Barker's early specialism was
ancient Greek philosophy. He later became interested in ancient
musical theory and the
music of ancient Greece. This led to an interest in the "points of intersection between
musical theory and philosophy". In 1970, Barker joined the Philosophy Department of the
University of Warwick as a lecturer in philosophy. In 1976, he joined the
Faculty of Classics, University of Cambridge as an
assistant lecturer in classics. From 1977 to 1978, he was also a
fellow of
Selwyn College, Cambridge, and its director of studies in classics and philosophy. He returned to Warwick in 1978 and was promoted to
senior lecturer in 1987. Wanting to move from a philosophy specialist to a
classicist, Barker joined the Classics Department of the
University of Otago in 1992. He was a senior lecturer in classics from 1992 to 1995, and was appointed a
Professor in 1995. He returned to England to join the
University of Birmingham in 1996 as
Reader in Classics. He was promoted to Professor of Classics in 1998. He also held a
British Academy Research Professorship between 2000 and 2003. He retired from full-time academia in 2008 and was appointed
emeritus professor. ==Personal life==