Proof revolves around a young woman, Catherine, and her reaction to her father’s recent death, her sense of self, her connection with her sister, and a new relationship with one of her father’s former students. On the night before her twenty-fifth birthday, Catherine prepares for her father’s funeral and her newly arrived sister, who has her own plans for Catherine. Catherine also deals with Hal, a scholar who is searching through her father’s numerous notebooks for new ideas and possible sparks of inspiration for new mathematical discoveries.
As the play opens, Catherine sits on the back porch and talks to Robert about her unknown plans for the future. Shortly, the audience realizes that Robert is a figment of Catherine’s imagination, a phantom or ghost. Hal enters and Robert disappears. Hal’s motives seem somewhat suspect to Catherine, who believes him to be completely self-serving. However, he convinces Catherine of his admiration for her late father, and she permits his continued search for her father’s brilliance through his 103 notebooks upstairs. As their relationship develops throughout the play, Catherine simultaneously deals with her estranged sister, Claire. Learning that Claire finds Catherine to be mentally fragile and plans to move her to New York, Catherine resentfully struggles to ascertain whether she has inherited any aspects of her father’s known insanity.
The work ends with the discovery of a proof that would be considered brilliant in the math world. The problem with its discovery is the murky identity of the author of the work. Catherine, claiming it hers, incites Hal’s doubt and Claire’s cynicism. Yet, once researched, Hal discovers not only that Catherine has inherited Robert’s genius, but also that she has indeed made a serious revolutionary discovery. At the same time, Catherine confirms her suspicions that she not only has inherited her father’s brilliance but also part of his mental illness. The play ends with Catherine agreeing to move with her sister to New York so that she will be close to family who will care for her. Yet, simultaneously, she is emotionally and psychologically satisfied in knowing that her work is indeed worthy and significant in a male-dominated field.