He grew up in a family of musicians and attended the Gymnasium at St. Stephan in Augsburg (a school offering a musical branch with music, Latin and English as core subjects from grade five onwards). He left the school at the age of 16 to devote himself entirely to music. He studied with Eldar Issakadze, Thomas Grossenbacher and David Geringas.
In 2005, he won the German Music Competition, in 2007 the ARD Music Competition with a trio he founded. At the age of 23 he received the post of the first solo cellist of the Bavarian Radio Symphony Orchestra. He left after four years to devote himself entirely to solo and chamber music work.
In 2011, he received the ECHO Klassik Prize as a young artist of the year, the Bavarian Kunstförderpreis in 2014 and the European Prize for the European Cultural Foundation in 2015.
In the United States, he has performed with the Florida Orchestra. Hornung will return to the Tampa - St. Petersburg area to play Antonín Dvořák's Cello Concerto with the Florida Orchestra January 19, 2018 and January 20, 2018.
- Jump! (with Milana Chernyavska, 2010)
- Saint-Saëns: Suite and Romance / Dvořák: Cello Concerto (2012)
- Gassenhauer (with Nils Mönkemeyer, 2013)
- Richard Strauss: Don Quixote & Cello Sonata, Op. 6 (2014)
- "Interview with Cellist Maximilian Hornung: Everything went right (Alles richtig gemacht)". Crescendo. February 2, 2015.
- "Lingotto Giovani, il violoncellista Maximilian Hornung alla Sala dei 500". Torino Today. February 24, 2017.
- "Cellist Maximilian Hornung shines as Florida Orchestra celebrates the waltz". Tampa Bay Times. January 9, 2016.
- "Florida Orchestra composes a 50th anniversary season of celebration". Tampa Bay Times. March 15, 2017. Retrieved 2017-03-21.