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Claude Fable produced a counterexample to the Jacobian Conjecture

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Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#311

Post by ethbr1 »

siddboots wrote: post #243
aizk wrote: post #112

This is a rare instance where feeding this groundbreaking information into an LLM gives _them_ psychosis. I fed this to claude code and watched it verify the result in 7 different ways to be 100% certain, and it was just flabbergasted. Quite remarkable.

I fed ChatGPT the map with no other context, just “tell me about this function”. It did a bit of work finding the Jacobean etc and eventually worked out the implications of what it was seeing. It then proceeded to check the arithmetic 4 times, and then decided to do a manual verification using an ad hoc symbolic checker in case its SymPy had been tampered with.

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.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#312

Post by aleph_minus_one »

tptacek wrote: post #61
rowbin wrote: post #55

Earlier quoted context omitted.

Maybe have a seasoned mathematician check if the counterexample is really bogus before saying people fell for ai psychosis.

I'm pretty sure you can just check this for yourself. The Sage POC is like 8 lines.

This assumes that you already have Sage installed, and you have some working knowledge in using Sage.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#314

Post by david-gpu »

InsideOutSanta wrote: post #298
0x1ceb00da wrote: post #284

Earlier quoted context omitted.

> some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization Why do you trust a random stranger so much? Will you hand over your car keys to a random stranger? Sharing the chat will take 30s of their time. > There's no reason to think that it won't provided if asked for But they didn't provide it.

If I came up with this counterexample, I sure as hell wouldn't give credit to Claude.

Indeed, the incentive is the opposite: hiding the fact that they used an AI would boost their own personal brand.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#315

Post by pedrocr »

civilchaos wrote: post #258

Because they've been proven equivalent, so too fall the Poisson Conjecture and the Dixmier Conjecture

That gave me something to play with with these models and this came out as a claimed disproof of the Dixmier Conjecture:

https://gist.githubusercontent.com/pedrocr/51157b9b2eed8152e...

It seems mathematics has at least gotten a powerful new tool to automate the work to cascade results after breakthroughs are made.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#316

Post by Lockal »

aizk wrote: post #112

This is a rare instance where feeding this groundbreaking information into an LLM gives _them_ psychosis. I fed this to claude code and watched it verify the result in 7 different ways to be 100% certain, and it was just flabbergasted. Quite remarkable.

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 systems that mark users and dialogues based on content (for topics about national security, biology, security, adult topics, etc.) - so there is a small chance a CEO of Google is now receiving a dozens of notifications about "ground-breaking results that could be attributed to Gemini, if act quick". So if any of thousands researchers have ever submitted this polynomial to Claude previously, any Anthropic employee can accidentally or intentionally "rediscover" the result of other researcher (and even hide the traces by deleting a dialogue of other user).

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#317

Post by cma »

Redoubts wrote: post #286
z7 wrote: post #285

> The incredible Yitan Zhang ( https://newyorker.com/magazine/2015/02/02/pursuit-beauty ) worked on proving this conjecture for 7 years. Moh, his advisor, wrote that Zhang "failed miserably" in proving the Jacobian conjecture, "never published any paper on algebraic geometry" after leaving Purdue, and "wasted seven years of his own life and my time". https://x.com/aminkarbasi/status/2079129649830137989 https://en.wik…

Zhang, Yitang’s life at Purdue (Jan 1985-1991) T.T.Moh - https://www.math.purdue.edu/~ttm/ZhangYt.pdf kind of a wild document to exist...

Interestingly: "For logic proof, it had been thought that AI could handle all logic problems in the near future, hence logic problems of solving conjectures might not be so interesting in the future."

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#318

Post by William_BB »

eru wrote: post #287
William_BB wrote: post #282

Earlier quoted context omitted.

There's a big difference between one shotting a counterexample using AI and using AI to find a counter-example by brute-force. Both are impressive, of course, but they're hardly comparable.

I'm not so sure. People had been trying to use brute force to find counterexamples before.

AI is great at reducing the search space and using human-like reasoning (in a brute-force way) to carry out the brute-force search. I'm not surprised by this result. This is exactly what AI should excel at, with human guidance.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#319

Post by auggierose »

rowanG077 wrote: post #251
auggierose wrote: post #247

Earlier quoted context omitted.

Or we just don't use LEAN but something better.

Does anything truly better exist? I'm not a mathematician but I did use Rocq and Lean during university. And I found lean to be better.

No, something truly better does not exist yet, but that doesn't mean that it won't. Lean is young compared to Isabelle or Rocq, but actually quite old in absolut terms (and especially in AI terms).

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#320

Post by TimorousBestie »

Redoubts wrote: post #286
z7 wrote: post #285

> The incredible Yitan Zhang ( https://newyorker.com/magazine/2015/02/02/pursuit-beauty ) worked on proving this conjecture for 7 years. Moh, his advisor, wrote that Zhang "failed miserably" in proving the Jacobian conjecture, "never published any paper on algebraic geometry" after leaving Purdue, and "wasted seven years of his own life and my time". https://x.com/aminkarbasi/status/2079129649830137989 https://en.wik…

Zhang, Yitang’s life at Purdue (Jan 1985-1991) T.T.Moh - https://www.math.purdue.edu/~ttm/ZhangYt.pdf kind of a wild document to exist...

The document says more about the kind of advisor Moh was than the kind of mathematician Zhang is.
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