Did Catherine write the proof?

The question of whether or not Catherine (Gwyneth Paltrow) wrote the mystery proof that mathematicians have been trying to solve for years is answered clearly in the movie. The proof found in a locked drawer in the desk in Robert’s (Anthony Hopkins) room after Catherine gives Hal (Jake Gyllenhaal) the key (this is extremely important because Robert is now dead and was crazy for his last five years, and to find that he had written an important proof during his last few years would’ve been huge). As Hal rushes down stairs exclaiming how important this proof is and how it could change their lives, after a dispute with Hal and her sister we find out that Catherine claims that she wrote the proof. Due to a flashback during the movie it shows both Catherine and her dad, Robert, working on what seems to be the proof. When Catherine thinks she has figured everything else she runs up stairs to her father’s room where he too is waiting with a “proof” in hand telling her it’s some of his best work. After Robert hands the proof to Catherine demanding that she read it, she finally reads his proof out loud. The proof that Robert has written has nothing to do with math at all, only proving more to him and Catherine that he is extremely crazy. This shows that Catherine wrote the proof because it is in her hand writing and she can explain the whole proof in detail, as she begins to do at the end for Hal. So the question of whether or not Catherine wrote the proof shouldn’t be asked because the movie clearly shows that she does. That being said I hated this movie and thought it was extremely boring.