Do professors frown upon students who don't take notes? I am a math student and never take notes in class. I feel like I am offending the professors by not taking notes. In general, do professors like students to be "active" during class? I have never learned much by taking notes. 

I see other graduate students furiously taking notes...and then I am afraid that professors may write that I am lazy in recommendation letters. So maybe I should just takes notes?
Sometimes I wish students would stop taking notes and actually think about what I'm saying. I provide the lecture notes before/after class anyway...