By National Academy of Sciences Office of the Home Secretary
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In the early years of our professional lives we were in constant intercourse over such matters. Each of us was seeking to clarify and simplify his subject. Neither of us regarded the theory of functions of a real or of a complex variable as an end in itself, for each had his own ulterior uses for the theory— Bôcher, his differential equations, both complex and real. In fact, for each of us the theory of functions was applied mathematics, and in presenting its subject matter and its methods to our students, our aim was to show them great problems of analysis, of geometry, and of mathematical physics which can be solved by the aid of that theory.
The later years of his life were not happy ones. Even as far back as the winter of 1913–1914 his strength was frequently inadequate for the daily needs. He never complained; in fact, he was unwilling to talk about himself even for a moment. But for one whose demands on himself were such as Bôcher’s it must have been a severe trial not to achieve the full measure of results of which the mind was capable and for which it longed to work. He was a Puritan, and with the virtues he had also the MAXIME BÔCHER 23 faults of the Puritan.
Bôcher’s advanced course in the first year of his professional life took the form of a seminary, the subject being curvilinear coordinates and functions defined by differential equations. A part of the instruction consisted of formal lectures on the latter topic, and he thus began, even at that early date, to treat topics in a field of analysis in which he was to become eminent. In the eighties, a number of American students of mathematics from various colleges went abroad, chiefly to Germany for further instruction and guidance in mathematics.