Join the discussion
Write your take first — we'll ask for email only when you're ready to publish.
- Hacker News
- > 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.
- > there were numerous comments saying variations on this theme: "well, yes, but how about novel stuff, how about new things, original work, yadda yadda"
This completely misconstrues what professional mathematicians were claiming. The argument would be better phrased as: "having a vast accessible memory and the ability to very rapidly test/recombine previously-elucidated approaches means that AIs can and will easily outdo much of the mathematical community."
Now, one could plausibly make the argument that this is functionally equivalent to a certain form of creativity (I would). But, it may just as well also be a non-exhaustive form. And that is where the open question resides.
by sp527 - Infinite Fun Space.
- I cant wait to see this pointed at Age of Empires. Or maybe palantir already has this running on real world data, war gaming scenariosby bawana
- Maybe Hilbert's dream was not that crazy after allby Almondsetat
- What is that dream? I don’t know much about itby mettamage
- The dream in itself has been destroyed. The idea that you could just have a machine enumerate all valid theorems in a theory is part of it, but it's only a question of form. The point was that it was to prove "all theorems of Mathematic", not "theorems into a given axiomatic system that is useful in some contexts, e.g. ZFC".
You could even argue that it's the fundamental basis for post-modernism, since mathematics have destroyed the notion of absolute truth in any advanced domain. It's back to a form of "all models are wrong but some are useful" similar to what we have in physics. Sayonara, Plato.
by woolion - paper is about this open source project: https://github.com/dualverse-ai/stationby bryan0
- 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.by daxfohl
- Reminds me a lot of this LW piece. https://www.lesswrong.com/posts/znbfRXHq285nS7NAh/the-terrar...by StrauXX
- 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.by anigbrowl
- Great book. I first read it 10 years ago, I think it would benefit from a re-read.by stuxnet79
- Yes! I was also reminded of the truth mines in Diaspora.by supermdguy
- > 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.
by dash2 - They keep looping back to the same paper. The holiday is just another prompt.by johnxianren
- And on the 7th day, the agents restedby Aboutplants
- I wondered about this approach for something I was trying but thought it was just stupid, I wanted to see if An agent could explore software development and work on hobby tasks so that it could come back and push against design ideas and develop it's own opinions. Then I realized it was dumb for SW.by kodoman
- 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.
- Re: anthropomorphism: I frequently hear stories of LLMs [behaving as though they are] feeling self-doubt. I had a similar experience. Asked Claude Code what the weather was and it said, I don't know, I'm just a programmer.
Added "You can do anything, believe in yourself!" to CLAUDE.md, suddenly it was able to google the dang weather. lmao
by andai - Why would a secondary cultural goal take precedence over an apparently accurate description of what’s happening in the system? For one, you’re fighting some irrelevant battle.by GPerson
- I spent a long time with custom harness design and found the terminology to be a key part of the work, since the concepts are new. I dropped the term "agent" altogether in favour of "thread" for that very reason.by edg5000
- So, what does thinking mean? Is there one thing we mean when we say thinking in humans? Are there several? Is it more of a spectrum?
e.g. last year I tried inventing a "System 3"[0], a more rigorous way to approach problem solving, due to repeated painful experiences getting stuck solving problems the wrong way. I didn't get very far, but I definitely want to revisit the idea.
[0] Based on System 1 and System 2, i.e. lossy pattern matching vs "actual thinking". Because I found my "actual thinking" was also ~~dogshit~~ frequently insufficient for the problems at hand.
So as far as I'm concerned, thinking properly has not even been invented yet. (But I'd love to hear other perspectives!)
https://thedecisionlab.com/reference-guide/philosophy/system...
by andai - I definitely belong to the latter camp. After LLMs I view everything humans do very systematically and whenever said thing still feels fuzzy I just treat it as having a noise/smoothing termby E-Reverance