OpenAI Shatters Unique Games Conjecture and 371 Other Math Problems in One Day
The Mathocalypse
OpenAI released 372 major mathematical results, including a proof of the Unique Games Conjecture that had eluded researchers for decades. The proofs, some with Lean certificates, are so complex that no human has yet fully understood them, sparking a race to digest the AI's alien-style mathematics. The event marks a seismic shift in theoretical computer science and mathematics.
It feels like something written by someone who’s on psychedelics. So much unclear and doesn’t make sense. Lots of name dropping of previous work without discussing why it can be used despite impossibility results.
- ks2048
> It feels like something written by someone who’s on psychedelics. So much unclear and doesn’t make sense. Lots of name dropping of previous work without discussing why it can be used despite impossibility results
> Basically the paper is so horribly written that it’s impossible to read it without AI help
That's interesting and haven't seen this in all the coverage of this event.
It sounds horrible to wade through - like trying to understand someone else's messy code that still produces the correct output.
- nostrademons
As a side note, you can tell this wasn't written by an AI by the first sentence:
> mommy, I heard you got cooked! I heard that a robot solved the math problem you worked on for your whole career! OOF!
My 8yo talks exactly like that. I could totally imagine him saying this, the same way, at the dining room table.
I asked ChatGPT "pretend you're an 8/9 year old today. how would you insult your mom about having her job be replaced by an AI?", and the responses it offered were:
> “Mom, AI took your job because apparently even robots were like, ‘Yeah… we can do this better.’”
> “Mom, congratulations! You got replaced by a computer. Even Siri has a job now and you don’t!”
> “Mom, AI took your job? Dang. I guess even a robot looked at your work and said, ‘I got this.’”
> “Don’t worry, Mom. You can still be useful… like teaching the AI how to make my lunch.”
All of these seem to have a vaguely Millennial flavor, aside from being pretty awkward and mechanical roasts. Trust the children and linguistic drift to be the best AI detector.
- ajjenkins
The line about “understanding the aliens” reminds me of Ted Chiang’s short story The Evolution of Human Science (2000).
Highly recommend reading it. Very prescient for something written 26 years ago.
https://gwern.net/doc/fiction/science-fiction/2000-chiang.pd...
- an0malous
> But it also appears that no human has understood just about any of these proofs yet
Has anyone verified any of the proofs produced by OpenAI or is everyone just assuming that it just be true because the Lean code checks out? Couldn’t the Lean code just be formulated incorrectly?
- softwaredoug
Aren’t there dozens of proofs of the Pythagorean theorem? The goal isn’t to just “prove” but create something well written and intuitive to the average practitioner. And by gaining a deeper understanding we can ask better questions.
- dualvariable
In addition to those issues that the wife in the story raised, here's some meta-analysis of the Navier-Stokes result that puts all of these solutions into question:
https://arxiv.org/abs/2610.08144
> Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be mechanically verified. The purpose of this article is to demonstrate why this process may offer no confidence in the original NL argument, owing to the various difficulties in performing the translation semantically faithfully. In particular, we highlight that the problem of resolving ambiguities in mathematical NL text, which is necessary in order to provide semantically faithful translation, is arbitrarily high up in the Solvability Complexity Index (SCI) hierarchy/arithmetical hierarchy (the SCI =∞). Hence, informally, providing semantically faithful AI autoformalisation is harder than any computational problem including the Halting problem (which has SCI =1). To demonstrate the effect of this result we provide several examples of AI mistranslations of NL statements and proofs into Lean in practice, resulting in mismatches between NL proofs and their Lean `verifications'. These include Op […]
- furyofantares
That this is just model capabilities and not swarms of agents is dizzying to me. How long until we get access to these capabilities? How long until we can run something like it locally?
And what the hell will the frontier labs have by then?
Maybe I'm overreacting, I'll have to screw my head back on before I can process this.
- GMoromisato
I liked the metaphor of a climber teleported to the top of a fog shrouded mountain. And I agree that now that the teleporter exists, we need to use it to reach more peaks and explore. There's no going back to a world where AI doesn't exist.