Michael Atiyah, in an interview in Mathematical Intelligencer (published long ago, in 1984):
Universities are institutions that are educational and involved in research. I think that is very important–there should be unity in the university and unity in the whole social structure that attempts to keep a broad balance between mathematical research and mathematical education. And when universities give courses for educational purposes, they should be sure that they are performing the right task for the students, not just giving courses in (say) advanced topology because they are interested in turning out research students. That’s a disastrous mistake.
Universities must try to balance two activities. They ought to know what’s useful for students to learn, bearing in mind what they are going to be doing later on. At the same time, they ought to foster research. Some people will be doing all research and some people will be mostly teaching, and mainly people will be in between. Although I am only involved with the research end of it, I live in the university, I have colleagues in the university, I know what they are involved with, so I am concerned to see that a proper balance is struck between the different functions of the university.
A good one!