HISTORY OF THE THEORY OF NUMBERS: AN HISTORICAL STUDY WITH MATHEMATICAL IMPLICATIONS

ABSTRACT. — In 1911, the research mathematician Leonard Dickson embarked on a historical study of the theory of numbers which culminated in the publication of his three-volume History of the Theory of Numbers. This paper discusses the genesis of this work, the historiographic style revealed therein, and the mathematical contributions which arose out of it. RÉSUMÉ.—HISTORY OF THETHEORY OFNUMBERS DE LEONARDDICKSON: ÉTUDE HISTORIQUE AVEC DES PROLONGEMENTS MATHÉMATIQUES.—En 1911, le mathématicien Leonard Dickson s’est lance ́ dans une étude historique de la théorie des nombres, qui a culmine ́ avec la publication de son History of the Theory of Numbers en trois volumes. Notre étude examine la genèse de ce travail, l’approche historiographique qui la sous-tend et les contributions mathématiques qui en découlent. In 1911, only a decade into what would become a forty-year-long career in the mathematics department at the University of Chicago, Leonard Dickson had a résume ́ which solidly identified him as a distinguished mathematician. He had, for example, authored roughly 150 mathematical papers (primarily in group theory at this point) and three books, served as editor of the American Mathematical Monthly from 1902 to 1908 and recently assumed this post for the Transactions of the American Math-ematical Society, and passed swiftly through the ranks from assistant to associate to full professor at one of the premiere mathematics institutions in this country. Yet, in 1911, he threw what seems a rather twisted turn into his professional plans by pursuing a historical project which woul