Franz Mertens studied at Berlin with Kronecker and Kummer. In 1865 he obtained a doctorate with a dissertation on potential theory.
He worked first in Krakóv, then in Graz, then from 1894 in Vienna.
Mertens was a number theorist who is best remembered for his elementary proof of the Dirichlet theorem which appears in most modern textbooks. He worked on analytic number theory and algebra.