m-hodges publishes AI-assisted proof of Conway's refinement conjecture
1 Sep 18 10:36 AM · 8d ago · 1 article · 1 post · 6 comments · 2 sources · development 1 of 5
A programmer spending a month of free time and substantial tokens working with Claude reports obtaining a Lean proof of Conway's refinement conjecture about omnific integers in surreal numbers. The author, self-described as a math noob, used Claude to select the problem and develop the proof. The proof has passed mechanical checks from the Palomar registry and received informal validation from experts in Lean and the field, though it has not been independently verified by mathematicians.
“It took me an entire month of my free time and a boatload of tokens, but I believe I've obtained a Lean proof of this conjecture posed by John Conway 50 years ago.”
m-hodgesm-hodges Programmer, proof authorClaude (Anthropic) AI modelJohn Conway Mathematician, originator of conjecture
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What was reported 1 claim about this development
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2 outlets I vibed a proof of Conway's conjecture
first by HN Best, 8d ago · also HN Frontpage
What people said 6 voices · verbatim
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A wonderfully made introduction to the surreal numbers and their surrounding game theoretic concepts is this video on Hackenbush[0], a winner in 3Blue1Brown's Summer of Math competition.[0]
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> In either case I believe people who can put AI to the most value are the mathematicians themselvesThe net output of math will increase, and mathematicians have more work now to unravel all this, and make it useful. AI plays the role of a monkey in the infinite monkey theorem [1]. We now need an LLM corollary - Something like: A finite number of…
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>I’ve emailed some of the mathematicians with a few proposed typo fixes, and I got confirmation that at least a few of those fixes seemed real. However, some of the problems that weren’t backed by Lean also turned out to be misunderstandings.I think this project is really neat, but is it appropriate to cold email specialists before you've put in…
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Really nice "proof guide": https://gaearon.github.io/conway-refinement/#/highlightsand "proof map":
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The Claude output in the first one-shot counterexample attempt is hilarious. I hate its writing most of the time but this stuff is next level deep-fried slop.> And the control column confirms the resonance-necessity conjecture empirically: break the skeleton alignment and the joint kernel dies at the constrained window, exactly as the…
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> On the second day, there are two gaps: “between nothing and zero” and “between zero and nothing”. Two numbers spawn in those two gaps. Call them –1 and 1.Got lost here. I think I'm officially too dumb for math.
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