March 28, 2026
Proofs, bots, and burger jokes
Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem
AI cracks Knuth’s puzzle, and the internet melts down: genius, gimmick, or both
TLDR: Humans, AIs, and a proof checker teamed up to finish Knuth’s tricky puzzle, turning a one‑off AI surprise into a full, verified solution. The crowd split between “this is the future of math,” “it’s just fancy grunt work,” and “help, are we all bots,” with jokes flying about math medals vs McDonald’s
Professor Donald Knuth literally opened with “Shock! Shock!” after Claude (an AI) found a wild new way to solve a long-standing puzzle about finding perfect round‑the‑world paths in a network. Now the sequel’s even messier and bigger: humans + multiple AIs + a proof checker have stitched together a full solution, with one team even verifying the tricky even cases and another formalizing parts in Lean (a math‑checking program). There are 11,502 possible routes in the smallest version, 996 scale to all odd sizes, and 760 of those make Claude‑style combos. The updated paper reads like a heist movie—except it’s math.
But the real fireworks are in the comments. One camp is hyped on the Fields Medal before flipping burgers meme: “AI will win a math prize before it can run a McDonald’s,” jokes one user, arguing math is perfect for machine brains. Another camp shrugs: “Cool, but AIs still need experts to aim them,” says a skeptic, calling the models great at grunt work but prone to blind spots. The conspiracy‑horror crowd? They’re staring at the thread whispering, is anyone here human? Meanwhile, someone’s already eyeing the ultimate boss fight—“so… P vs NP next?”—as if this victory unlocked New Game+.
Verdict: breathtaking team win for human‑AI math—and a comment section doing its own Turing test.
Key Points
- •For m=3, there are exactly 11,502 Hamiltonian cycles; 996 generalize to all odd m.
- •Knuth identifies exactly 760 valid “Claude-like” decompositions among the odd-m generalizations.
- •Claude Opus 4.6 first solved the odd-m construction in about one hour after 31 explorations.
- •Dr. Ho Boon Suan used GPT-5.4 Pro to prove the even case for all m ≥ 8, with computational checks up to m=2000.
- •Dr. Keston Aquino-Michaels found simpler constructions using GPT + Claude, and Dr. Kim Morrison formalized the odd-case proof in Lean.