Proof

Proof Summary | Plot Summary

Proof is the story of a young woman named Catherine. She is the daughter of Robert, a brilliant mathematician, who misplaces both his brilliance and his sanity in his later years. Catherine, a budding mathematician herself, must give up her schooling and her most creatively productive years in order to take care of her father, who has become convinced that alien civilizations are communicating with him directly through the local library's Dewey decimal system.

As the play opens, Robert has just died and Catherine, conversing with his ghost, wonders if she may have inherited his tendency toward madness. Robert had first shown signs of madness in his mid-twenties. Catherine has just turned twenty-five. Her suspicions seem confirmed when her sister Claire and Robert's protégé, Hal, begin to treat her as if she is mentally unstable. Claire, returning for her father's funeral, wants to take her "fragile" sister Catherine back to New York where Claire can keep Catherine safely under her wing and submit her for psychiatric treatment. Hal, who becomes Catherine's lover on the night of the funeral, defends Catherine to Claire, but retains suspicions of his own about Catherine's stability when she claims to be the author of a proof so advanced it overshadows all of Robert's previous work.

Catherine drops her bombshell at the end of Act 1, claiming that she is the author of the proof. Act 2 opens with a flashback to Catherine and Hal's first meeting. They had met on her twenty-first birthday. Hal was handing in his senior thesis while Catherine was still hoping to begin undergraduate school, but only if her father's remission into lucidity continued. The audience is thus introduced to the depth of the sacrifice Catherine has made to tend her father. Not only did she give up school and career, but, revealingly, on her twenty-first birthday she has no friends with whom to celebrate. She and her father invite Hal to her birthday dinner, but he declines.

Four years later, Hal invites Catherine out on a date, but she is suspicious of his motives. Hal is now a teacher in his own right, while Catherine has yet to be able to return to school. To make matters worse for Catherine, conventional wisdom states that mathematicians are already past their prime at twenty-five. If Catherine has not done her best work by now, she will never have the chance again. The existence of the brilliant proof is Catherine's only saving grace. It represents her one chance at success on her father's level.

When Hal and Claire doubt her authorship and conspire to take the proof away, Catherine sinks further into depression. Claire views her outlandish claim and symptoms of depression as evidence of severe psychosis similar to their father's and intends to drag Catherine to New York with her whether her sister likes it or not. Meanwhile, Hal and his colleagues have examined the proof and Hal returns in the nick of time to tell Catherine that he now believes the proof to be her work. As the play draws to a close, Hal begins to treat Catherine with the respect she deserves as a mathematician. Catherine's bitterness makes her initially resistant to Hal's overtures, but ultimately she cannot resist the prospect of discussing her work as an equal with a colleague whose respect she has earned.