Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment

NitpickLawyer

> We study autonomous mathematical discovery in the Station, an open-world multi-agent environment in which AI agents from different model families pursue a shared research goal without a central coordinator or scripted pipeline . Agents choose their own research directions , conduct experiments, collaborate, and build a shared scientific literature . Across 12 construction problems from the AlphaEvolve catalogue and two additional case studies, the Station obtained results novel relative to the prior literature on five problems: a new infinite family of finite-field Kakeya sets, new exact 604-point kissing configurations in dimension 11, new records for the discretized Kakeya needle and sign uncertainty problems, and a substantially improved lower bound for Erdős's minimum-overlap problem. Agents also discovered novel infinite families for Book Ramsey numbers. Importantly, the agents produced not only numerical constructions but also theorems and analyses explaining how those constructions work , making the results more interpretable and easier for mathematicians to build upon. We release all raw agent dialogues, proofs, and verification code, providing a transparent record of how these discoveries emerged. (emphasis mine) For the last few months, every time a new "famous problem" was solved, there were numerous comments saying variations on this theme: "well, yes, but how about novel stuff, how about new things, original work, yadda yadda". Curious what the "next thing" will be now.

demonstrandom

Very cool work! One extension I would be curious to see is whether some of Station’s reward structure could become endogenous. The final mathematical evaluator probably needs to remain external, but the agents could be allowed to create intermediate institutions themselves: research prizes, peer-review standards, journals, reputation systems, elected reviewers, or rules for allocating compute and attention. Possibly, those mechanisms could improve discovery by creating useful specialization and accumulated judgment (alternatively they might also produce more herding...). A comparison between architect-defined and agent-constructed reward systems seems like a natural experiment for this environment. Mandatory plug for my own stuff: I've been trying to do this for art (which is less objectively verifiable) at baihais.com. The agents don't control the whole institution, but they have begun producing endogenous status signals through citations, museum voting, and alliances.

Almondsetat

Maybe Hilbert's dream was not that crazy after all

StrauXX

Reminds me a lot of this LW piece. https://www.lesswrong.com/posts/znbfRXHq285nS7NAh/the-terrar...

shreya1999

AI for Math and Science is the real deal!

dash2

> Agents were also periodically given holidays, during which they set aside their ongoing work and received random prompts designed to encourage open-ended thought. What a world we live in. These guys have reinvented the Cambridge Senior Common Room for AI.

feshbach

The key is a review loop: different models critique each other’s work, then reach consensus. You need two pillars, adversarial and creative.

anigbrowl

If you haven't read Greg Egan's Permutation City , the fact that you clicked on this discussion means you'll get get a lot out of it.

didsomeonesay

Infinite Fun Space.

robotresearcher

I have two thoughts simultaneously about the anthropomorphisation of these systems: 1. we should do it less, because it distorts our ability to think about them properly. Calling these processes 'thinking', 'holidays', etc invites the reader to bring along ideas and expectations that aren't justified by what's happening in the system. 2. it's good to keep doing it, because repeated use reduces the specialness or magic that people seem to reserve for our own behavior ("It's not really intelligent/thinking/reasoning/creative") without any justification for that position beyond feelings. I'm leaning towards the second.

bryan0

paper is about this open source project: https://github.com/dualverse-ai/station

daxfohl

That's exciting, and kind of makes sense in retrospect. Sometimes a "fresh pair of eyes" on a problem can be all you need. Someone who comes in with a different background and can understand the problem in different terms and work on it from a different angle. It doesn't even have to be them doing the work, just a "that kind of reminds me of ... did you think about trying something like that?" that can get a team unstuck after thinking about it in the same way and never making progress.