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A digestion of the Jacobian conjecture counterexample

terrytao.wordpress.com

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Re: A digestion of the Jacobian conjecture counterexample

#11

Post by hyperhello »

fhdkweig wrote: post #9
greenavocado wrote: post #2

[flagged]

Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?

It will make mistakes if you tell it to, so I assume it will make no mistakes if you tell it not to.

Re: A digestion of the Jacobian conjecture counterexample

#12

Post by minimaxir »

fhdkweig wrote: post #9
greenavocado wrote: post #2

[flagged]

Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?

It's a meme. Telling it to "make no mistakes" doesn't do anything because LLMs don't have an inherent concept of a mistake and they are already RLHFed to code correctly.

However, if you tell it to not do particular behaviors explicitly—some of which would be considered mistakes—it will not do said behaviors and with enough checks and balances, you'll get output without "mistakes".

One example of this from the OpenAI Unit Distance prompt: https://cdn.openai.com/pdf/04d1d1e4-bc75-476a-97cf-49055cd98...

> Do not return merely because current approaches fail or agents report theorem-strength gaps. Continue launching new rounds, reopening blocked approaches only when there is a genuinely new mechanism, and searching for fresh formulations. Return only when a complete affirmative proof has been found and survives adversarial audit.

> Do not return a reduction, partial result, isolated missing lemma, “best effort” summary, or explanation of why the problem is difficult.

Re: A digestion of the Jacobian conjecture counterexample

#13

Post by jewel »

fhdkweig wrote: post #9
greenavocado wrote: post #2

[flagged]

Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?

I believe it's a reference to a joke meme that goes something like "Write Windows 12 from scratch. Make no mistakes." At least that's the first context I heard it in.

Re: A digestion of the Jacobian conjecture counterexample

#14

Post by saganus »

fhdkweig wrote: post #9
greenavocado wrote: post #2

[flagged]

Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?

It's just a meme at this point.

Re: A digestion of the Jacobian conjecture counterexample

#15

Post by alpinisme »

hyperhello wrote: post #10
Jtarii wrote: post #7

Earlier quoted context omitted.

People are upvoting this because Tao is a celebrity.

He’s famous, but I don’t believe he is a celebrity, as he is not famous for his persona.

He’s a hacker news celebrity but not a global celebrity

Re: A digestion of the Jacobian conjecture counterexample

#16

Post by hackinthebochs »

foobarqux wrote: post #4
tptacek wrote: post #3

The introduction to this piece was easy to follow, but as soon as he got into recapitulating it with algebra he lost me (because I'm bad at math). But he includes the GPT5 prompts for his conversation, which are easier to follow: https://chatgpt.com/share/6a5fdc7a-d6f8-83e8-bbea-8deb42cfed...

[flagged]

A news aggregator is a community above all. Upvoting content that you may not personally be interested in but will attract the right people is a net benefit for the community[1].

[1] https://news.ycombinator.com/item?id=44575026

Re: A digestion of the Jacobian conjecture counterexample

#17

Post by pavel_lishin »

Jtarii wrote: post #7
foobarqux wrote: post #4

Earlier quoted context omitted.

[flagged]

People are upvoting this because Tao is a celebrity.

I'm upvoting this because it's interesting. I don't have to fully understand something to find it interesting.

Re: A digestion of the Jacobian conjecture counterexample

#18

Post by vanderZwan »

> While this is an extremely quick verification, the construction presented in this fashion appears like a massive miracle. The polynomial {F} has degree seven, so a priori the Jacobian {\mathrm{det} DF} ought to be a polynomial in three variables of degree as large as {3 \times 6 = 18}, so the fact that all non-constant coefficients of this polynomial vanish looks like a massive cancellation involving {\binom{18+3}{3}-1 = 1329} coefficients, which is much larger than the {\binom{7+3}{3} = 120} degrees of freedom for a generic degree seven polynomial of three variables. So finding such a polynomial looks highly unlikely to be located by brute force.

Sounds like the most interesting part would be learning what approaches the LLM did use to see if that's reusable elsewhere. I'm guessing that's what the rest of the article is about? Because I also couldn't follow the maths any more.

Re: A digestion of the Jacobian conjecture counterexample

#19

Post by greenavocado »

jewel wrote: post #13
fhdkweig wrote: post #9

Earlier quoted context omitted.

Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?

I believe it's a reference to a joke meme that goes something like "Write Windows 12 from scratch. Make no mistakes." At least that's the first context I heard it in.

Precisely

Re: A digestion of the Jacobian conjecture counterexample

#20

Post by none_to_remain »

hyperhello wrote: post #11
fhdkweig wrote: post #9

Earlier quoted context omitted.

Honest question. Does asking "make no mistakes" actually change the output? Does it make mistakes if you don't bother to ask for no mistakes? Is it just to make the human feel more secure?

It will make mistakes if you tell it to, so I assume it will make no mistakes if you tell it not to.

When this news came out I amused myself by asking Claude to prove that 0.999... != 1. First it did so for the hyperreals. To do it for the reals I had to tell it it was allowed to make mistakes, although it didn't end up interestingly wrong - just very fuzzy and vague.
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