One day about twenty years ago I was admitted to the study of Professor Landau, seeking advice as to a subject for a thesis. After some preliminary inquiries as to my experience and preferences, he handed me a long sheet of paper, and directed me to take notes as he enumerated some dozen or fifteen topics in various fields of analysis and number theory, with a few words of explanation of each. He told me to think about them for a few days, and to select one of them, or any other problem of my own choosing, with the single reservation that I should not prove Fermat's theorem, an injunction which I have observed faithfully. Guided partly by natural inclination, perhaps, and partly by recollection of a course on methods of approximation which I had taken with Professor Bôcher a few years earlier, I committed myself to one of the topics which Landau had proposed, an investigation of the degree of approximation with which a given continuous function can be represented by a polynomial of given degree. When I reported my choice, he said meditatively, in words which I remember vividly in substance, if not perfectly as to idiom: ‘Das ist ein schönes Thema, ich beneide Sie um das Thema… Nein, ich beneide Sie nicht, aber es ist ein wunderschönes Thema!’ [That is a beautiful topic, I envy you that topic… No, I do not envy you, but it is a wonderful topic.]