Further human + AI + proof assistant work on Knuth's "Claude Cycles" problem
twitter.com
March 28, 2026
1 min read
Summary
Claude found an odd-m construction for the open Hamiltonian decomposition problem, impressing Prof. Donald Knuth, who titled the resulting paper "Claude’s Cycles." The updated research reveals that for the base case m=3, there are 11,502 Hamiltonian cycles, with 996 generalizing to all odd-m, and 760 valid "Claude-like" decompositions identified.
Key Takeaways
- Claude found an odd-m construction for Prof. Donald Knuth's open Hamiltonian decomposition problem in about an hour of guided exploration.
- The updated paper reveals there are exactly 11,502 Hamiltonian cycles for the base case m=3, with 996 generalizing to all odd-m.
- Dr. Ho Boon Suan used GPT-5.4 Pro to produce a 14-page proof for all even m≥8, while Dr. Keston Aquino-Michaels utilized GPT and Claude together for simpler constructions.
- The problem is now fully resolved through a collaboration of multiple AI systems and human contributions, demonstrating a new mathematical ecosystem.
Community Sentiment
MixedPositives
- AI's ability to discover new mathematical concepts highlights its potential in advancing fields like mathematics, which could lead to groundbreaking discoveries.
- The idea of using AlphaGo-style reinforcement learning on Lean syntax trees suggests a promising direction for AI's capability to tackle complex mathematical problems over longer timescales.
Concerns
- The comment about AI winning a Fields Medal before managing a McDonald's reflects skepticism about AI's practical applications in everyday tasks, indicating a gap between theoretical and practical capabilities.
Source
twitter.com
Published
March 28, 2026
Reading Time
1 minutes
Relevance Score
60/100
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