Medieval universities were in many ways similar to the higher education part of medieval madrasas. Both started as religious schools that expanded to teach a wide range of subjects. The difference is that the university tradition thrived because Europe prospered, while the madrasa tradition stagnated because the Islamic world fell behind.
The real question is a matter of definitions. Is a university a insitute of higher education that follows the university tradition? Or is it any institute with a similar role in the society, regardless of its traditions?
The real question is a matter of definitions. Is a university a insitute of higher education that follows the university tradition? Or is it any institute with a similar role in the society, regardless of its traditions?