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Comment by danabramov | Hacker News Reader

Author here. No one's asking mathematicians to check the generated proof. I explain it in this part: https://overreacted.io/how-i-vibed-a-proof-of-conways-conjec...

The only thing that needs a check is this 500-line file: https://github.com/gaearon/conway-refinement/blob/264445c93b.... If this file is correct and Lean kernel is correct, the proof is correct.

Moverover, the version I linked above is intentionally paranoid so it doesn't use any third-party code except Mathlib. If you allow usage of CombinatorialGames and trust its definitions, the part that needs to be checked narrows down to exactly 20 lines of code: https://github.com/gaearon/conway-refinement/blob/264445c93b...

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> If this file is correct and Lean kernel is correct, the proof is correct

There are two ifs in this sentence.

What is your point, exactly? Increasing number of people working in and around mathematics are relying on Lean kernel's correctness. That's kind of the point of tools like Lean. Why is it a problem for me to publish a result that relies on it? How do you think other Lean proofs work?

My point is what I said. Without understanding you are only able to say your proof is "likely" to be correct. It's clear from your writing that you understand that your proof will only be accepted once thoroughly reviewed by human mathematicians, who will certainly not be just verifying the definition. Bugs in Lean exist (you're a programmer and it's a program, why would you assume they don't?) and reward hacking and finding bugs are both well established LLM behaviours.

> Why is it a problem for me to publish a result that relies on it?

Bit over-sensitive here. I never said it was a problem for you to publish a result. You can do what you like on your blog and spend your tokens however you choose, just as I'm free to have my own opinions on the value of such an effort. I was responding to, and disputing, a commenter's assertion that understanding and problem-solving ability are "now ... not connected".

I see, we don't seem to disagree much.

While Lean is tightening things up after the recent LLM-driven hacks, I agree that bugs are possible. Although usually code that exploits them is obviously aggressive and is deliberately using the more obscure features related to metaprogramming. Also note that my solution has passed the nanoda kernel as well (https://palomar-registry.org/entry?id=PALOMAR-2026-09-03-000...).

That said, again, I never implied that I'm asking mathematicians to "laboriously [check] the generated proof" which is what your parent comment says. The value to mathematicians is knowing that the conjecture is probably right, and knowing the rough path the LLM has taken to it. Instead of checking the Lean proof line by line, what mathematicians are interested in doing (at least, the ones I've been in contact with) is finding a shorter and more direct proof now that they're aware of the outline and main intermediate claims. As for how much value they find in that, I presume they would be able to speak to that when/if they would like to make their research public.

> The value to mathematicians is knowing that the conjecture is probably right, and knowing the rough path the LLM has taken to it.

Ah, or is the value to mathematicians that their LLMs can build results on top of this? (In which case, did this do more than save them some tokens?) Or is the value the deep mathematical insight that this result incidentally gives a few mathematicians the confidence to develop for their own personal satisfaction (e.g. if they decide to go and prove it for themselves, and come to the same result after a lot of work)?

(IMO, the deep, scary question: what if it’s soon impossible to make anything at all that anyone who doesn’t know you personally would bother to look at or use? https://www.smbc-comics.com/comic/crack)

I disagree with the other guy. I think you’re a bad person flippantly participating in the destruction of a culture, wasting people’s time.

Be more specific. Is he a bad person for having an amateur interest in mathematics, for exploring that interest through language models, or for writing a blog post about his experience?

> flippantly participating in the destruction of a culture

I apologize to Dan Abramov for venting my frustrations about things outside of either of our control and unfairly using him as a punching bag. He seems to be an intelligent person and I hope he continues learning mathematics using whatever tools he sees fit, including AI. It was wrong of me to do this and I will take a break from this website for one week.

What is your point? Please don't be obtuse, it is more constructive to make your points clearly.

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