521–530 of 562 posts
the conjecture held for 85 years and the counterexample was announced in a format that expires after seven days
The surprising thing is that the counterexample seems relatively "simple" in that it's low degree, with coefficients that aren't too large. Does anyone more familiar with this know why this _wasn't_ found earlier, when it seems like you could brute-force through some low-order polynomials?
I am a number theorist and a graduate math student at Bonn. It is eery to see that all of a sudden everyone cares about pure math. Anyhow, I think such incidents like this one are only to happen more often in the coming days, and while many mathematicians are concerned about their role in the community; I believe since we are still very early stages of AI-driven discovery, we still need the appropriate infrastructure…
At least the fact that frontier models are not optimized primarily on formal math reasoning is in itself is good for not putting mathematicians out of their jobs, isn't it?
How do these results (and the future painted by them) affect your profession; do you expect a similar route as in software, where junior developers are unemployable, LLM-assisted development is the norm, and that great developers stand out partly through better communication with their managers?
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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 "…
> 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 d…
Can I see it?
No.
I am a number theorist and a graduate math student at Bonn. It is eery to see that all of a sudden everyone cares about pure math. Anyhow, I think such incidents like this one are only to happen more often in the coming days, and while many mathematicians are concerned about their role in the community; I believe since we are still very early stages of AI-driven discovery, we still need the appropriate infrastructure…
> without which, these discoveries do not help much at advancing the field, At least the fact that frontier models are not optimized primarily on formal math reasoning is in itself is good for not putting mathematicians out of their jobs, isn't it? How do these results (and the future painted by them) affect your profession; do you expect a similar route as in software, where junior developers are unemployable, LLM-a…
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> and yet the counter example is something a grad student in 1997 could have found w a ~3 day computer search Is that true? Even restricting this to f(x,y,z) and coefficients and powers to 1 ≤ x ≤ 10, there are a lot of polynomials to check, and checking requires checking the Jacobian determinant and, if it’s a non zero constant, finding two points for which the polynomial produces the same value. Or is there a way t…
I mean you’d probably just generate random low descriptive length f(x,y,z), check for a const determinant then poke for invertibility. Be fun to ask Fable to write a search program to find more counter examples using only early grad theory to guide the search.
That’s true, but for “a ~3 day computer search”, it seems you would have had to be extremely lucky to find a counterexample. Might have had more chance playing the lottery.
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i'm doing the same thing but for type theory
This is very interesting to me. Care to share your process?
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I fed it to Google AI Studio, enabling tool execution and disabling web access. It also quickly verified it with SymPy, then went into psychosis. 5 minutes later: all previous chats are loading fine, but the only "Counterexample to the Jacobian Conjecture" chat is not loading. Well, I'm not a conventional conspiracy theorist. But everyone knows that in every major LLM provider there are hell of hidden guarding system…
> 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...
Based on what I see of American politics, it seems like the thing to do, then!
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Accuse the enemy of propaganda; insist there's plenty of evidence without linking a single source... Have you considered maybe reading this comment out loud in front of a mirror?
umm have you considered that you can go to youtube and verify my claim whereas the other interlocutor explicitly refers to unverifiable personal anecdotes? and did you want to verify that I explicitly accused someone of propaganda?
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 isolated incident if no more recent incidents have since occurred, or it is considerably harder to find than you imagine.