I'm a little confused on the fact that you're going to try and prove your professor wrong, so that he will give you more homework.
... Which is a good thing...
Ah. I'm trying to generate Respect. Respect is generated in one of three ways:
1. Asking interesting questions
2. Proving that a mathematician made a mistake and, more importantly, fixing things so that they're sailing smoothly again.
3. Solving hard problems or, even better, really hard problems (or, even better, Riemann's Hypothesis >_>). Extra points if you do it with clarity and elegance.
The reason why you want Respect is because, should you gain sufficient amounts of it, you are set for life. Mathematicians care for their own. It's a tight-knit community full of gentle (though admittedly extremely argumentative) people. The trouble is that when you don't have Respect, you don't get to talk to the interesting folks who have done great things. It's a societal taboo. If you're a lowly student seriously trying to break into mathematical society, you can't really ask for help. Your job is to work hard until you can do the above three things consistently, and then you're a Promising Student who is Clearly Well-Motivated (and you really don't need to ask for help anymore, because you're probably more skilled than most post-docs >_> Don't get me started on Algebra Guy.).
The other thing is that solving problems is ... well, it's really fun. I'll admit that at first it's extremely frustrating, but after a while it's sort of like walking along a big fence, finding a hole in the shrubbery, and popping into a secret garden of sorts. It's easy and natural, and not really hard work at all. It also builds concentration, diligence, and patience.
... Also, I'm incredibly arrogant at the same time as being irritatingly insecure in my abilities. I want the validation of being the most talented student in this honors course, which routinely assigns problems that stump PhD students.
I happen to think I deserve it.