John Butcher discusses his schooling in New Zealand, first exposure to computers in Australia, and his contributions to numerical analysis. After suffering poor (and sometimes violent) math teachers in high school and failing to receive admittance to Cambridge for graduate school, Butcher accepted a research studentship at the University of Sydney, which was completing a copy of the ILLIAC computer, and received his PhD in physics. While completing his dissertation on cosmic ray physics, he was one of the first people to run a program on a computer in Australia using a paper-tape (pre-punch-card) system, and he initially took up numerical analysis as a hobby. Butcher argues that, just as classical diatonic music still dominates music, established mathematical tools continue to be more popular than newly developed methods for most problems. He eschews theory for its own sake, pursuing instead problems with applicability or inherent interest, although he believes that matching theoretical tools to real-world phenomena is a job best left to scientists. The tools Butcher developed to represent computationally significant quantities are nearly identical to those of Hopf algebras commonly used by physicists today. He notes that although some great thinkers can break the rules successfully, too many scientists think they are “masters.” Given the rapid and unexpected evolution of computing and numerical analysis since World War II, Butcher dares not speculate about its future.