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Donald Knuth, the godfather of computer science, says an AI solved a math problem he was stuck on for weeks [1]

['Ellsworth Toohey']

Date: 2026-03-03  

Donald Knuth is 88 years old. He's been writing The Art of Computer Programming — the most important book series in computer science — since 1962, and he's not done yet. He gave up email in 1990. He pays $2.56 to anyone who finds an error in his books. He is, by any measure, a living legend of the field.

He's also not an AI hype guy. So when Knuth published a paper this week titled "Claude's Cycles" that opens with "Shock! Shock!" and goes on to celebrate an AI solving a problem he'd been stuck on for weeks, people noticed.

The problem involved something called Hamiltonian cycles in directed graphs — it was going to be included in a future volume of his book. His friend Filip Stappers fed the exact problem to Claude Opus 4.6, Anthropic's reasoning model. In about an hour and 31 systematic explorations, Claude tried brute-force searches, invented what it called "serpentine patterns," hit dead ends, changed strategies, and eventually found a construction that worked for all odd-numbered cases. Stappers tested it for every odd number up to 101. It checked out every time.

Knuth wrote the rigorous mathematical proof himself — the AI found the answer, but couldn't prove it was right. He also discovered that Claude's solution was just one of 760 valid approaches. "I think Claude Shannon's spirit is probably proud to know that his name is now being associated with such advances," Knuth wrote. "Hats off to Claude!"

The even-numbered case remains unsolved. When Stappers asked Claude to keep going on it, the AI "seemed to get stuck. In the end, it was not even able to write and run explore programs correctly anymore."

Previously:

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