KRONECKER, kro'nek-r-r, LEOPOLD (1823 91). A German mathematician, born at. Lieguitz. Ile studied at the universities of Berlin. Bonn, and Breslau, and received his doctor's degree at Berlin in 1845. In 1860 he became a member of the Academy of Sciences at Berlin. and the next year lie began giving lectures on mathe matics in the university. ln 1883 he was made professor of mathematics. Kroneeker was one of the greatest of German algebraists. He gave a simpler treatment of eyelotomie equa tions than Gauss, improved the proof of Abel for the insolubility of the general algebraic equation of degree higher than the fourth, and made a thorough investigation of Abelian equa tions, lle also worked out the arithmetical and algebraic problems involved in the theory of elliptic functions, and materially improved the general theory. Ile attempted to do away with all special ideas of number, such as frac tions and irrational numbers. and to construct a scientific arithmetic on the basis of the one concept 'number.' 'die Anzahl.' This problem
was. more recently. further elaborated by Klein. Kroneeker's most important works are: Grand ziige arith m et ;sell, n Theorie ff, r byr braischra Gros.wn ( 1882) : flehrr d. n Zahlhegriff (18:71; Vorlesunyen (edited by 'Hensel and Netto. you. i.. 15941. His Werke, edited by Hen sel. were published at Leipzig in H95-99. Ile assisted also in editing Crelle's Journal fur Nathematik. Many of hi- published articles are found in the Monatsberiehte of the Academy of Berlin, in the Comptes rend us of the Academy of Sciences of Paris, and in the Annales de l'Ecolc Normoic Supc'ricure of Paris. His corre spondence with Dirichlet appeared in the Got tingische gelehrte An:eigen (1885), Consult: Frobenius, "Gediichtnisrede auf Leopold Kro necker." in the Abhandhingcn of the Berlin Academy of Sciences (1893) : and the catalogue of scientific papers of the Royal Society of Lon don.