Davies was schooled in Wales where his father was a teacher of mathematics. He went on to graduate with a first class degree from University of Oxford where he stayed to complete his D.Phil with thesis Some Problems in Functional Analysis in 1968.

Davies has spent his teaching career at the University of Oxford and then King's College London teaching mathematical analysis to undergraduate, postgraduate and doctoral students. He was appointed the Head of the Department of Mathematics at the college from 1990 to 1993.

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