Brentjes is the daughter of archaeologists, orientalists, and Islamists and Helga Wilke Brentjes. She earned a diploma in mathematics from
TU Dresden in 1973 and completed her doctorate (
Dr. rer. nat.) there in 1977. Her doctoral dissertation,
Untersuchungen zur Geschichte der linearen Optimierung von den Anfängen zur Konstituierung als selbständige mathematische Theorie - eine Studie zum Problem der Entstehung mathematischer Disziplinen im 20. Jahrhundert, concerned the history of
linear programming, and was supervised by
Hans Wussing. She earned a second diploma in Near Eastern studies in 1982 from
Martin Luther University of Halle-Wittenberg, a second doctorate (
Dr. sc. nat.) from
Leipzig University in 1989, and a
habilitation from Leipzig University in 1991. She worked as an assistant professor in the Karl Sudhoff Institute for the History of Medicine and Sciences at Leipzig University from 1976 to 1997, with tenure beginning in 1980. After holding a sequence of research positions at the
Max Planck Institute for the History of Science, Institute for the History of Science at
Goethe University Frankfurt, and
University of Oklahoma, she became an associate professor at the
Aga Khan University Institute for the Study of Muslim Civilisations in 2004. Since 2007 she has been a researcher at
LMU Munich, the
University of Seville, and the Max Planck Institute for the History of Science, where she has been affiliated since 2012. ==Recognition==