The Football Player and the Infinite Series

1430 NOTICES OF THE AMS VOLUME 44, NUMBER 11 The Football Player The air buzzed with anticipation as the football team crowded excitedly into the lecture hall. The country’s top halfback was about to defend his Ph.D. thesis in mathematics! It soon became apparent that the proceedings were a mere formality, as the candidate’s dissertation on summability methods for divergent Dirichlet series was a masterful piece of work. This scenario is no fantasy from a 1990s television sitcom; it is a true story. The place was Copenhagen, the year was 1910, and the sport was “football” as the word is understood internationally (“soccer” in American lingo). The star halfback played in the 1908 Olympics on Denmark’s silver-medal football team, a team that is still in the record books [21, p. 172] for the most goals scored in a single game. (Denmark defeated France by the lopsided score of 17 to 1.) The dissertation title was Contributions to the Theory of Dirichlet Series (well, actually Bidrag til de Dirichlet’ske Rækkers Theori), and the candidate’s name was Harald Bohr. (Devotees of American football remember Frank Ryan, who wrote his Ph.D. dissertation [23, 24] on geometric function theory while quarterback for the Cleveland Browns, champions of the National Football League at the time. But that’s another story [18, 22].) Among mathematicians, Harald Bohr is best remembered today for his theory of almost periodic functions [10]; students of complex analysis also know him for the Bohr-Mollerup theorem (see, for example, [3, Theorem 2.1], [12, §§274–275]) that characterizes the Γ function on the positive real axis as the unique positive, logarithmically convex function f such that f (x + 1) = xf (x) for all x and f (1) = 1. In his native land Bohr’s early fame as a sports hero and his subsequent prominence as a distinguished academician were eclipsed by his status as the kid brother of Niels Bohr. Brother Niels, a prime architect of modern atomic theory and recipient of the Nobel prize for physics in 1922, was Denmark’s most honored citizen during his lifetime.