Mr. Leopold Kronecker

A German mathematician who worked on number theory and algebra. He criticized Cantor's work on set theory, and was quoted by Weber (1893) as having said, "God made integers; all else is the work of man". He was a student and lifelong friend of Ernst Kummer. He was born in Liegnitz, Prussia (now Legnica, Poland) into a Jewish family. In 1845, he wrote his dissertation at the University of Berlin on number theory, giving special formulation to units in certain algebraic number fields. Peter Gustav Dirichlet was his teacher. After obtaining his degree, he managed the estate and business of his uncle, producing nothing mathematical for eight years. In his 1853 memoir on the algebraic solvability of equations, He extended the work of ?variste Galois on the theory of equations. He accepted a professorship at Friedrich-Wilhelms University (today: Humboldt University) of Berlin in 1883. He also contributed to the concept of continuity, reconstructing the form of irrational numbers in real numbers. In analysis, he rejected the formulation of a continuous, nowhere differentiable function by his colleague, Karl Weierstrass. In an 1850 paper, On the Solution of the General Equation of the Fifth Degree, He solved the quintic equation by applying group theory (though his solution was not in terms of radicals, since this was already proven impossible by Abel?Ruffini theorem). His finitism made him a forerunner of intuitionism in foundations of mathematics. He published ?Vorlesungen ?ber Zahlentheorie?, Berlin, New York: Springer-Verlag, ISBN 978-3-540-08277-4, MR529431; and Hensel, Kurt, ed., ?Leopold Kronecker's Werke. B?nde I?V?, New York: Chelsea Publishing Co., MR0237286. In ?Turing?s Cathedral? by George Dyson it is noted by Morse, ?One cannot decide between Kronecker and Weierstrass by a calculation,? Morse continued, warming up. ?There is a center and final substance in mathematics whose perfect beauty is rational, but rational ?in retrospect.?