Cantor, Moritz Benedikt

(b. Mannheim, Germany, 23 August 1829; d. Heidelberg. Germany, 9 April 1920),

mathematics.

Cantor’s father, Isaac Benedikt Cantor, was from Amsterdam; his mother, Nelly Schnapper, was the daughter of a money changer. Cantor married Tilly Gerothwohl, from Frankfurt am Main.

Cantor was first taught by private tutors and completed his secondary education at the Gymnasium in Mannheim. In 1848 he began studying at Heidelberg under Franz schweins and Arthur Arneth, and from 1849 to 1851 he worked at Göttingen under Gauss and Moritz Stern. He took his degree at Heidel berg in 1851 with the thesis Ein wenig gebräuchliches Coordinatemystem. During the summer semester of 1852 he studied in Berlin under Dirichlet and Jakob Steiner and qualified for inauguration at Heidelberg in 1853 with Grundzüge einer Elementar-Arithmetik.

Cantor was greatly influenced by Arneth’s Geschichte der reinen Mathematik in ihrer Beziehung zur Entwicklung des menschlichen Geistes and was encouraged in his work by Stern and the cultural philosopher E. M. Roeth. During a stay in Paris he became a close friend of Chasles and of Joseph Bertrand. From 1860 he lectured on the history of mathematics. In 1863, as a result of his Mathematischen Beiträge zum Culturleben der Völker, Cantor was appointed extraordinary professor. The Rö mischen Agrimensoren and ihre Stellung in der Geschichte der Feldmesskunst (1875) led to his appointment as honorary professor; in 1908 he became full professor, and in 1913 he became emeritus.

From 1856 to 1860 Cantor was coeditor of Kritischen Zeitschrift für Chemie, Physik and Mathemalik, and from 1860 of Zeitschrift für Mathematik and Physik; from 1877 to 1899 he edited Abhandlungen zur Geschichte der Mathematik. He published many short papers and reviews in periodicals devoted to pure mathematics and the history of science and, from 1875, wrote most of the biographies of mathematicians in Allgemeine Deutsche Biographie.

Together with Curtze and Günther, Cantor was one of the leading historians of mathematics in Germany at the turn of the century. He is best known for the once highly praised Vorlesungen über Geschichte der Mathematik, which, despite many contemporary emendations (such as those of Braunmühl, Gustaf Eneström, and Wieleitner), has not been equaled in content and extent. Although the Vorlesungen is now dated, it gave a definite impetus to the development of the history of mathematics as a scholarly discipline.

BIBLIOGRAPHY

I. Original Works. Cantor’s best-known work is Vor-lesungen über Geschichte der Mathematik, 4 vols. (Leipzig, 1880–1908). His other writings include Ein wenig gebrä uchliches Coordinatensystem (Frankfurt, 1851); Grundzüge einer Elementar-Arithmetik (Heidelberg. 1855); Mathematischen Beiträge zum Culturleben der Völker (Halle,1863); and Romöschen Agrimensoren and ihre Stellung in der Geschichte der Feldmesskunst (Leipzig, 1875).

II. Secondary Literature. Writings on Cantor or his work are Karl Bopp, “M. Cantor †, Gedächtnisrede, gehalten im Mathematischen Verein zu Heidelberg am 19. VI.1920,” in Sitzungsberichte der Heidelberger Akademie der Wissenschaften, Math.-nat. Kl., Abt. A (1920); and “Cantor, M.,” in Deutsches biographisches Jahrbuch, II (Stuttgart Berlin Leipzig, 1928). 509–513, with complete bibliography; M. Curtze, “Verzeichnis der mathematischen Werke, Abhand-lungen and Recensionen von M. Cantor,” in Zeitschrift für, Mathematik and Physik, 44 , supp. (1899), 625–650, with portrait; and “Zum 70. Geburtstage M. Cantors,” in Bibliotheca mathematica, 3rd ser.” 1 (1900). 227–231; and J, E. Hofmann, “Cantor, M. B.,” in Neue Deutsche Biographie, III (Berlin, 1957), 129.

J. E. Hofmann