Proof Trivia Quiz

Answer: Her birthday

Prompted by her father -- a ghost? a memory? a hallucination? -- she goes to the refrigerator and removes a bottle of champagne that he had bought for her. It actually isn't champagne at all, but wine, which she drinks anyway. Catherine is not exactly at her best; she and her sister will bury their father in only a few hours.

Answer: her father's notebooks

Catherine's father Robert (Anthony Hopkins), a brilliant mathematician, slid into dementia and became a graphomaniac. He wrote obsessively, filling the house with scores of notebooks of scribbled nonsense. Hal Dobbs, his former Ph.D. student, has been searching these notebooks after his death to discover whether his mind ever cleared enough to make one more contribution to mathematics.

Catherine is torn between her belief that her father never recovered enough to work again, and her borderline paranoia that Hal is stealing her father's work to claim as his own. After she calls the police on him, she does find that he has taken a notebook, but it holds no mathematics: Hal was going to present it to her as a gift, since it contains a beautiful note about her.

Answer: She fears that Catherine has inherited their father's madness as well as his talent.

Neither sister really likes or understands the other, but they do love each other. From the moment Claire arrives she goes into Mom mode, from buying Catherine a dress for the funeral to giving her a new shampoo ("You'll love it -- it has jojoba"). Underlying it all is the knowledge that their father's madness began at age 26, and that Catherine is now 27 and often behaves irrationally.

Answer: Because it was Catherine who dropped out of college to take care of their father.

By the time of their father's final relapse into dementia, Claire had already moved to New York. By no means did she abandon her father and sister; she worked long hours to pay both her own rent and also the mortgage on the family home in Chicago. But, as Catherine points out later, Claire "had a life." Catherine believed their father would do better in his own home than in an institution, and so Catherine had to become completely devoted to her father's well-being.

Answer: Hal Dobbs

Hal and Catherine overcome the awkwardness of the previous evening, joking about mathematicians. Catherine shows off her knowledge of prime numbers with a casual reference to Germain primes, developed in the 19th century by Sophie Germain, whose parents punished her for her interest in mathematics and who spent the first several years of her career writing under a male pseudonym.

The attraction between Hal and Catherine is palpable, and she invites him to spend the night with her.

Answer: It's written in a notebook just like the ones he used, he had a better education, and the handwriting looks just like his.

Catherine gives the key to Hal because she believes she can trust him, but he doesn't know her well enough to trust her claim that she wrote the proof (which he describes as important enough to warrant press conferences and a rethinking of prime number theory). After all, it's her father who's the proven genius (even if he was insane); she hasn't even finished her bachelor's degree!

Answer: Her handwriting looks like her father's, she had access to the same books and materials that he did, and he had not produced anything else that was lucid during his illness.

"You've seen the other notebooks!" Catherine reminds Hal. "You know there isn't anything in there!" Her father hadn't done any real work during his years of madness, and his most important work was done decades ago in his twenties. Hal agrees that sometimes people's handwriting closely resembles that of their family members (a fact which I can personally attest to), but he just thinks it's more realistic that her father would have written it. Claire suggests that Catherine prove her claim by reproducing the proof from memory, but that's impossible: it's over 40 pages long!

Answer: Packing up the family house so that she can sell it.

Claire is the one who paid the mortgage, so she owns the house. She's made a life in New York, though -- she's planning to get married soon -- and so she is selling the house back to the University of Chicago, which has wanted it for a long time. Catherine is distraught by this idea -- "I live here!" she points out -- but there's nothing she can do. Claire offers to go apartment-hunting with her in New York, where she can watch over her sister; she also thinks she'll be able to get better mental health care for her there.

She loves Catherine and worries about her, but has no idea how to express her concerns without offending her.

Answer: The pages aren't dated, in contrast with Catherine's father's undisputed notebooks, and the proof is too "hip" to have been written by the aging mathematician.

He runs to the house to tell her, as soon as he's verified the proof and realized that she wrote it, but she tells him it's too late: "You should have trusted me." By this time, we've already learned through flashbacks that she had written it. Her father, excited at the return of his mathematical capabilities, had been trying to solve the same problem concurrently -- but it was a cruel illusion, and the proof he wrote was really a disjointed ramble. "Let x equal the quantity of all quantities of x," he wrote. "Let x equal the cold ..."

This was the moment when Catherine realized that his madness had returned after a remission of almost a year; this was when she dropped out of college to take care of him, working on her own version of the proof in her spare time and using "hip" mathematical concepts developed long after her father had finished his education.

Answer: Catherine sits with Hal on the University of Chicago campus, explaining her proof to him line by line.

Catherine, depressed and sullen, goes to the airport with Claire to fly to New York. But she has the notebook with her proof, given to her at the last moment by Hal, and as she holds it she realizes that her life is not over despite her fragile psyche.

She flees the airport, ignoring Claire's protests, and finds Hal at the University of Chicago. "You can't prove I wrote it," she tells him. He notes that they can prove she was capable of writing it, and so they sit on a bench outside and begin to work through it. I found it a beautiful ending to a deeply moving film. I hope you've enjoyed this quiz!