Troppfke, Johannes

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(b Berlin, Germany, 14 October 1866; d. Berlin, 10 November 1939)

history of mathematics.

Tropfke came from a wealthy family. A bright student, he was encouraged to study a number of different subjects at the Friedrichs Gymnasium, and his wide-ranging interests at the University of Berlin are reflected in the list of subjects Tropfke prepared for the state examination in 1889: mathematics, physics, philosophy, botany, zoology, Latin, and Greek. His dissertation dealt with a topic in the theory of functions. An enthusiastic teacher, he was director of the Kirschner Oberrealschule from 1912 to 1932.

Tropfke’s program for changing the secondary school mathematics curriculum, presented in 1899, was published in expanded form as Geschiche der Elementarmathematik in systematischer Darstellung (1902–1903). Even in this form, however, it was still based mainly on a study of secondary literature that was largely unchecked by an examination of original sources. Tropfke subsequently produced a second, seven-volume edition (1921–1924) that benefited from the constructive and sympathetic criticism of Heinrich Wieleitner and Gustaf Enestöm. This work offered what was, at the time, an excellent overall account of the subject, enriched by a wealth of extremely valuable citations and references. Moreover, it exerted a decisive influence on the reorganization of mathematical education, encouraging teachers to devote greater attention to historical development.

Advances in the study of the history of mathematics led Tropfke to undertake a third, revised and enlarged edition of his work; but it was not completed. He died shortly after the beginning of the war; and the remaining volumes, already in manuscript, were destroyed.


Tropfke’s writings include Zur Darstellung des elliptischen Integrals erster Gattung (Halle, 1889), his disertation; Erstmaliges Auftreten der einzelnen Bestandteile unserer Schulmathematik Darstellung, 2 vols. (Leipzig, 1902–1903; 2nd ed., 7 vols., Leipzig-Berlin, 1921–1924; 3rd ed., 4 vols., Leipzig-Berlin, 1930-1940); “Archimedes und die Trigonometrie,” Archive für Geschichte der Mathematik, der Natunwissenschaften und der Technik, n.s. 10 (1928), 432–461; “Zur Geschichte der quadratischen Gleichungen über dreieinhalb Jahrtausende,” in Jahresberichte der Deutschen Mathematicker-vereinigung43 (1933), 98–107; and 44 (1934), 26–47, 95–119; and “Die Siebenecksabhandlung des Archimedes,” in Osiris, 1 (1936), 636–651.

An obituary by J.E. Hofmann, with portrait and bibliography, is in Deutsche Mathematik, 6 (1941), 114–118.

J. E. Hofmann