Some comments from a numerical analyst

A description is given of life with A. M. Turing at the National Physical Laboratory in the early days of the development of electronic computers (1946--1948). The present mood of pessimism among numerical analysts resulting from difficult relationships with computer scientists and mathematicians is discussed. It is suggested that in light of past and present performance this pessimism is unjustified and is the main enemy of progress in numerical mathematics. Some achievements in the fields of matrix computations and error analysis are discussed and likely changes in the direction of research in numerical analysis are sketched.