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

arxiv.org

31–40 of 48 posts

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

#31
post #11

> 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.

They keep looping back to the same paper. The holiday is just another prompt.

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

#33

Maybe Hilbert's dream was not that crazy after all

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.

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

#34

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 magi…

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...

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

#35

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 magi…

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

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

#36
post #11

> 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.

They keep looping back to the same paper. The holiday is just another prompt.

I have been given the mandatory assignment of not working today.

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

#37

Maybe Hilbert's dream was not that crazy after all

What is that dream? I don’t know much about it

The Entscheidungsproblem. Basically, is there an algorithm such that, taking an arbitrary statement as input, can output wether it is true or false? Turing and Church both independently proved that no such algorithm exists.

https://en.wikipedia.org/wiki/Entscheidungsproblem

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

#38
post #11

> 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.

And on the 7th day, the agents rested

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

#39

Earlier quoted context omitted.

I disagree for several reasons, but I don't want to spoil the plot with an explanation of why.

So why comment then

To let potential readers know there’s more to the story than the presented interpretation.

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

#40
post #5

> 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…

> 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 o…

We’re watching a repeat of the arguments against Chess and Go engines.

It’s all computation, humans just can’t always experience or explain the computation they are doing at the time so we call it creativity instead.

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