This is a supplement to aeismail's and JeffE's excellent answers.

I understand it may be hard to drop the class or move to another class for some reasons. For your best interests, it's better to follow the instructor for now.

The professor is incompetent to the extent that he does not understand proofs written by an undergrad.

I have a suggestion for you. Sign in to our sister site Math SE. Present your proofs. See what people think. After you verify your proofs, you'll know your professor is incompetent or not.

If your professor is indeed incompetent, you should seriously consider dropping the class. You don't want to waste your precious time. However, if it turns out that you do have serious flaws in your proof, I would listen to my professor if I were you.

This is a supplement to aeismail's and JeffE's excellent answers.

I understand it may be hard to drop the class or move to another class for some reasons. For your best interests, it's better to follow the instructor for now.

The professor is incompetent to the extent that he does not understand proofs written by an undergrad.

I have a suggestion for you. Sign in to our sister site Math SE. Present your proofs. See what people think. After you verify your proofs, you'll know your professor is incompetent or not.

If your professor is indeed incompetent, you should seriously consider dropping the class. You don't want to waste your precious time. However, if it turns out that you do have serious flaws in your proof, I would listen to my professor if I were you.