Mathematician at Stanford University. In 2026 Knuth and his colleague Filip Stappers were working on a problem akin to the travelling salesman problem, in which the shortest route must be found for a salesman to visit a number of cities once before returning home. They turned to Claude Opus 4.6, an LLM developed by Anthropic. After several different approaches, Claude solved the problem for cases when, at each stop, an odd number of routes remained. But when pushed to solve the problem for all even numbers, the model malfunctioned—"very weird", wrote Stappers. Even so, Dr Knuth was impressed by the way Claude tackled the problem. Another researcher later built on this work using ChatGPT 5.4 Pro, an LLM by OpenAI, to solve the problem for even numbers.
The most costly of all follies is to believe passionately in the palpably not true. It is the chief occupation of mankind.