In the field of computer science, if there is someone who can represent the pinnacle of "logic" and "rigor," it must be Donald Knuth, a Turing Award winner. This elder master, who wrote the "Bible" for programmers, "The Art of Computer Programming," invented the TeX system, and never uses email, has recently been completely "shocked" by AI. In his latest short essay, "Claude's Cycles," he marvels at how Claude Opus 4.6 solved a mathematical problem that he had studied for weeks, or even one that could be traced back to 30 years ago, in just one hour.

The problem that made Knuth "lose his hair" belongs to the field of graph theory: how to decompose all arcs in a 3D grid graph into three non-overlapping Hamiltonian cycles? When Knuth's friend posed this question to Claude, something miraculous happened. The AI did not fall into the trap of rote memorization or brute-force search, but instead demonstrated astonishing structural thinking.

From the initial exploration to the 15th attempt introducing the concept of "fiber layers" to reduce dimensionality, and then to the 21st attempt where it had a sudden insight using the "serpentine construction" to find patterns, Claude derived a general algorithm applicable to all odd dimensions within just 31 attempts.

What most amazed Knuth was Claude's extremely clear reasoning process. It not only provided the final Python code (which Knuth later transcribed into C language and verified as correct), but also clearly showed how it learned from its mistakes and redefined the problem. This process of "automatic deduction and creative problem-solving" deeply impressed the master, who had previously held reservations about generative AI, and he ended the article with a respectful statement: "I remove my hat to Claude!"

Interestingly, this tribute also contains a romantic easter egg: the Claude that Knuth mentioned refers not only to the current AI model, but also to the founder of information theory, Claude Shannon.

When an 88-year-old cornerstone figure in computer science met the cutting-edge AI in the vast sea of mathematics, it was not just the end of a difficult problem, but also a prelude to a new era of human-AI collaboration. As Knuth said, AI has broken through the thickest window, and the rest of the journey will be witnessed by us together.