Artificial Intelligence Model, Claude Opus 4.6 Solves Long Standing Computer Science Problem

Anthropic’s AI model, Claude Opus 4.6, recently solved a longstanding computer science problem concerning directed Hamiltonian cycles that had remained unsolved for years.
The model, prompted by a particular problem posed by Filip Stappers, systematically documented its attempts to solve the problem and shifted strategies as it explored different mathematical approaches.
Renowned computer scientist Don Knuth, who had previously tackled a limited case of the problem, expressed surprise and admiration for the AI’s solution, indicating he might revise his views on generative AI.
The problem involved determining if a directed graph with specific ‘m’ nodes can be decomposed into three Hamiltonian cycles—where each cycle visits each node exactly once.
During its journey, Claude attempted heuristic methods like simulated annealing but eventually realized the need for rigorous mathematical approaches to establish a universally applicable solution.
It discovered a solution involving modular arithmetic operations and constructed a rule for the traversal of vertices based on the sum of their coordinates modulo ‘m’.
Despite initial experiments using probabilistic techniques, Claude highlighted the necessity of pure math to provide a formal proof of the solution.
The AI successfully found a construction for odd values of m, with a particularly satisfying resolution coming early on in its attempts.

You may have missed