March 3, 2026
Knuth blesses AI; HN melts down
Claude's Cycles [pdf]
An AI cracked Don Knuth’s puzzle — HN yells “put KNUTH in the title”
TLDR: Don Knuth says Claude helped solve a tricky math puzzle, and HN erupted over credit and headline wording and whether that’s real “reasoning.” It matters because a computing legend publicly shifted his stance on AI, fueling a broader debate on its problem‑solving chops.
Hacker News erupted after Don Knuth — yes, the legendary author of The Art of Computer Programming — revealed that Anthropic’s Claude Opus 4.6 helped crack a puzzle he’d been wrestling with. The task? Think of a huge 3D grid of points with arrows; the challenge was to find three perfect loops that cover everything. Knuth says he’ll have to rethink generative AI, and the crowd went full popcorn mode.
Strongest take: people demanded KNUTH be in the headline. Top comment: “Please put this in the title!” Folks joked they almost scrolled past a once‑in‑a‑decade nerd miracle. There’s meta-drama about HN formatting too: one user begged for ~knuth to display like social media handles. Others linked the previous thread for lore.
Then the hot debate: Did the AI truly reason, or was it heavily coached? Claude methodically documented a plan, tried “serpentine” patterns (picture snake-like routes), and used a layered “fiber” trick. Fans called it a watershed for “automatic deduction.” Skeptics rolled eyes at cherry‑picking and human guidance from Filip Stappers, who steered the process with strict “update plan.md” prompts.
Memes flew: “snake code,” “Gray code but make it glam,” and “Knuth blessing AI = papal bull.” Whether miracle or meticulous spreadsheet energy, the vibes were pure internet theater.
Key Points
- •Knuth reports that Claude Opus 4.6 solved a graph decomposition problem: partitioning arcs of a 3D digraph with m³ vertices into three directed Hamiltonian m³-cycles for all m>2.
- •Prior to the AI-assisted solution, Knuth solved m=3, and Filip Stappers empirically found solutions for 4 ≤ m ≤ 16, suggesting general existence.
- •Claude reformulated the task via per-vertex permutations σ: Z_m^3 → S_3 and tested a cyclic scheme using a single function g, finding linear/quadratic g insufficient.
- •A brute-force DFS over σ for m=3 was infeasible; Claude then identified 2D serpentine cycles in a Cayley digraph and extended to a 3D pattern equivalent to a modular m-ary Gray code.
- •Subsequent analysis included residual graph structure and a fiber (layered) decomposition via φ(i+j+k mod m), which contributed to the ultimate general solution.