From about 1950, Davenport was the obvious leader of a "school", somewhat unusually in the context of British mathematics. The successor to the school of mathematical analysis of G. H. Hardy and J. E. Littlewood, it was also more narrowly devoted to number theory, and indeed to its analytic side, as had flourished in the 1930s. This implied problem-solving, and hard-analysis methods. The outstanding works of Klaus Roth and Alan Baker exemplify what this can do, in diophantine approximation. Two reported sayings, "the problems are there", and "I don't care how you get hold of the gadget, I just want to know how big or small it is", sum up the attitude, and could be transplanted today into any discussion of combinatorics. This concrete emphasis on problems stood in sharp contrast with the abstraction of Bourbaki, who were then active just across the English Channel.