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Comment by rfgplk | Hacker News Reader

This is pretty standard. Important to note that these "errors" (* not really errors) themselves were caught by an LLM, further proving their usefulness.

* The reason you shouldn't consider the withdrawals to be caused by errors is because this is pretty standard in math and development. "Errors" like this are a core aspect of science and it happens _all the time_. And from my research LLMs have a far lower error rate than even the best human scientists.

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It's so funny to see people on Hacker News talk about academic communities that they clearly are not part of. To be clear to anyone reading, no, retracting papers is _not_ standard in math. In math, people submit papers after they have checked with colleagues, they give seminars, they submit it for peer review, etc. It is not shotgunning papers and retracting incorrect ones on the regular. Retracting papers is rare and embarrassing.

It is wild to me how much stock mathematicians put into the social aspects of math. The whole social framework you are describing _did not exist_ for almost the entire history of math. It might very well be seen as a historical anomaly, like renaissance mathematicians challenging each other to solve cubic equations.

What do you mean by "the social aspects of math" here? Even some of the earliest known mathematical texts (like the Rhind Papyrus) contain evidence of a social aspect of math. And certainly mathematical discussions occurred among the ancient Greeks. People have been exchanging mathematical ideas for millennia. If you mean to say that the current academic organization of mathematics is a recent phenomenon, that's certainly true. But pretty much all the math history we know has been people communicating with each other, evaluating each other's ideas and developing them further. Given this, I understand why people are worried if the field should suddenly take a non-social form.

Euclidean geometric proofs would often be performed outside in public places.

First of all, people retract papers all the time. I can't give you the exact figures, but surely at least half of all academic researchers have retracted a paper at least once in their lives... Second, is it so hard to believe we are going through a complete paradigm shift in academia? People can now produce hundreds of high quality papers in a matter of weeks/days (with enough compute). Even if the error rate goes up (which it likely won't) we're still being exposed to a monstrous amount of novel information.

Even Einstein retracted one of his earlier papers re the cosmological constant... And he is one of the greats. Although not purely math related, it still counts.

Wait, what? Well, yes, you're correct, AND flipping a sign in a draft paper that your buddy catches in a pre-read is SUPER common. People don't do math in a vacuum. Well, many do not. Some do.

Would you care to share your research? What was your methodology? Did you write it up? Is it published?

Or is it the kind of research you'd prefer to keep shrouded in mystery?

Thanks for the question. It's difficult to quantify but it basically comes down to how many obvious errors LLMs produce amortized by the processing time.

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