up with something like jscpd, then tell it to step through with a debugger, gather profiling traces, etc... very likely it will yield meaningful improvements or catch some corner cases. If it doesn't, anyone with experience is going to tell it to try something else, or that it isn't good enough, as opposed to accepting the first result. You can recreate this by disabling web search and asking a model about the conjecture and then giving it his post. I've tried a few and their initial responses range from "this is a meme I'm not even going to verify it" to vaguely insulting chains of thought, concerns about the need to be careful because you're clearly nuts or stupid, then falling back on remedial explanations. After a few nudges they all eventually work through it, accept it, and apologize. IMO its reasonable to imagine a situation where someone is having a beer or two watching The Big Game, asking an LLM to do something stupid for fun and landing somewhere like this on the magic jump to conclusions mat.
castedo 2mo ago
I know it's temping to hope there is a single simple factor that does the "real" work, but this feat of mathematics is likely best explained by multiple interacting factors, one of them being the mathematical insights of the human mathematician that tweeted the counterexample. I don't doubt that an LLM is also one of the multiple factors. It is premature to assume the author is not going to share more information in the future about the mathematical insights to narrow down the search space for this counterexample.

jasonfarnon 2mo ago

Not just an assumption, I saw the LLM saying it used sympy.

deleted 2mo ago
[deleted]

tptacek 2mo ago

I think you can reasonably assume that frontier models are using SymPy or something like it any time interesting math gets into the picture, and the person driving Fable here is an accomplished mathematician, but I don't think we can reasonably assume either extensive prompting or brute-force compute in any sense other than what it normally takes Fable to, say, whip up a calculator app.

somenameforme 2mo ago
The two big discoveries both came from the negligible handful of mathematicians working at OpenAI/Anthropic in spite of many orders of magnitude more mathematicians using them outside of the companies. I don't see any way to explain this without assuming that the limiting factor is the ability to burn a few rainforests worth of tokens in pursuit of something publishable. I think it would also explain their opacity towards the process. Being able to solve such well known problems in a nice replicable 1-2-3 way would be far more effective marketing than their complete opacity outside of the result, which suggests that they feel transparency is not in their best interest for some reason.
- tptacek 2mo ago
  Would you ordinarily be able to "explain this", if a mathematician had come up with this on their own? How would that story go?
  - somenameforme 2mo ago
    Bayesian probability. Were outcomes being driven by 'normal' usage of LLMs then it's extremely improbable that both big discoveries would come from the small number of people working at the companies. That suggests working at the companies is more the decisive factor than the LLMs in and of themselves. And what do you get from working at the company? Likely a rather massive token/processing budget. The companies opacity towards the path to these discoveries also makes this further probable as 'spend millions of dollars in tokens' is a somewhat less attractive narrative than the implied narrative of 'just use Fable.'
- 2mo ago

impendia 2mo ago

I have no idea what actually happened behind the scenes, but the human prompter, Levent Alpöge, indeed has deep math expertise. Princeton PhD, Harvard postdoc, and some excellent research (prior to this) to his name. https://alpo.ge/ https://alpo.ge/

vatsachak 2mo ago

Yeah more or less. I proved a SOTA result using Gemini 3.1 Pro a year ago and it was a lot of back and forth. We're definitely still in the computer chess phase.