ELECTED F.R.S. 1948

most of his life was spent outside of Germany, but his mathematical roots remained in the great school of mathematics that existed in Germany between the two world wars. Above all Mahler lived for mathematics; he took great pleasure in lecturing, researching and writing. It was no surprise that he remained active in research until the last days of his life. He was never a narrow specialist and had a remarkably broad and thorough knowledge of large parts of current and past mathematical research. At the same time he was oblivious to mathematical fashion, and very much followed his own path through the world of mathematics, uncovering new and simple ideas in many directions. In this way he made major contributions to transcendental number theory, diophantine approximation, p-adic analysis, and the geometry of numbers. Towards the end of his life, Kurt Mahler wrote a considerable amount about his own experiences; see ‘Fifty years as a mathematician ’ [209], ‘How I became a mathematician ’ [192], ‘Warum ich eine besondere Vorliebe für die Mathematik habe ’ [214], ‘Fifty years as a mathematician II ’ [222]. There is also a recent excellent account of his life and work by Cassels (1991). In preparing thi