The play begins with Catherine alone in her backyard. Her father, Robert, enters with champagne. He wants to celebrate her 25th birthday, but she complains about not having accomplished anything worthwhile in mathematics. Robert is a brilliant mathematician who accomplished a great deal by his mid-20s. Robert tells her she can still do something great, but gives her a hard time about her more de-motivated depressive habits, like reading magazines.
We learn that Robert has a mental illness that has ruined his grip on reality and Catherine is scared that she has inherited it. He comforts her, but suddenly points out to her that he died a week ago, and he is now a figment of her imagination.
Hal, a student of Robert's, comes out of the house where he has been studying Robert's notebooks, which number in the hundreds. He's looking for anything of Robert's that could be published. Catherine says that they only contain scribbles, as her father was not well mentally when he wrote them. Hal then invites her to go see his band play later that night. Immediately Catherine demands to see what's in Hal's backpack, suspicious that he's stolen something, but she finds nothing. As he's leaving, however, a notebook falls out of Hal's jacket and Catherine rashly calls the police. Hal tells her he was only going to give the notebook back to her as a birthday gift, as it contains a sweet journal entry about her, written by her father. Hal leaves as Catherine begins to cry and we hear the sounds of police sirens coming.
In the next scene Catherine's sister, Claire, is visiting from New York for the funeral and arranging a party for afterward. Claire tells Catherine she is getting married and invites her sister to come stay with her and her fiancé in New York. Catherine agrees to come for the wedding, but refuses to leave Chicago. Claire confronts Catherine about the fact that she called the police the previous night, and is worried about her mental wellness. Hal enters and asks to continue going through Robert's notebooks. Catherine agrees and Claire tells her to flirt with him, which annoys Catherine.
After Robert's funeral, Claire hosts a party at her father's home for friends and student's of her dad. Hal is there. Catherine breaks away from the party to the porch where Hal finds her and gives her a beer. He tells her of his insecurity about his mathematical abilities and kisses her after she tells him some facts about an unsung female mathematician from history. He apologizes for stealing her dad's notebook and she apologizes for calling the police. They kiss once more and Hal asks if she remembers meeting him years before. She says that she does; the conversation continues, and they start an affair.
Outside the next morning Catherine is alone. Hal comes out of the house and says he wants to spend the rest of the day with her. Euphoric about their romance, she gives him a key to her dad's desk and he goes to look through more of the notebooks. Claire appears, hungover, and Catherine does her best to be nice to her sister. Claire continues to push the move to New York and reveals that she is selling the Chicago house. Catherine accuses Claire of leaving her to take care of their father while she was in New York. Claire says that she left so she could make enough money to pay for the house and for Catherine's education. Catherine reveals that she had to drop out of school in order to take care of their father, and accuses Claire of trying to have her committed to a mental institution. Hal re-enters, having found a very important proof in Robert's notebook. Catherine tells Claire and Hal that she wrote the proof.
The beginning of Act 2 is a flashback to Robert on the porch. Catherine tells her father that she is going to go to college and that Claire has funded it for her. Robert wants to know why she waited so long to tell him and she explains that he hasn't been well recently. Hal then steps in to go over his thesis with Robert, when Robert remembers that it's Catherine's birthday and offers to take her to dinner. Catherine asks Hal to join, but he declines.
The next scene picks up where the first Act left off. Hal and Claire don't believe that Catherine wrote the proof. Hal asks if he can show it to some of the other professors to confirm that it's legitimate. Catherine is upset that her sister and lover do not believe her, and insults Hal. He leaves, upset, and Catherine has a breakdown. Hal returns later to apologize, but Claire refuses to let Catherine speak to him. He tells Claire that Catherine is stronger than she gives her credit for. He asks again for the notebook to confirm the proof with fellow mathematicians. Claire lets him take it. She then tells him that she is taking Catherine to New York the following day as she is concerned about her sister's mental health.
The play flashes back to Robert in the backyard writing on a cold day. Catherine tells him to come inside, but he insists that he is inspired in his mathematical work. She is excited to hear that his mental troubles have subsided, and Robert asks her if she would be willing to quit school and collaborate on a proof with him. When she reads what he is working on, it is a rambling paragraph about winter and books and the cold, and has nothing to do with mathematics. Dejected, she agrees to stay with her father.
Back in the present day, Claire prepares to move Catherine to New York. As Catherine begins to mock her, Claire leaves the backyard in tears. Hal comes in and tells Catherine that the proof checked out with the other mathematicians and apologizes to her. She tells him that he can claim it for himself as there's no proof she wrote it. Hal says he believes she is the author and offers to go through it with her. Catherine admits that she is petrified of becoming like her father, but Hal comforts her, and asks her to go over the proof with him. They begin to talk through it.
