Catherine, the play’s protagonist, turns 25 at the start of Act I. She has spent the last several years caring for her father, Robert, as his mental health declined. Like her father, Catherine is a gifted mathematician, and she worries that she might also have inherited his mental illness.

When the play begins, Catherine’s father has just died. To care for Robert, Catherine is forced to drop out of Northwestern in the first semester of her undergraduate degree. Over the past several years, Catherine has become invisible, focusing her life on her father while failing to take care of herself. Robert accuses her of wasting her life and her talent by not using the time she has to work. Catherine is emotionally guarded but opens up to Hal when he demonstrates that he sees her as an entity separate from Robert.

In response to the sudden intimacy that Catherine finds with Hal, she reveals that she has not, in fact, wasted the years she spent caring for her father. While Robert was asleep, she spent her nights working on a proof, a mathematical argument that proves a mathematical statement (or theorem) is true. Her proof solves a long-standing and fundamental mathematical problem and uses techniques that are complex even for Hal, who has a doctorate in

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