Kronecker wrote his 1845 dissertation, at the University of Berlin, on number theory, giving special formulation to units in certain algebraic number fields.

After obtaining his degree, however, Kronecker managed the estate and business of his uncle, producing nothing mathematical for eight years. In his 1853 memoir on the algebraic solvability of equations, Kronecker extended the work of Évariste Galois on the theory of equations. He accepted a professorship at the University of Berlin in 1883.

Kronecker also contributed to the concept of continuity, reconstructing the form of irrational numbers in real numbers. In analysis, Kronecker rejected the formulation of a continuous nowhere-differentiable function by his colleague, Karl Weierstrass. In his 1850 paper, *On the Solution of the General Equation of the Fifth Degree*, Kronecker solved the quintic equation by applying group theory.

Kronecker's finitism made him a forerunner of intuitionism in foundations of mathematics.