impromptu speech, berating everyone for not being there for her father while he was alive. She describes his descent into insanity, and that at one time he would borrow piles of books believing that aliens were sending him messages encoded in their Dewey Decimal codes. She ends by saying she is glad her father is dead and walks out of the church mid-funeral. Claire decides to sell Robert's house back to the university and wants Catherine to come with her to New York; Catherine is upset that she will be forced to leave the house. It becomes evident that Claire suspects that Catherine may be struggling with mental illness, as their father had. A wake held at the house the night after the funeral is attended by many academic mathematicians. Hal appears and chats up Catherine. Softening up to Hal, Catherine sleeps with him. In flashbacks, Robert is shown suddenly invigorated, believing he has seen the beginnings of a new mathematical proof that will prove his triumph over mental illness. In the present, Catherine gives Hal a key to Robert's desk and tells him to check the locked drawer for a notebook, which itself contains a lengthy but apparently very important proof. He is very excited and shows the discovery to Catherine and Claire. He asks Catherine how long she knew about this and why she did not tell him about it. She tells him that she wrote it. Catherine claims the work is hers and not her father's despite evidence to the contrary. Neither Hal nor Claire believe Catherine. Hal believes the mathematics of the proof are beyond Catherine, while Claire simply suspects that Catherine is suffering the onset of mental illness. Catherine says she can't describe the proof without the notebook because it "is not a muffin recipe". Hal decides to take it to the math department the next day to verify the proof's accuracy. He returns as Claire and Catherine are leaving, with news that the math department believes the proof to be valid. Hal tells Claire that he doesn't think that her father wrote the proof because it employs newer mathematics and wants Catherine to explain it to him sometime. Catherine remains stung by his earlier lack of trust, and the sisters leave for the airport. Hal sprints after the car and throws the book through the window and onto Catherine's lap. At the airport, Catherine