Gotthold Eisenstein

Gotthold Eisenstein (1823–1852) was a German mathematician whose work shaped number theory, elliptic functions, and the theory of algebraic forms.

Connect

Number theory: The study of integers and the relationships among them. Eisenstein’s work on primes and reciprocity belongs to this broader field.
Eisenstein's criterion: A test for polynomial irreducibility using divisibility of its coefficients by a prime. This named criterion gives a concise example of Eisenstein’s algebraic ingenuity.
Carl Friedrich Gauss: A German mathematician whose work transformed number theory, geometry, and mathematical physics. Gauss praised Eisenstein’s talent and helped bring attention to his early work.
Berlin: The capital of Germany and a major European center of scholarship and government. Eisenstein studied, taught, and pursued much of his mathematical work in Berlin.
Elliptic function: A meromorphic function with two independent periods in the complex plane. These functions formed one of Eisenstein’s central research subjects.
Eisenstein series: A family of modular forms constructed by summing powers over lattice points or integer pairs. These series connect Eisenstein’s work on elliptic functions with modern modular-form theory.
Alexander von Humboldt: A Prussian naturalist and explorer who supported scientific and intellectual life in Berlin. Humboldt advocated for Eisenstein and helped secure financial support for him.
University of Berlin: A Prussian university founded in Berlin in 1810, later known as Humboldt University of Berlin. Eisenstein studied mathematics there and later received an academic appointment.
Modular form: A complex analytic function with prescribed transformation properties under a modular group. Eisenstein series became foundational examples in this theory.
Cyclotomic polynomial: A polynomial whose roots are the primitive roots of unity of a given order. Cyclotomic polynomials supplied tools for Eisenstein’s work on irreducibility and reciprocity.