I had a professor for a real analysis class that I really enjoyed. I was curious about his research. I asked him to do a senior thesis and in doing so, he introduced me to area of math/physics that I love (stochastic dynamics, as applied to quantum/stat mech). It was an amazing experience looking back. We met up frequently and just talked. We talked about whatever we wanted to talk about. Granted, it was aimed at a point, but sometimes he would just teach me things he thought were important. We talked one time for 3 to 4 hours (always at least 1 or 2 hours). Just about math, science, philosophy, etc. I have learned so much from this guy. He is crazy smart, not only in science and math, but in philosophy and life as well. He trusted me, and actually asked me to lecture at a seminar HE goes to. I am an undergraduate and these were graduate students and professors. He trusted me enough and gave me the experience, which was amazing. I did fine, and it was a great experience. He's helped me develop so much professionally. There are so many little tidbits of information he gave me. I sometimes would come to him with random ideas or things I thought were cool from my math or physics classes. He would explain it to me in depth and I always got a good perspective from him. I remember once I had a passing idea, I brought it up and he lectured for like an hour and a half. He always fostered ideas and encouraged me to think and question. The biggest thing he did though, was basically get me into grad school. I asked for a letter of rec and he did me one better. He has a friend who is working on what I want to, and long story short I should be going to graduate school and working with his friend. It's paid as well. He gave me what I want to study, what area I want to go into. He taught me so much about math and science in general. He taught me about philosophy, life, academia, science (in the larger picture). He gave me the experience of the lecture. He got me into grad school. This guy helped me develop professionally and personally so much, it's truly remarkable.