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Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

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Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#1

Post by mean_mistreater »

Knuth Claude's Cycles note update: problem now fully solved, by LLMs - https://news.ycombinator.com/item?id=47306926 - March 2026 (2 comments)

https://chatgpt.com/share/69aaab4b-888c-8003-9a02-d1df80f9c7...

Claude's Cycles [pdf] - https://news.ycombinator.com/item?id=47230710 - March 2026 (362 comments)

Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem
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Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#4

Post by NitpickLawyer »

brcmthrowaway wrote: post #3
adrithmetiqa wrote: post #2

Super interesting but what does this mean for us mere mortals?

Learn plumbing

I know your reply was half joking, so please take this the same way, but ... are you sure about that? https://www.youtube.com/watch?v=p1ip68Vv7NE

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#5

Post by dataviz1000 »

adrithmetiqa wrote: post #2

Super interesting but what does this mean for us mere mortals?

I got Claude to self reference and update its own instructions to solve making a typed proxy API of any website. After a week, scores of iterations, it can reverse engineer any website. The first few days I had to be deeply involved with each iteration loop. Domain knowledge is helpful. Each time I saw a problem I would ask Claude to update its instructions so it doesn't happen again. Then less and less. Eventually it got to the point it was updating and improving the metrics every iteration unsupervised.

Edit: This is going to have huge ramifications for the tech security industry as these systems will be able to break security systems as easily it solved the proof. The sooner the good guys, if there are any left, understand this the better it will be for everybody.

> Super interesting but what does this mean for us mere mortals?

I would go for a 2 or 3 hour walk with my phone using the remote control feature looking every 5 - 10 minutes to make sure it doesn't need human help. I went to the coffeeshop and drank very good coffee listening to music. Then at night I sat and had a beer thinking about T.S. Eliot's 'The Wasteland', the effect of industrialization in England at that time and his views of how ennui affected the aristocracy.

Re: Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem

#7

Post by TrainedMonkey »

adrithmetiqa wrote: post #2

Super interesting but what does this mean for us mere mortals?

My understanding is that, if confirmed, this demonstrates that AI can find novel solutions. This is a strong counterpoint to generative-AI-is-strictly-limited-to-training-data.
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