The founding, during the course of the fourth century, first of Plato's Academy and then of Aristotle's school, the Lyceum or Peripatos, had far-reaching significance not just for what may be called higher education, but also for scientific research. The Alexandria became pre-eminent in many branches of scientific research in the third century, even though Athens remained supreme throughout antiquity in philosophy. Already in the mid fourth century BC Plato and Isocrates distinguished between two main types of reasons for studying mathematics, that is broadly the practical and the theoretical. Both geography and astronomy have on the one hand a descriptive and on the other a theoretical, mathematical aspect. The history of medicine and the life sciences in the Hellenistic period illustrates several of our principal themes, the increase in specialization, but also the fragmentation of scientific research, the role of royal patronage, and the patchy success in the application of scientific knowledge to practical ends.