Proof

1. Proof Family Relations, Memory and Madness (2)

2. General Introduction: The Play & Mathematicians inspiring the play The Film: What’s Added The Play: What’s Deleted Questions Moments of Doubts and Validation Family Conflicts: Catherine and Claire Ending (1): Catherine’s Guilt and Breakthrough Ending (2): Robert’s Last Work Mathematics and Art Reference Outline

3. The Play & the Related Mathematicians Proof by David Auburn; Pulitzer Prize in 2001 The stage: a revolving one so that the audience can see it from different perspectives. Mathematicians related to the play: Paul Erdös who began taking amphetamines to keep working ( Hal’s description of the conferences he goes to); Andrew Wiles –worked on Fermat's Last Theorem in solitude for 7 years (ref. Audrey) ( Catherine’s proof)

4. Catherine’s work: “It looks like it proves a theorem... a mathematical theorem about prime numbers, something mathematicians have been trying to prove ....” Conjecture =假設 ; Theorem: conjecture which mathematicians believe in but haven’t been able to prove e.g. Fermat's Last Theorem X3+Y3=Z3，若X、Y、Z都是非零正整數的話，就沒有解。三次方可以換成任何一個次方，只要大於２就好了。Later proved by Wiles Mathmatics

5. Mathematicians 3. John Forbes Nash, Jr, -- the subject of A Beautiful Mind (1998)— produced his thesis on game theory at the age of 21, then suffering from paranoid schizophrenia. resumed living a normal life and studying mathematics and was awarded the Nobel Prize in 1994. According to Hal: Robert [like Nash] made major contributions to three fields: game theory, algebraic geometry, and nonlinear operator theory. Nash’s son, John Charles Nash, inherited the disease. Nash himself liked the play when seeing it at the age of 73. (ref. Audrey)

6. Comments? The lines between genius, solitude and madness short-lived genius vs. long-term solitary work, which can happen to any academic pursuit I-Scene 3 “It' not about big ideas. It's work. you've got to chip away at a problem. ” Maybe these are dominant types, but don’t turn them into stereotypes. e.g. "Geek“ (boring and not fashionable), "nerd“ (unattractive, socially awkward), "wonk“ (a person who works or studies too much) "Dilbert," "paste-eater.“

7. The Play and the Film • More dramatic and emotional intense; • Focused more on Catherine’s relation with Hal • Claire seems more calculative

8. Added to the film: Scenes outside the house • the church memorial scene (chap 5) • Catherine at school • The Airport scene • Catherine’s sense of guilt • The scene where both Catherine and Robert are busy working  Coexistence of the father’s and the daughter’s proofs. (chap 13 1:24) • Catherine’s expression of guilt A.  more dramatic B.  more emotional intensity

9. Deleted from the Play • I: scene 3 -- About Sophie Germain in the 18th century, who wrote to a male mathematician with a pseudonym. Later • Finding out that he was a woman, he wrote to her: "A taste for the mysteries of numbers is excessively rare, but when a person of the sex which, according to our customs and prejudices, most encounter infinitely more difficulties than men to familiarize herself with these thorny researches, succeeds nevertheless in penetrating the most obscure parts of them, then without a doubt she must have the noblest courage, quite extraordinary talents, and superior genius." •      (Now self-conscious) I memorized it... • Claire: [excerpt pp. 20-21] • Robert’s views of Chicago in September: [excerpt pp. 15]

10. Robert’s Interest in Students and their Browsing • (Act 2 scene 1) I love Chicago in September. Perfect skies. Sailboats on the water. Cubs losing. Warm, the sun still hot... with the occasional blast of Arctic wind to keep you on you toes, remind you of winter. Students coming back, bookstore full, everyboddy busy. •     I was in a bookstore yesterday. Completely full, students buying books... browsing...

