A contributor to the concept of continuity and the reconstruction of irrational numbers in real numbers, Kronecker was a German mathematician who worked on number theory and algebra. He was born in Liegnitz, Prussia (now Legnica, Poland) into a Jewish family. He was a student and lifelong friend of Ernst Kummer, and Peter Gustav Dirichlet was also among his teachers.
In 1845, Kronecker wrote his dissertation at the University of Berlin on number theory, giving special formulation to units in certain algebraic number fields. 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 Évariste Galois on the theory of equations. 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 the Abel–Ruffini theorem.
Kronecker 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. His finitism made him a forerunner of intuitionism in foundations of mathematics.
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." His published works included "Vorlesungen über Zahlentheorie," Berlin, New York: Springer-Verlag, ISBN 978-3-540-08277-4, MR529431; and Hensel, Kurt, ed., "Leopold Kronecker's Werke. Bände 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.'"
