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

65 points - today at 6:38 PM


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)

Source
  • gnarlouse

    today at 8:25 PM

    out of curiosity, i wonder if people are taking stabs at p!=np

    • adrithmetiqa

      today at 7:18 PM

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

        • dataviz1000

          today at 7:34 PM

          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

              today at 8:04 PM

              > 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

                  today at 8:12 PM

                  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

                today at 8:10 PM

                > 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

              today at 7:35 PM

              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.

                • artninja1988

                  today at 7:48 PM

                  [dead]

              • brcmthrowaway

                today at 7:23 PM

                Learn plumbing

                  • oytis

                    today at 7:37 PM

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

                    • incognito124

                      today at 8:06 PM

                      Where I live it's bathroom and kitchen tiling

                      • NitpickLawyer

                        today at 7:30 PM

                        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

                          • today at 7:40 PM

                        • dakolli

                          today at 7:34 PM

                          AI isn't replacing anything, get over yourself.

                            • brcmthrowaway

                              today at 7:36 PM

                              Arent you using Claude?

                      • heliumtera

                        today at 8:05 PM

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