Hochbruck went to high school in Krefeld, and studied Technomathematics at the Karlsruhe Institute of Technology from 1983 to 1989. She completed her Ph.D. at Karlsruhe in 1992.[1] Her dissertation, Lanczos und Krylov-Verfahren für nicht-Hermitesche lineare Systeme, was jointly supervised by Wilhelm Niethammer and Michael Eiermann.[3]
After postdoctoral research at ETH Zurich, she became an assistant at the University of Würzburg in 1992, and moved to the University of Tübingen in 1994. She obtained her first professorship in 1998, in applied mathematics at the University of Düsseldorf, declining two offers of professorships at other German universities in the same year. In 2010 she returned to Karlsruhe as a professor.[1]