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

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)

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62 points

mean_mistreater

2 hours ago


15 comments

adrithmetiqa an hour ago

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

  • dataviz1000 an hour ago

    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.

    • DrewADesign 16 minutes ago

      > 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.

      Well, for those among us that are not aristocracy already, except for the vanishingly small number of people required to oversee such processes, we’re probably the closest we’re going to get to it. If they don’t need people to do the tech labor, we’ve got way more people than we need, so that’s a huge oversupply of tech skills, which means tech skills are rapidly becoming worthless. Glad to see how fast we’re moving in our very own race to the bottom!

      • drfloyd51 8 minutes ago

        I kind of feel like software engineers working on improving AI are traitors working against other SE’s trying to make a living.

        However…

        I have to acknowledge my craft of SE has been putting people out of work for decades. I myself came up with business process improvement that directly let the company release about 20 people. I did this twice.

        So… fair play.

    • frizlab 10 minutes ago

      > 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.

      That is a nightmarish scenario tbh

  • TrainedMonkey 44 minutes ago

    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.

  • brcmthrowaway an hour ago

    Learn plumbing

    • oytis 43 minutes ago

      There is no reason why market for plumbing will get much larger than it is now (which is not too large)

    • incognito124 14 minutes ago

      Where I live it's bathroom and kitchen tiling

    • dakolli an hour ago

      AI isn't replacing anything, get over yourself.

  • heliumtera 15 minutes ago

    That llms in the middle of everything will continue until morale improve because llms can generate text on top of bullshit made up problems