Interestingly, even Qwen 3.6 27B was able to verify the solution, but I didn't get any glazing for discovering it. Instead, it thought that someone named Shestakov had already found a counterexample in 2004.

GLM 5.2 whiffed, it insisted the counterexample wasn't valid.

VibeThinker 3B also recognized that the counterexample was valid. But it kept trying to convince itself that it wasn't, over and over, since it's an "unsolved problem." Eventually it just answered "-2."

I told Gemini Pro I woke up after having dreamt that polynomial and asked if it was related to the Jacobian conjecture. It spent some time thinking and referenced this tweet announcement, saying:

"If you truly dreamt about that specific polynomial, you might be mathematically clairvoyant."

In the rest of the answer, it maintained a cautious skepticism about my claim, saying:

"Here is exactly why the math world is currently scrambling to verify the polynomial you "dreamt" about."

I love how it put "dreamt" in quotes.

Connecting it to a Coding Agent seems much better.

I connected DeepSeek in OpenCode and told it that I dreamed of this counterexample. It called SymPy tools to verify it, said my dream was "surprisingly accurate", and suggested consulting an expert in algebraic sets for independent verification.

Current LLMs behave very counterproductively around unsolved problems, especially if they learned that humans consider them difficult. This has many straight up preventing themselves from attempting anything...

> Matches! This is bizarre. A Jacobian counterexample has been sitting here in a prompt? Wait... is this map a known "fake" counterexample from the literature? Many mathematicians have tried and failed. This specific map might come from a paper or a forum where it was proposed and then debunked. Or... is it actually correct?

Gemma's having trouble accepting it too. A solution?! At this time of year? At this time of day? In this part of the country? Localized entirely within my own prompt?

More anecdata: When I just tried Qwen 3.6 27B (Q6_K_XL) it (ultimately, after a lot of going back and forth) claimed it was not a counterexample and claimed the Jacobian wasn't constant (which I'm guessing is incorrect). It also mentioned a whole bunch of names it attributed the example to, in its thinking trace.

I think vibethinker is heavily overtrained on not attempting to solve open problems.

I had a fun time taking some open problems and disguising them algebraically so that vibethinker 3b would work on them. It managed to prove some interesting things that I didn't know and would be publishable, but for the fact that they already have been. :) (though hard to know if this was because it had been exposed to that knowledge even though it didn't reconize the hidden problem).

Under some maskings it would eventually figure out the problem was equivalent to an open problem then immediately shut down.

It also managed to make some false proofs for various things that duped some other more powerful models.

> that someone named Shestakov had already found a counterexample in 2004.

Qwen has the sprit of a grad student