Compiled outcome of exploring this problem with coding agents for some time
I wanted to share a writeup that came out of spending a quite some time exploring Collatz with coding agents:
https://github.com/RAMPKORV/collatz-exploration/blob/main/book.pdf
This project served as my go-to way to learn and test coding agents in practice. I used Lean, Neo4j, GAP, Maxima, and Node.js throughout.
One thing I found was that the agents were often more useful when I asked them to run creative experiments and see what patterns popped out, rather than asking them to "make the best possible progress" in a straight line.
If you read it and wonder why "Royal number" keeps appearing: that was a name an agent came up with at one point, I thought it was fun, and it stuck.
I want to be clear that I cannot really judge how much of this is genuinely new, how much is rediscovery, and how much is just elaborate bookkeeping. So I am not posting this as a claim of having solved anything. But quite some work went into it, and if any part of it is useful, interesting, or points someone toward something better, I would be happy.
I also want to acknowledge at least some visible influences: Tao’s triangle viewpoint, and at least one formulation that was inspired by Septembrino’s matrix-based posts/comments here.
EDIT: Just some clarification. This is not just "I fed this into AI and got this out" but a compilation of experiments accumulated over time. I'm distributing this not because it constitutes a conclusion of any revolutionary result. The content was generated by a ralph-loop by going through all the .lean files. I am moving on to other projects and just want to share in its entirety every result acquired. It's not intended to be a nice paper but an accurate representation of the results collected. I get that some people will immediately dismiss it because "This is long" and "AI was involved". It is not intended for those people.