In my opinion, this play has a few themes. The first theme: Do not underestimate people. Hal and Claire did not believe Catherine when she said she wrote the "Proof" because she did not have a college degree. Since the handwriting looked like Robert's writing, they thought he had written it. Catherine was underestimated. Hal and Claire neglected to look at the fact that Catherine had the same math ability as her Dad, Robert. She did not need a degree. All she needed to write the "Proof" was what her Dad taught her and her own math talent.
The second theme has to do with the importance of family. This play reminded me of my wife and her Dad. They are both very similar and they have great admiration and respect for each other the way Catherine and her Dad did. My father-in-law suffers from diabetes and high blood pressure.
My wife is always making sure he is well-taken care of and is getting plenty of rest. In fact, she is always telling her Dad to rest, in the same manner Catherine tells her Dad. I know that if my father-in-law were bed ridden, my wife would be there at his side. I also know that if my father-in-law had done something great, my wife would not feel as if she were in his shadow. In my opinion - based on a comparison to the relationship between my wife and her father - I do not think Catherine feels overshadowed by her Dad. I think Catherine is an unselfish person who simply wants to help her Dad in his time of need.
In Emily Dickinson's poem "I'm nobody! Who are you?" the girl seems to enjoy being anonymous. I think in a certain way Catherine enjoys being anonymous as well. First, at the end of the play, she says that her "Proof" does not flow as smoothly as her father's work did. It was almost as if she was trying to take the attention away from her own work. Second, she gives Hal the key to the drawer where she keeps the "Proof" she wrote. I think she does this hoping that he will publish and take credit for it. Saying and doing what she did makes me believe that she enjoys her anonymity.