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I vibed a proof of Conway's conjecture

I vibed a proof of Conway's conjecture

m-hodges

Comments (86)

  • bwfan123
    > 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 LLM agents will almost surely find all theorems given an infinite token budget.[1] https://en.wikipedia.org/wiki/Infinite_monkey_theorem
  • unholiness
    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]https://www.google.com/search?q=video+introduction+to+surrea...
  • sigmar
    >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 enough hours of effort to describe yourself as more than an "amateur"? OP's emails may have been helpful, but billions of people use these LLMs to wade into new areas and email is already low signal-to-noise.
  • howunfortunate
    > 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.
  • mihau
  • makerofthings
    Here's my conjecture. Large Language Models are the great filter. They represent a local maximum in the technological advancement of a species from which we will not escape.
  • renyicircle
    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 transversality heuristic predicted.> The den has air in it.> Drift fuel exists.
  • cyclopeanutopia
    Someone please vibe-prove that ZFC is inconsistent.
  • vatsachak
    That's awesome! Congratulations!I'd imagine that in three months when we all have access to communicating agent swarms this should be easier
  • msteffen
    I find this whole post fascinating in the context of https://news.ycombinator.com/item?id=49738091 and particularly this excerpt from Gowers:> Instead, I have a more complicated view, which I actually expressed in my essay The Two Cultures of Mathematics a quarter of a century ago, and which can be summarized by saying that there is a spectrum of attitudes in mathematics to the relationship between problem-solving and conceptual understanding. At one end of the spectrum you have mathematicians who are primarily motivated by the wish to solve problems, who see conceptual understanding as a very important means to that end. At the other you have mathematicians who are primarily motivated by the wish to attain conceptual understanding, who see problem-solving as a very important means to that end.Before, understanding and problem-solving-ability were so interdependent that distinguishing between the two was practically very difficult and probably wouldn’t have changed anyone’s research agenda. Now, they’re not connected, and this guy just did the ultimate meta-experiment of seriously undertaking a project that is intentionally 100% problem-solving and 0% understanding to prove it (maybe 99% and 1% but pretty close. In his transcripts, he never asks ChatGPT about the math, only about its opinions of the math).As we (as a society) sit around asking ourselves what mathematicians (and software engineers, and anyone in deep technical fields) should be doing all day, we now have this case study to show us how wide our range of options has become.
  • alikatyc
    free time spent talking to llm, what an achievement!
  • nialv7
    I don't know why the author could claim this is "their" proof, and they kept saying "they" did this, "they" built that. but in reality everything is done by the LLM and the author is merely asking it to do things. i guess they did contribute money at least...> Me: btw how’s your mood overall?LOL. mood??
  • 31276ahq
    Finally, you might be wondering about the token cost. I wasn’t running this project in a particularly token-efficient way and have repeatedly maxed out my 20x Pro subscriptions for both Claude and ChatGPT every week. I also briefly had access to a prerelease model in the last few days, which did not have a usage cap. I was not tracking my actual token usage consistently. Some AI analysis from the recovered logs roughly estimates that we’re totaling around 40 billion tokens, of which around 210 million were output tokens. Over 95% were cache reads.Who can pay for a 20x Pro subscriptions and also get prerelease models? something weird is going on here.
  • math_dandy
    [dead]
  • tonetheman
    [dead]
  • GPerson
    [flagged]