KRONECKER, LEOPOLD

born Dec. 7, 1823, Liegnitz, Prussia [now Legnica, Pol.] died Dec. 29, 1891, Berlin, Ger. German mathematician whose primary contributions were in the theory of equations and higher algebra. Kronecker acquired a passion for the theory of numbers from Ernst Kummer, his instructor in mathematics at the Liegnitz Gymnasium, and earned his doctor's degree at the University of Berlin with a dissertation (1845) on those special complex units that appear in certain algebraic number fields. He managed the family mercantile and land business until the age of 30, when he was financially able to retire. While in business he pursued mathematics as a recreation. From 1861 to 1883 Kronecker lectured at the University of Berlin and in 1883 succeeded Kummer as professor there. Kronecker was primarily an arithmetician and algebraist. His major contributions were in elliptic functions, the theory of algebraic equations, and the theory of algebraic numbers. In the last he created an alternative to the theory of his fellow countryman Julius Dedekind. Kronecker's theory of algebraic magnitudes (1882) presents a part of this theory; his philosophy of mathematics, however, seems destined to outlast his more technical contributions. He was the first to doubt the significance of nonconstructive existence proofs and for many years carried on a polemic against the analytic school of the German mathematician Karl Weierstrass concerning these proofs and other points of classical analysis. Kronecker joined Weierstrass in approving the universal arithmetization of analysis, but he insisted that all mathematics should be reduced to the positive whole numbers. In some of his strictures on classical analysis he was justified by 20th-century research on the foundations of mathematics. The Kronecker delta function is named in his honour.