Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a gymnasium, the German equivalent of high school, where he inspired the mathematical career of Leopold Kronecker.

He was awarded a PhD from the University of Halle in 1831 for writing a prize-winning mathematical essay (De cosinuum et sinuum potestatibus secundum cosinus et sinus arcuum multiplicium evolvendis), which was published a year later.

The Kummer surface results from taking the quotient of a two-dimensional abelian variety by the cyclic group {1, −1} (an early orbifold: it has 16 singular points, and its geometry was intensively studied in the nineteenth century).

His methods were closer, perhaps, to p-adic ones than to ideal theory as understood later, though the term 'ideal' was invented by Kummer.

Kummer further conducted research in ballistics and, jointly with William Rowan Hamilton he investigated ray systems.