More and more experts in scientific fields are finding out that AI systems are now matching — and bettering — them at specific tasks.
The latest to discover this is none other than Donald Knuth, the Stanford computer scientist widely considered one of the founding giants of the field and the author of the multi-volume magnum opus The Art of Computer Programming. In a note dated February 28, 2026, Knuth described his reaction to learning that Claude Opus 4.6 — Anthropic’s hybrid reasoning model, released just three weeks earlier — had cracked a mathematical problem he had been working on for several weeks.
“Shock! Shock!” Knuth opens his note, before going on to call the development “a dramatic advance in automatic deduction and creative problem solving.” He added that he would “have to revise my opinions about ‘generative AI’ one of these days.” Coming from a figure who has historically been skeptical of AI hype, the statement carries significant weight.
The Problem
The problem at the center of all this involves a branch of mathematics called combinatorics — specifically, the decomposition of directed graphs into Hamiltonian cycles. In plain terms, Knuth was trying to find a general rule for navigating a three-dimensional grid of points, visiting every point exactly once, and doing so in a structured, repeatable way for grids of any size.
Knuth had solved the problem for the smallest non-trivial case (a 3×3×3 grid) and posed the general version as an exercise in a forthcoming volume of his landmark series. A colleague, Filip Stappers, had empirically verified solutions for grids up to 16×16×16 — suggesting a general solution likely existed — but no one had found a construction that worked for all values.
Claude’s Approach: 31 Explorations in One Hour
It was Stappers who decided to put the question directly to Claude Opus 4.6, and the results were striking. The AI did not stumble upon an answer by chance. Instead, over the course of roughly one hour, it conducted a systematic, 31-stage investigation — testing linear formulas, attempting brute-force searches, developing new geometric frameworks, applying simulated annealing, and ultimately arriving at an elegant construction that works for all odd values of the grid dimension.
Knuth documents Claude’s reasoning process in detail, and he is clearly impressed. At one point, he notes that Claude independently recognized the mathematical structure of the problem as a “Cayley digraph,” a classical concept from group theory, and reformulated its approach accordingly. At another, he observes that a pattern the AI called a “serpentine” turns out to be a classical sequence known to mathematicians as the “modular m-ary Gray code.”
The final solution — a compact set of rules expressible as a short C program — was verified by Stappers to produce valid decompositions for all odd grid dimensions from 3 to 101.
Not Without Caveats
Knuth is careful to situate the achievement honestly. Claude’s solution required human guidance: Stappers had to repeatedly remind the model to document its progress, and the session was interrupted by errors that caused some earlier search results to be lost. The AI also ran into a wall on the even-dimension case — the problem remains entirely open for even-sized grids — and appeared to “get stuck” when Stappers tried to push it further in that direction.
A rigorous mathematical proof, moreover, still had to be constructed by Knuth himself. The AI found the construction; the verification and formalization of why it works fell to the human expert.
A Landmark Moment, Carefully Framed
What makes Knuth’s account notable is not just the result, but who is delivering it. He is not a tech booster or an AI company executive. He is an 87-year-old legend who built the theoretical foundations of computer science, and who has for years expressed measured skepticism about the depth of AI systems’ capabilities.
His note ends with characteristic warmth and dry humor. “Hats off to Claude!” he writes — adding, with a nod to AI history, that “Claude Shannon’s spirit is probably proud to know that his name is now being associated with such advances.”
Knuth isn’t the only technologist that’s finding out that AI can be a useful aid for research. Linux creator Linus Torvalds is vibe coding using Google Antigravity, and the President of the American Mathematical Society has said that Gemini came up with a mathematical insight he’d be proud to come up with himself. Meanwhile, several AI systems have been helping solve the notoriously hard Erdos problems. For the broader AI industry, these episodes offer a more grounded benchmark than the contests and leaderboards that typically dominate headlines: world-class experts are beginning to use AI to help with their research.