That is also true. But sometimes you need a mentor of sorts to help you when you need it, and some professors can do that well.

At this juncture, a professor stops being a professor and becomes a colleague.

EDIT: What I am trying to say is that a professor/student relationship is one of inequality. When the relationship moves beyond only one side influencing the course of discussion/discovery, then a relationship of equals is established, albeit a relation of equals where one side is more equal than the other (and that relationship may swap over the course of time).

I like that phrasing. And most bright kids never get a "colleague" like that. I just finished reading Lockhart's Lament, and it made me sad that even though I was one of the best students in my IB program in high school, then got a BS in CS, I had to learn from the internet 10 years later that math is a journey of creative discussion.

The first time through a Bachelor's program I made the same mistake. I wanted so much to get out of school and head into the business world. The result was a finance degree and an intense urge to go back to school to pursue math and computer science. Now I am going back to pursue those two at Bowling Green, and I will not make the same mistake again.