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Comment by fancyfredbot | Hacker News Reader

When You See One Cockroach, There's Probably More.

This can and should erode our trust in every single proof OpenAI published. The model is clearly faliable despite the lean proof, and clearly the output was't actually checked properly before release. Once these proofs are peer reviewed and published in a journal we might be able to trust them again but until then they are just slop, sadly.

I think OpenAI actually did the right thing by sharing everything with the whole community right now but I also hope that some significant credit will now go to the reviewers who confirm these 'proofs" actually work.

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Fantastic. Let’s also apply this reasoning to math papers written by humans too?

Humans produce flawed Lean proofs. Indeed LLMs were successful at finding and fixing many issues in the “core” standard library if I recall correctly. Humans regularly produce flawed papers and have minor issues require fixing. And when it happens it often isn’t as prompt and clear as this.

Super-intelligence that’s going to end mathematics as we know it surely must be held to a higher standard than puny humans?

More seriously the problem is the complete utter lack of care OpenAI has shown in their desperation to demoralize mathematicians with their new LLM. In their words, it took 3 hours of ChatGPT pro per result, why not spend a hundred hours per result formalizing it, checking if the formalization matches the natural language proof, and whether the argument could be made more simpler and readable. Any human paper has hundreds of hours of work put into it, but OpenAI who is absolutely adamant in demoralizing the mathematical community and demonstrating their superior “intelligence” will only spend 3 hours, write unreadable, inscrutable proofs, not formalize all of them, and then dump it on the mathematical community for some reason.

I think you are implying that my suggestion is unreasonable and exceeds the standards applied to science produced by "normal" human processes.

In fact we already follow exactly this process for human papers and have done for a very long time. Publications without peer review are treated with great suspicion. This is how we end up with journals of varying levels of prestige and rigour.

The process isn't flawless and there are huge problems with retractions, as well as weird financial incentives and rent extraction but there is definitely an increased level of trust in a paper published in Nature.

Undermining your point is that math papers don’t get published in nature and most math papers just go up on arxiv not journals. Are you sure you’re familiar with how academic mathematics works?

I picked Nature because it's the best known academic Journal. I'm aware it's not a mathematical journal. I don't think that undermines my point since mathematical journals obviously exist although they lack name recognition with a general audience.

I am pretty sure that journal publication is the norm. I do know mathematics although I am not one myself. The mathematicans I know want/need journal publications as unpublished research isn't counted in their research output. I know Arxiv is typically used for preprints while awaiting review but publication is always the aim.

Don't take it from me though. zbMath did a study finding 60-70 percent of arxiv papers on math end up in peer reviewed journals. https://ems.press/content/serial-article-files/47210.

> The mathematicans I know want/need journal publications as unpublished research isn't counted in their research output

If they’re untenured sure. Tenured mathematicians care a significantly deal less.

> Don't take it from me though. zbMath did a study finding 60-70 percent of arxiv papers on math end up in peer reviewed journals.

Elite journal capacity didn’t expand. There’s just a bunch of mid-tier journals helping to absorb the increased publishing to help these ~indentured~ untenured professors.

Tenured mathematicians care about publication. My impression is that this is because they believe in the process of peer review. However they also have other incentives as their publication record affects their ability to attract research grants. They also typically share authorship with untenured students and postdocs who need publications for their own Tenure tracks.

You are right that most work gets published in mid tier journals. These are still peer reviewed. The difference is that they have a lower bar for impact. The bar for correctness is still very very high however.

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