Alright. I'm a Math major who takes upper division Math classes and only aim for Honor or hard classes. So anybody who's the same with me or at least looking for a good professor, listen up. He's very motivating and encouraging a professor. Even most of Math TAs like him. His lectures are disorganized from times to times, but that's his style. He gives you a lot of intuitions about what's going on, you have to understand for it, after all, he's half-artist, the man plays violin. His homework is extremely difficult but it's very focused; it gives you insights on topology. His exams aren't so hard, they're doable, IF AND ONLY IF you do and understand the homework. Trust me, the exams are 5 times easier than the homework, so don't freak out. I mean, I took this class before 131A, which is a prerequisite, and I got A. Prof. Greene helped me a lot to understand things. He's like my guru now. He's very caring as well. His personality is a bit funny, but he's not cold. Upper division students might find this smart man as a great professor whilst lower divisions ones just can't stand his lecture style. There you go; it's my opinion.