OpenAI withdraws three mathematical results

OpenAI withdraws three mathematical results(twitter.com)

38 points by sashank_1509 2 hours ago | 26 comments

rich_sasha 34 minutes ago |

I’m a little confused - I thought their proofs were all driven by Lean proofs - is that not right? So even if the quality of the work is low in some metrics, it either passes the test or not..? No space for changing your mind either way.

autuni 27 minutes ago | |

No, in their original blog they wrote:

> As part of our GitHub repository, we are sharing formalizations of many of the proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer. We will update the repository with more formalizations as we obtain them.

Meaning they published all results before checking all of them, and intended to add more Lean proofs later. In the linked post they state ~42% of the posted results now have formalized proofs, some were added, some verified, and I assume this means that some results turned out to be wrong.

mrpopo 22 minutes ago | | |

This is extremely disappointing. It means they are sharing unproven work for PR, forcing the mathematicians community to do the verification job for them, while so-called "accelerationists" surf on the hype and help with the pro-AI propaganda.

If your AI tool can help advance mathematical research, share the tool with mathematicians. Using it like this is irresponsible.

"AI will kill us all": no. Greedy humans will kill us all. With AI.

AlanYx 28 minutes ago | |

Only a subset contain Lean formalizations. And even for that subset, there's the potential that the formalization is semantically off (that is, it's a formalization for a slightly different problem).

stavros 29 minutes ago | |

If you wrote twenty million lines of Lean to verify something, my suspicion is you've been fuzzing the Lean solver rather than coming up with new math.

rich_sasha 27 minutes ago | | |

Well, fine - but my understanding is, if a fuzz-generated Lean proof is correct, that’s end of story. It can’t be “incorrect” if it “passes”.

You might think this is not very useful, maybe - but that’s not a reason to retract..?

Thorentis 16 minutes ago |

How do we even know the premises of the "verified" Lean proofs are correct? The more I think about these results, the more I'm convinced this is like a junior engineer who writes 100 unit tests and shares a screenshot of Pytest being all green, but you check the code and most of them are just doing assert True.

nryoo 35 minutes ago |

Were the withdrawn ones actually Lean-checked or not? seems like that matters

samrus 31 minutes ago |

How? What about the lean verification?

ekjhgkejhgk 1 hour ago |

Just the other day I was thinking, if unsupervised maths will descend into "oops we found a bug in some code, branch XYZ of maths is no longer true".

literalAardvark 46 minutes ago | |

If you go far enough to the edge that's already how math works, since everything is very interpretation-sensitive.

There is however a new problem of scale. Erdös was a human and still managed to create work for an entire generation of mathematicians, how much of a mess will an automathician create?

doginasuit 34 minutes ago | | |

> automathician

I vote for "automathon"

jjgreen 47 minutes ago | |

c.f. Italian differential geometry

rapsey 42 minutes ago | |

Sure but if the results have practical implications then the validity will be self evident. If they do not, not much of consequence has been lost.

Interesting that math gets so much attention, when actual advances to material science, biology and chemistry have much higher ramifications and economic benefits. I assume progress there is kept under wraps until they can capture the economic benefits. If they can do that, then the insane valuations may actually be valid.

plastic-enjoyer 32 minutes ago | | |

> I assume progress there is kept under wraps until they can capture the economic benefits. If they can do that, then the insane valuations may actually be valid.

Or progress is not as straight forward in those fields as in math.

sashank_1509 2 hours ago |

Early sentiments are a lot of the write ups still read like slop and it feels very rushed and not very polished.

illwrks 1 hour ago | |

I wonder if the issue is that not many people within OpenAI can validate the output. Therefore what reads well looks good, and then was published.

If that’s the case in a way its a similar delusion that average people are experiencing with their own AI use.

IsTom 27 minutes ago | | |

I've tried reading one of these, it was an unreadable mess with some strong smells. It might have something to it, but it'd take a decent amount of labor to validate it, especially with how many references to other papers it had.

ssfdg 48 minutes ago | | |

This is almost certainly the case. I very much doubt that anyone there of any importance in the decision-making process around this actually cares about the math, just the headlines they can get from pushing it out.

SequoiaHope 47 minutes ago | | |

I am certainly experiencing what seems like some mania or computer addiction from these technologies. I’ve never been able to produce such results as I can today. I lose sleep staying up late working on it (though to be fair this has always been an issue). But the volume of work is so hard to audit. It makes it difficult to make flawless results. That doesn’t excuse the mode of publication. They could have had humility in their announcement. “We are seeing some interesting results and seeking community validation.” Maybe they did, I did not read their full announcement. But that would have been the right move if they can’t verify something fully.

bbor 13 minutes ago | |

Yes, of course. Wasn't that the whole point? To get more humans involved earlier in the process, with more transparency?