[A2A] Here are a few reasons:
- Self-education: You learn the most by explaining to others. I know more about MOS-transistors after teaching a class on MOS transistors last semester than I ever did by taking three classes taught by three different teachers on this subject during my graduate and undergraduate studies.
- Cheap-labor: in form of graduate students. In a research lab setting, it is really hard to find collaborators, but who needs collaborators when you can have really smart people working for you for practically free?
- Control on information: How many scientists do you know who work at Microsoft Research or IBM Research? Even if you know them, these companies keep most of their research secret, so you probably don't know about their work. But, professors have complete control over how much information they want to release to public.
- Recognition: One has to be a really great scientist to be known. But, professors get recognition quite easily through teaching so many students and open nature of universities.
- Posterity: A professor's Ph.D. students keep his name and field alive even after he retires or dies.
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