March 3, 2026
Math daddy vs machine baddie
Claude's Cycles: Claude Opus 4.6 solves a problem posed by Don Knuth [pdf]
AI ‘solves’ legend’s math puzzle – but did it really, or is the internet doing the heavy lifting
TLDR: A famous computer science pioneer says an AI tool helped crack a tough math puzzle he’d been working on for weeks, shocking many who saw him as an AI skeptic. The comments explode over whether this means AI is now a true problem‑solver or just a flashy assistant getting too much credit.
Donald Knuth, the 86‑year‑old coding legend whose books are basically the Bible of computer science, just admitted an AI model from Anthropic helped crack a tricky math puzzle he’d been stuck on. On paper, it sounds like a sci‑fi moment: the grand master of algorithms stunned that a chatbot found a path he’d missed. But the internet immediately grabbed the mic and turned it into a full‑blown drama.
One camp is thrilled, calling this proof that modern AI can actually reason, not just remix text. Commenters gush about the “summoning spell” vibe: you type the right magic words, and a robot mathematician pops out solutions anyone can use, no PhD required. Others gleefully point out that Knuth himself used to be pretty dismissive of chatbots, linking old quotes where he basically said, “I’ll stick to real, trustworthy ideas.” Now? He’s praising Claude’s “creative problem solving” and people are savoring the plot twist.
But the skeptics are loud too. Some accuse the writeup of being “misleading,” arguing Claude didn’t really solve the problem so much as spit out examples that Knuth then turned into a real proof. Another commenter highlights the glitchy side: after some success, Claude reportedly started fumbling its own code and got stuck. Cue the memes about AI geniuses who can discover deep math patterns… but forget how to run their own script. The vibe: impressive, unsettling, and definitely not settled science.
Key Points
- •Knuth describes an open combinatorial problem about decomposing arcs of a directed graph on m³ vertices into three directed m³-cycles for all m > 2.
- •Empirical work by Filip Stappers found decompositions for 4 ≤ m ≤ 16, suggesting general existence beyond m = 3, which Knuth had already solved.
- •Filip Stappers posed the problem verbatim to Anthropic’s Claude Opus 4.6 and required it to document each exploration step in a plan file.
- •Claude reformulated the problem via vertex-wise permutations, attempted algebraic and brute-force search strategies, and then exploited the structure of Cayley digraphs to find 2D and 3D “serpentine” cycle patterns.
- •Later explorations introduced a fiber decomposition using the quotient map (i, j, k) ↦ i+j+k (mod m), revealing a layered structure of the digraph that supported further analysis toward a general solution.