By National Academy of Sciences Office of the Home Secretary
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Ann. Math. 13(2):167-86. 1913 Boundary problems in one dimension. Int. Congr. Math. 1:163-95. MAXIME BÔCHER 39 1914 On Gibbs’ phenomenon. Crelle’s J. 144:41-47. 1917 Leçons sur les Méthodes de Sturm dans la Théorie de Équations Différentielles Linéaires et leurs Développements Modernes, professées à la Sorbonne en 1913-1914. (Recueillies et rédigées par G. Julia), (Collection de Monographies sur la Théorie des Fonctions, ed. Borel), Paris. Courtesy of Photographic Laboratories, University of Minnesota, St.
With Klein it was not a question of developing a method for its own sake, or even of caring for method, except in so far as he was thus able to uncover the natural interrelations of parts of the science which hitherto had seemed foreign to each other. A pupil of Clebsch and Plücker, Klein early became acquainted with the geometric advances that group themselves about the names of Monge and Poncelet, of Steiner and von Staudt. In analysis, the theory of functions, as developed by Cauchy and his followers, was already beginning to come into its own.
Not that, with him, there was no place for intuition in mathematics. Quite the reverse. He recognized clearly that rigor is relative, depending on the domain of conceptions and the logical maturity of the student, and he was a master of diagnosis in determining what his students required or could receive, and what their minds must reject. His contributions of the kind we have been considering were not confined to improving proofs already complete. He discovered gaps and filled them; as in the case of the theorem that a function which is harmonic in the neighborhood of a point, that point excepted, and becomes infinite there, must be of the form (when n = 2): MAXIME BÔCHER 35 u = k log r + ω, where ω is the harmonic at the point, also.