Counterexample to Jacobian conjecture:
((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0)
GPT wrote some SymPy code to check it. The response?
"As written, this is an explicit counterexample to the Jacobian conjecture. I checked it using exact symbolic algebra.
I do not see an algebraic catch in what you typed. Unless a term or exponent differs from the intended expression, it appears to disprove the conjecture. This deserves serious independent checking rather than casual dismissal."
"Any idiot could have done this, it's just high school calculus and just a counterexample anyway. Stochastic parrot, spicy autocomplete, AI psychosis. Wake me up when an AI does something real."
The great thing about these mathematical mopping up type operations is that no person will waste their time trying to prove it to be true anymore. If anything that’s a win.
It would be great if an LLM could settle the Collatz conjecture next, god knows how many man-years have been burned on that by unsuspecting victims.
The funniest thing about LLMs is the cognitive dissonance they cause people. People clearly recognize (and bemoan) the fact that LLMs produce derivative breathless prose ie they fundamentally fail at "unstructured creativity" (something the might accurately labeled intelligence) but are then shocked that the same LLMs can do math.
It's reasoning from a flawed premise that math universally requires intelligence and creativity. It does not. Anyone that's proved things via "diagram chasing" can affirm that. The conclusion you should draw is that math (at least the kind they excel at) isn't actually a creative endeavor.
>Imagine you had a frozen [large language] model that is a 1:1 copy of the average person, let’s say, an average Redditor. Literally nobody would use that model because it can’t do anything. It can’t code, can’t do math, isn’t particularly creative at writing stories. It generalizes when it’s wrong and has biases that not even fine-tuning with facts can eliminate. And it hallucinates like crazy often stating opinions as facts, or thinking it is correct when it isn't.
>The only things it can do are basic tasks nobody needs a model for, because everyone can already do them. If you are lucky you get one that is pretty good in a singular narrow task. But that's the best it can get.
>and somehow this model won't shut up and tell everyone how smart and special it is also it claims consciousness. ridiculous.
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"As written, this is an explicit counterexample to the Jacobian conjecture. I checked it using exact symbolic algebra.
I do not see an algebraic catch in what you typed. Unless a term or exponent differs from the intended expression, it appears to disprove the conjecture. This deserves serious independent checking rather than casual dismissal."
Waiting for someone to write the Lean proof.
> The Jacobian conjecture is notorious for the large number of published and unpublished proofs that turned out to contain subtle errors.
https://en.wikipedia.org/wiki/Jacobian_conjecture#cite_note-...
I have no idea what any of this stuff even means, but my AI thinks I’m a legend level mathematician!
It would be great if an LLM could settle the Collatz conjecture next, god knows how many man-years have been burned on that by unsuspecting victims.
https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...
It's reasoning from a flawed premise that math universally requires intelligence and creativity. It does not. Anyone that's proved things via "diagram chasing" can affirm that. The conclusion you should draw is that math (at least the kind they excel at) isn't actually a creative endeavor.
Highly relevant comment <https://np.reddit.com/r/singularity/comments/1jh9c90/why_do_...>:
>Imagine you had a frozen [large language] model that is a 1:1 copy of the average person, let’s say, an average Redditor. Literally nobody would use that model because it can’t do anything. It can’t code, can’t do math, isn’t particularly creative at writing stories. It generalizes when it’s wrong and has biases that not even fine-tuning with facts can eliminate. And it hallucinates like crazy often stating opinions as facts, or thinking it is correct when it isn't.
>The only things it can do are basic tasks nobody needs a model for, because everyone can already do them. If you are lucky you get one that is pretty good in a singular narrow task. But that's the best it can get.
>and somehow this model won't shut up and tell everyone how smart and special it is also it claims consciousness. ridiculous.