Leopold Kronecker



Leopold Kronecker (December 7, 1823 – December 29, 1891) was a Prussian mathematician and logician who argued that arithmetic and analysis must be founded on "whole numbers."

Quotes

 * Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk.
 * God made the integers, all the rest is the work of man.
 * In a lecture to the Berliner Naturforschung-Versammlung, 1886; quoted in the obituary “Leopold Kronecker”, by H[einrich] Weber, in Jahresbericht der Deutsche Mathematiker Vereinigung, 1893, page 19
 * Quoted in "Philosophies of Mathematics" - Page 13 - by Alexander George, Daniel J. Velleman - Philosophy - 2002


 * Es handelt sich um meinen liebsten Jugendtraum, nämlich um den Nachweis, dass die Abel’schen Gleichungen mit Quadratwurzeln rationaler Zahlen durch die Transformations-Gleichungen elliptischer Functionen mit singularen Moduln grade so erschöpft werden, wie die ganzzahligen Abel’schen Gleichungen durch die Kreisteilungsgleichungen.
 * from a letter to Richard Dedekind, Berlin, 15th March 1880. Leopold Kronecker's Werke, ed. Kurt Hensel, 5th volume, 1930, p. 455 books.google, See also Kronecker's Jugendtraum.

Quotes about Kronecker

 * Now it is time for us to realize that, in his Grundzüge, Kronecker did not merely intend to give his own treatment of the basic problems of ideal-theory which form the main subject of Dedekind's life-work. His aim was a higher own. He was, in fact, attempting to describe and to initiate a new branch of mathematics, which would contain both number-theory and algebraic geometry as special cases. This grandiose conception has been allowed to fade out of our sight, partly because of the intrinsic difficulties of carrying it out, partly owing to historical accidents and to the temporary successes of the partisans of purity and of Dedekind. It will be the main purpose of this lecture to try to rescue it from oblivion, to revive it, and to describe the few modern results which may be considered as belonging to the Kroneckerian program.
 * André Weil: "Number-theory and algebraic geometry." In Proc. Intern. Math. Congress, Cambridge, Mass., vol. 2, pp. 90–100. 1950. (quote from p. 90)