Klein, Mittag-Leffler, and the Klein-Poincaré Correspondence of 1881–1882

If a modern-day Plutarch were to set out to write the “Parallel lives” of some famous modern-day mathematicians, he could hardly do better than to begin with the German, Felix Klein (1849–1925), and the Swede, Gösta Mittag-Leffler (1846–1927). Both lived in an age ripe with possibilities for the mathematics profession and, like few of their contemporaries, they seized upon these new opportunities whenever and however they arose. Even when their chances for success looked dismal, they forged ahead, winning over the skeptics as they did so. Although accomplished and prolific researchers (Klein’s work has even enjoyed the appellation “great”), they owed much of their success to their talents as lecturers. Indeed, as teachers they exerted a strong influence on the younger generation of mathematicians in their respective countries. Klein’s German students included such prominent figures as Ferdinand Lindemann, Walther von Dyck, Adolf Hurwitz, Robert Fricke, Philipp Furtwängler, and Arnold Sommerfeld. His influence on North American mathematicians was, if anything, even stronger, as will be briefly described in this essay. Since Stockholm’s Högskola, founded in 1878, could hardly compete with the much older universities where Klein taught, most notably Leipzig and Göttingen, Mittag-Leffler was clearly not in a position to draw large numbers of doctoral students. Nevertheless, he attracted several, four of whom left their mark on modern mathematics: Edvard Phragmén, Ivar Bendixson, Helge von Koch, and Ivar Fredholm. (Stubhaug 2010)