11. Present—right after the death of the father Present – discovery of the book Present – work on checking the proof (11:9:40); Catherine’s collapse Past – Catherine’s bumping into Hal Past – Catherine’s going to school Catherine’s and Robert’s working The Film: Double plotlines The play: moves back and forth in Act II between the past (scenes 1 and 4; four years ago) and the present

12. Discussion Questions Proof: What does the title mean? What are the moments of proof in the film? Family Relations: How do the two sisters (Catherine and Claire) relate to each other? How do they differ in their ways of thinking and their relations to the father? Memory: What is bothering Catherine feel about Robert? Why does she say at one point “I stole it from him”? Gender Relations: How are Catherine and Hal related to each other both professionally and personally? Why can’t they trust each other until the end? Mathematical Proof & Madness: What does its “being elegant” mean? What does the film say about the “madness” of Robert? How is mathematical proof different from or similar to literary analysis?

13. Moments of Doubts and Proof (Validation) In the following four cases, complete trust is difficult, since there is always room for doubt and miscommunication. • Catherine’s suspicion of Hal’s taking away some notebook. (Hal does have a notebook in his coat pocket) • Whether Harold Dobbs exists or not: (chap 4: 20:28) (Claire suspicious, and Catherine overreacting to both the policemen and her sister.)

14. Moments of Proof (Validation) (Whether Catherine’s dress is good or not) • Whether their night together is good or not: The 2nd Morning (chap 7 39:45) • Who wrote the proof, Robert or Catherine – e.g Robert’s notebook, handwriting, Catherine’s lack of education (suspicion of women’s abilities), her closeness to her father.

15. Proof and Trust • Symbols: key – to lock away her work, to release it; • Coffee: Claire’s way of care-taking

16. Family Relations: Catherine and Claire Claire -- efficient, practical, and successful sister, not as negative in the play as she is in the film. • has made a career in New York as a currency analyst. • feels responsible for Catherine's welfare and wants her to move to New York  she is caring but unable to understand Catherine (always suspecting that Catherine has mental problems), while sometimes Catherine does over-react. • Suspects that Catherine inherits Robert’s mental instability. • Her argument with Catherine over how to care for their father.  She has a point, though maybe Catherine’s “sacrifice” may be a blessing in disguise. • In the film, she is presented as more pragmatic, making lists all the time and checking things out when they are done.

17. Catherine’s Breakthrough • Guilt over her father’s lack of accomplishment during his remission; over her own accomplishment, which is encouraged by the father. • Released from her past and her sense of guilt • How many days have I lost? How can I get back to the place where I started? I'm outside a house. Trying to find my way in. But it is locked and the blinds are down. And I've lost the key. And I can't remember what the rooms look like or where I put anything. And if I dare go in inside. I wonder... will I ever be able to find my way out? • Not sure if she can make it. • She still takes the initiative to “talk through her proof” with Hal.

18. Robert’s Last Work "Let X equal the quantity of all quantities of X. Let X equal the cold. it's cold in December. The months of cold equal November through February. There are four months of cold and four of heat, leaving four months of indeterminate temperature. In February it snow. In March the lake is a lake of ice. In September the students come back and the bookstores are full. Let X equal the month of full bookstores. The number of books approaches infinity as the number of months of cold approaches four. I will never be as cold now as I will in the future. The future of cold is infinite. The future of heat is the future of cold. The bookstores are infinite and so are never full except in September..." • X = cold; • X = Sept • 4 months of cold • Infinite coldness • 1. Sept: full bookstore • 2. Never full otherwise ambiguities

19. Mathematics and Art • Mathematics: the studies of numbers to formulate theorems 數學裡那一些永恆的肯定句，我們稱之為一個定理，一個Theorem。這跟天文、物理或化學所說的Theory意思是不太一樣的。它們那個東西也叫做一個理論，但是數學上的Theorem是經過證明，已經肯定它是一個永恆肯定的一個敘述。(單維彰) • Literature digs out the complexities of human lives • Similarities: search for ‘elegant’ form/ways of telling their “truths.” • John Madden –an elegant proof//story-telling//film-making: ”make it shorter, make it better, more economical […]the simpler way, the most compressed way, the most transparent way”

20. Reference • Bryan Aubrey, Critical Essay on Proof, in Drama for Students, Vol. 21, Thomson Gale, 2005. • 單維彰. 〈究竟證明了什麼數學命題？〉