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If you haven’t seen it yet, Donald Knuth — yes, *that* Knuth, the man behind *The Art of Computer Programming* and TeX — just published a paper called [“Claude’s Cycles”](https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf), and it opens with the words “Shock! Shock!” That alone should tell you something unusual happened.

Here’s the backstory. Knuth had been grinding on an open problem for several weeks: a conjecture about Hamiltonian cycle decomposition in directed graphs, material he was preparing for a future volume of TAOCP. His friend Filip Stappers decided to throw the problem at Claude Opus 4.6, Anthropic’s hybrid reasoning model that had only been out for about three weeks at that point. In roughly an hour and across 31 systematic explorations, Claude tried brute-force searches, invented what it called “serpentine patterns,” hit dead ends, pivoted strategies, and eventually landed on a construction that worked for all odd-numbered cases. Stappers tested it for every odd value of m up to 101. It held up every single time.

Now, the important nuance: Claude found the answer, but it couldn’t *prove* it. Knuth himself wrote the rigorous mathematical proof, generalized the result, and discovered there are exactly 760 valid “Claude-like” decompositions. He also noted that when they pushed Claude to tackle the even-numbered case, it got stuck and eventually couldn’t even write correct exploration programs anymore. So no, this isn’t “AI replaces mathematicians” — it’s more like a very persistent research assistant that got lucky in a deeply informed way.

What really got people talking is Knuth’s closing line: “It seems I’ll have to revise my opinions about generative AI.” Coming from someone who has been publicly skeptical about AI hype, that carries real weight. The paper immediately shot to [#1 on Hacker News](https://news.ycombinator.com/item?id=47230710) with over 526 points and 225 comments. [Bo Wang’s tweet](https://x.com/BoWang87/status/2028935492977475623) summarizing the paper went viral, and [Boing Boing](https://boingboing.net/2026/03/03/donald-knuth-the-godfather-of-computer-science-says-an-ai-solved-a-math-problem-he-was-stuck-on-for-weeks.html) picked it up the same day. [Simon Willison](https://simonwillison.net/2026/Mar/3/donald-knuth/) highlighted the key quote on his blog, and the broader discussion has been fascinating — ranging from “this changes everything” to “it’s just pattern matching on steroids.”

Personally, I think the most interesting thing here isn’t that an AI solved a math problem. It’s that Knuth, at 88 years old, looked at the result, did the hard proof work himself, and gave credit where it was due. He named the paper after the AI. That kind of intellectual honesty — from someone with nothing left to prove — is what makes this moment feel genuinely significant.