Earlier quoted context omitted.
"Implicit search" with pruning?
Why not? Lasker said, “when you see a good move, look for a better one.” That was tree pruning advice for an implicit search.
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Claude Fable produced a counterexample to the Jacobian Conjecture
551–560 of 562 posts
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#552Earlier quoted context omitted.
"Implicit search" with pruning?
Why not? Lasker said, “when you see a good move, look for a better one.” That was tree pruning advice for an implicit search.
Sorry, that's just egregious abuse of terminology. Either you're pruning the branches of a tree (or other graph, potentially) when you're doing a tree search, or you don't do pruning. Specifically advice taking (if that's what you mean) is not pruning.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#553Earlier quoted context omitted.
The model is very capable of checking this counterexample, was my point.
Checking, it how? I mean can you describe the mechanism? How does an LLM "check" that something is (or isn't) a counterexample? Does that involve pattern matching, formal verification or model checking, some other approach?
In this case, the same way I would -- calling out to SymPy.
Once you verify (with SymPy or another CAS, like Mathematica) that the given function has the claimed Jacobian determinant (which involves only taking partial derivatives and taking a determinant) and the given inputs map to the same output (which involves only evaluating polynomials with some inputs), you're done.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#554Earlier quoted context omitted.
This is very interesting to me. Care to share your process?
one agent to write the C code, one agent to write the Agda code, and an agent to bridge the two and make sure that the C code does what the Agda code says it does. https://gitlab.com/igravious/lettuce.git
Sounds cool. Your repo might be private, I can't view it.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#555Earlier quoted context omitted.
Checking, it how? I mean can you describe the mechanism? How does an LLM "check" that something is (or isn't) a counterexample? Does that involve pattern matching, formal verification or model checking, some other approach?
In this case, the same way I would -- calling out to SymPy. Once you verify (with SymPy or another CAS, like Mathematica) that the given function has the claimed Jacobian determinant (which involves only taking partial derivatives and taking a determinant) and the given inputs map to the same output (which involves only evaluating polynomials with some inputs), you're done.
Why do people on this site always barge in when someone is having an argument and move the goalposts? That's not at all what the OP said.
Besides which you have no idea whether that's how the Jacobian conjecture counterexample was verified. Nobody does because no details were released.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#556Earlier quoted context omitted.
With what accuracy? And with how many intermediate tokens? We can replace multiplication with any class of problems which should go from 0->100% solution almost immediately if there was actually a concept learned. There is not. Because they are plain ol' fits. And there are no "emergent" features that pop out without having a sufficient set, where "sufficient" is absolutely gigantic and equivalent to memorizing enoug…
> With what accuracy? And with how many intermediate tokens? So you are arguing here that LLMs should just "know" the result of a multiplication when the operands are in context, ie, that a hidden multiplier circuit should emerge in their weights. Is this how you do multiplication, if I give you two 12 digit numbers, does the 24 digit multiplication result just pop in your head? Don't you have to follow a learned alg…
They don't. "Emergence" is some ridiculous hype that a bunch of kids with money peddled to get valuations.
And yes, if "emergence" and the "there's something else going in there!" ridiculousness was true, there would be some other architecture which can do more than its symbol prediction.
Everyone can see the code. Everyone can see the math. Everyone can see the failures of the claims. And there's now about 5 years of everyone watching the lies come undone one-by-one.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#557Earlier quoted context omitted.
No one can figure out where you're coming from here. If the human solved a significant open problem without relying on AI, don't you think they'd have claimed the credit for themselves? The suggestion that a human, working at Anthropic or elsewhere, did the hard work needed to disprove the Jacobian Conjecture yet chose to claim falsely that their AI did it, amounts to an extraordinary accusation that requires extraor…
I guess? But I didn't say anything like that. >> No one can figure out where you're coming from here. No, I think it's just you and I think that's because you have preconceived ideas about the only possible positions that people can assume in this debate. I'm sorry, of course, because that's not conducive to productive dialogue, but it's not my fault. I think what I wrote so far is very simple, no technical jargon, n…
I'm a research mathematician.
I can see that you're arguing in good faith, and indeed I have a lot of respect for anyone willing to argue an unpopular position. That said, I do find your suggestion to be completely farfetched.
The Jacobian Conjecture was one of the most notorious open problems in algebraic geometry, something that generations of grad students have daydreamed of solving. I've seen more immediate buzz around the Jacobian conjecture than around any other mathematical breakthrough of the last five years, at least. For example Terry Tao, arguably the most famous mathematician in the world, dropped what he was doing to study Alpoge/Fable's counterexample in detail, and wrote this blog post:
https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the...
For Alpoge to have solved it on his own, and then falsely claim to have used AI? That's like an athlete winning an Olympic gold medal, and then falsely claiming to have cheated and used illegal steroids. I agree that it's not completely out of the question, but it's beyond the bounds of human behavior that I can reasonably fathom.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#558Earlier quoted context omitted.
And my point is it’s a strawman. Advanced math is obviously creative to those who practice it, and it’s disingenuous to boil it down to grade school triangle proofs That would be like saying Shakespeare isn’t creative , since grade school grammar doesn’t feel creative
I have at least some level of experience with advanced maths, but the thing that always struck me was how amenable to automation that a lot of it seemed. While it might be creative for a human to come up with the Schreier refinement theorem, for example, I don't think it fundamentally requires creativity. On some level, I think the most straightforwardly creative work in maths comes from building up useful generaliza…
Sure in the same way you could automate Shakespeare plays by having a room full of monkeys with typewriters.
The space of mathematical statements is infinite. Having the taste, insight, and creativity to reach points in that space that are meaningful to humans is the entire game
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#559Earlier quoted context omitted.
I attempted that. In videos from the last year the only things I could find were some people protesting ICE, A person accusing a mayor of sexual assault, some republican party events with protestors, and a few of people speaking out of turn being walked off by security. Without the specific examples you described I have no idea what you are talking about. It is either sufficiently old that it could be considered an i…
I believe that I have witnessed at least 3 videos of americans being forcibly removed from town halls for speaking out against data centers. you are correct that search engines are not showing anything at all when searching for data centre forced removal. it took me ten minutes to find the most recent example from my memory[0]. something strange is happening, and when I see you act ostensibly in support of the side t…
Seems a lot like you want me to accept your "unverifiable personal anecdote" about these videos...
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#560Earlier quoted context omitted.
I believe that I have witnessed at least 3 videos of americans being forcibly removed from town halls for speaking out against data centers. you are correct that search engines are not showing anything at all when searching for data centre forced removal. it took me ten minutes to find the most recent example from my memory[0]. something strange is happening, and when I see you act ostensibly in support of the side t…
Seems a lot like you want me to accept your "unverifiable personal anecdote" about these videos...
i referred that way to the other commentor's anecdotes. regarding my end i provided evidence, and you can see other commentors in the same thread who also claim to have seen what i claim to have seen. maybe you misread the thread. either way, may things get better for you soon.