Michael Powell discusses his career and research. Powell was born in London and lived in Sussex and Surrey. He had a governess in mathematics when he was very young, and because he enjoyed looking at mathematics books, often just doing the exercises, he was ahead of his classes in mathematics. He became an undergraduate at Cambridge, finishing in three years, two years for part 2 of the Mathematical Tripos and then taking a diploma in numerical analysis and computing in his third year. He joined the Atomic Energy Research Establishment at Harwell, and stayed for seventeen years. At Harwell, he started the Harwell Subroutine Library, one of the first libraries of numerical algorithms, and began his research career. He discusses the origin of the DFP (Davidon-Fletcher-Powell) formula and subsequent methods that overtook it. After leaving Harwell, he returned to Cambridge in 1976 as a Professor and continued his research career. He received a Doctor of Science degree in 1979 at Cambridge. He discusses his subsequent work in optimization and approximation, the differences between research at Harwell and Cambridge, and his preferences in conducting research, including his tendency to publish by himself. Powell retired from Cambridge in 1996.