Can a philosopher be a politician at the same time?

Today in class, we were learning about the first philosophers in Miletus. My teacher explained that one of the reasons philosophy started there was because they were rich and had spare time to practice philosophy. However, then he said that to really be able to practice it, the person has to be free of every burden/task thus not engaging in business or politics. After the lesson I discussed it with him: I believe practicing politics and philosophy at the same time is perfectly doable. Aren't there a lot of philosophers that did both (he said that Marx is an exception)? Am I wrong?