She received the Sofia Kovalevskaya Award in 2006[1] and the European Mathematical Society Prize (2008).

At the age of 15, she was selected for a high school that specialized in mathematics, which she graduated from two years later.

Holtz attended the South Ural State University in Chelyabinsk (1995) and the University of Wisconsin–Madison (2000), staying on at the latter until 2002 in a postdoctorate research position after earning her Ph.D. She then spent 1.5 years in Germany with a Humboldt research fellowship at the Institute of Mathematics of Technische Universität Berlin, before returning to the United States in 2004, where she held a Morrey Assistant Professorship at the Department of Mathematics of the University of California, Berkeley from 2004 to 2007.

After winning a €1,000,000 Sofia Kovalevskaya Award in 2006, Holtz built her research group at Technische Universität Berlin,[3] where she became a Professor of applied mathematics while concurrently serving as an Associate, then Full Professor of Mathematics at University of California, Berkeley.

[4] Holtz, who considered a career in music before deciding on mathematics, performs with the Berlin Philharmonic Choir and practices ballroom dancing.