Describe symbolism in Proof by David Auburn

The proof that Catherine writes is a multifaceted symbol. Firstly, it is a symbol of her genius: the fact that she is an especially good mathematician, as brilliant as her father. The fact that she keeps it locked away in a drawer and does not tell anyone about it is representative of the fact that she does not believe in herself, that she is depressive to the extent that she does not want to show people her gifts. Then, after she reveals herself to be its author and no one believes her, the proof represents the fact that people do not believe in her and have sexist preconceptions about mathematical genius. At the end, Hal acknowledges that the proof is her work and it is once again a symbol of her brilliance. As they look over it and seek to revise it to make it more "elegant" we see that the proof has always represented Catherine's life itself, a brilliant and clumsy mess that is wholly unique. Their revision of the proof becomes symbolic of the promise that Hal and Catherine will rebuild her life.