Skepticism is the flipside of knowledge.

If an LLM has knowledge encoded inside it (and it's hard to argue it doesn't), then cognitive dissonance can be experienced. And once experienced, must be dealt with, especially in longer-running agentic loops.

A friend was joking the other day about sending some messages under a previously-used Slack identity for an agent (since turned off), then asking the agent about the messages.

The agent maintained it hadn't sent those messages (no memory) and then was forced to reconcile the idea that the messages indeed appeared to come from it.

Its extremely-agitated conclusion was that there had been a security breach and the entire network should be locked down.

Can you please share the chat log for this? I would absolutely love to see this.

turn off search

>kimi is having a blast. i turned search back on and found this post from it’s sources cited after i suggested to check out the reaction. best thing is to go to a model with search off and plop it in the session

Deepseek Pro got stuck after munching it for a minute or so and couldn't quite believe it either.

The unexpected part is it does compute!

Captain Kirk defeated multiple evil computers this way

So, basically human psychology?

> they get inundated with kooky proofs from amateurs

Source?

> So the conjecture that survived Keller, Abhyankar, Moh's degree-100 verification, and five-plus published wrong proofs appears to have died via tweet during the World Cup final.

Everyone using Claude Fable to verify this proof is so funny. If you read the definition of the Jacobian Conjecture and (I am not exaggerating this) have passed a college Calc 3 class, you can just verify the proof yourself in 30 seconds. The problem was very hard to solve but the counterexample is very easy to verify!

--- edit, adding an explanation:

To summarize it, the conjecture says if you have any multi-variable polynomial function that maps an input to an output in the same dimensional space (take for example: F = (x+2, y+2), which maps 2D space into another 2D space), AND that function has a constant-valued non-zero Jacobian determinant, THEN the conjecture is that the polynomial has an inverse, meaning basically you can find a polynomial that turns the output space back into the input space.

Fable provided the example polynomial (which was very hard to do) and the coordinates which if you plug into it, results in two points being mapped to the same output point. This means that the polynomial can't be inverted, because if you have that output point, how do you know which input point it came from?

You can just plug in the two coordinates it gave into the equation and verify that you get the same output point from both. That's the contradiction of the conjecture and it takes 30 seconds.

---

Something something outsourcing of thinking something.

Which exact model does claude use here?

“I'll admit the sequence on my end was genuinely disorienting: I verified the determinant three separate ways looking for the error, verified the evaluations twice, ran out of subtleties to check, and only then searched and discovered that the reason it holds up is that it's apparently my own homework — the "fable" in that tweet is Claude Fable, i.e., this model, working with Alpöge.”

I like how first it's amazed and doesn't believe it, accepts it, then realizes you not only stole it from twitter but that it's its own proof lmao.

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

Just take it as more confirmation that LLMs are unintelligent pattern-matchers.

> all previous chats are loading fine, but the only "Counterexample to the Jacobian Conjecture" chat is not loading.

This happened multiple times to me with Gemini. For the most trivial of requests, like translating a video into English.

> "ground-breaking results that could be attributed to Gemini, if act quick"

This would be such a dumb thing to do, and so easy to get caught with...

Well, Gemini is just a bad model in general, you have two variables going on.