German mathematician and logician who vociferously opposed the work of Georg Cantor. He insisted that arithmetic and analysis should be based on whole numbers and is credited with saying, "God made the natural numbers; all else is the work of man" (Bell 1986, p. 477). He was a student and lifelong friend of Kummer. His dissertation was on number theory and dealt with units in certain algebraic number fields.

After obtaining his degree, however, Kronecker managed the estate and ran the business of his uncle following his death. For eight years, Kronecker produced no mathematical work. Then, in his 1853 memoir on the algebraic solvability of equations, he extended Galois's work on the theory of equations. He studied continuity and irrational numbers, and vigorously opposed Weierstraß's continuous nondifferentiable function. In On the Solution of the General Equation of the Fifth Degree (1858), he obtained a solution to the quintic equation similar to Hermite's using group theory.

Galois, Hermite, Weierstrass

Additional biographies: MacTutor (St. Andrews)