{"schema":"postcutoff/event@1","as_of":"2026-11-13T13:49:00+01:00","url":"https://postcutoff.com/e/2026-02-28-knuth-claudes-cycles/","md":"https://postcutoff.com/e/2026-02-28-knuth-claudes-cycles/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-02-28-knuth-claudes-cycles","date":"2026-02-28","date_precision":"day","short_title":"Claude Opus 4.6 solves an open Hamiltonian-cycle problem, Donald Knuth reports","deck":null,"takeaway":null,"category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Donald Knuth: Claude's Cycles (PDF)","url":"https://www-cs-faculty.stanford.edu/~knuth/papers/claude-cycles.pdf","type":"paper","group":"primary","domain":"www-cs-faculty.stanford.edu"},{"n":2,"title":"GitHub: kim-em/KnuthClaudeLean (Lean formalisation)","url":"https://github.com/kim-em/KnuthClaudeLean","type":"code","group":"primary","domain":"github.com"},{"n":3,"title":"Adafruit blog: Don Knuth wrote a paper thanking Claude","url":"https://blog.adafruit.com/2026/03/03/don-knuth-wrote-a-paper-thanking-claude-for-solving-an-open-math-problem/","type":"press","group":"press","domain":"blog.adafruit.com"}],"official":2,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Anthropic","Stanford University"],"title":"Donald Knuth's 'Claude's Cycles': Claude Opus 4.6 solves an open Hamiltonian-cycle problem ('Shock! Shock!')","summary":"Donald Knuth published a note opening 'Shock! Shock!' describing how Claude Opus 4.6 found, in about an hour of guided exploration, a general construction decomposing the arcs of a 3D torus digraph on m³ vertices into three Hamiltonian cycles for all odd m. Knuth had worked on the problem for weeks for a future TAOCP volume. He then proved Claude's construction correct.","key_facts":["Note dated 28 Feb 2026, revised 4 Mar 2026","Graph: vertices (i,j,k) mod m, arcs increment one coordinate; goal: split all arcs into 3 directed Hamiltonian cycles","Claude found the odd-m construction in 31 guided explorations over about an hour; the even case remains largely open","Knuth wrote the proof; the result was later formalised in Lean (kim-em/KnuthClaudeLean)"],"key_numbers":[],"tags":["math","combinatorics","graph-theory","claude","knuth"],"science":{"field":"mathematics","subfield":"combinatorics / graph theory","problem":"Decomposing the 3D torus digraph on m³ vertices into three Hamiltonian cycles","result":"General explicit construction for all odd m, found by Claude and proved by Knuth.","open_since":"","ai_system":["Claude Opus 4.6"],"human_role":"AI-assisted: colleague Filip Stappers ran the Claude session; Knuth verified and proved","verification":{"key":"lean","label":"Lean-verified","text":"Human proof by Knuth; formalised in Lean"},"status":"confirmed","shock":"The author of The Art of Computer Programming titled his note's opening 'Shock! Shock!' after an AI solved a problem he had been stuck on."},"body_md":"## What happened\n\nKnuth posed a Hamiltonian-cycle decomposition problem he planned for TAOCP. Working through it with Claude Opus 4.6 over dozens of explorations, a collaborator got a pattern that works for every odd m. Knuth then proved it and wrote up the story.\n\n## Why it matters\n\nComing from one of computing's most respected and AI-sceptical elders, the note became a cultural marker that frontier LLMs could contribute original mathematical constructions.","disputed":[],"related":[{"id":"2026-02-05-claude-opus-4-6","url":"https://postcutoff.com/e/2026-02-05-claude-opus-4-6/","date":"2026-02-05","date_precision":"day","short_title":"Anthropic releases Claude Opus 4.6 with 1M context, adaptive thinking and agent teams","deck":null,"takeaway":"It made 1M-token context and adaptive thinking standard features of Anthropic's flagship line.","category":"model-release","category_label":"Model releases","importance":3,"confidence":"high","status":{"key":"confirmed","labels":["Confirmed"]},"sources":4,"official":1,"filed":"2026-09-29","updated":"2026-09-29","orgs":["Anthropic"]}],"people":[],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-09-29","type":"filed","text":"Created"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-09-29","run":null,"sources_read":null,"updated":"2026-09-29","human_review":null,"version":{"date":"2026-10-07"}},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":null,"in_training_data":true},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":null,"in_training_data":true},{"model_id":"gemini-4-hydrogen","name":"Gemini 4 Hydrogen","cutoff":"2026-03","days_after":null,"in_training_data":true},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":null,"in_training_data":true}],"short_url":"https://postcutoff.com/s/donald-knuth-claude-cycles"}