## Proof: Three Reviews

*Proof*, a movie based on David Auburn?s Pulitzer Prize winning play, was released in September. Featuring Gwyneth Paltrow, Anthony Hopkins, and Jake Gyllenhaal in the main roles, the movie had a mixed reception by the critics. Given the important role of mathematics in the story, we decided to ask three people to have a look and tell us what they think. Harry Waldman is Head Writer for FOCUS. He works at MAA headquarters in the Publications Department, but in his spare time Harry has a strong interest in the cinema and has written several books about films. Melanie Wood is a graduate student at Princeton and a winner of the Morgan Prize for undergraduate research. Jackie Giles is a member of the FOCUS editorial board who teaches at Central College, part of the Houston Community College System.

**Harry Waldman**

At a key point in the new film *Proof*, the cinematic adaptation of David Auburn?s award-winning play, Robert Llewelyn (Anthony Hopkins), in his early 60s, a former distinguished University of Chicago mathematics professor, says, ?All cylinders are firing? the machinery is working.? The ?machinery? he?s referring to, as his daughter Catherine (Gwyneth Paltrow) knows, is his mind. A world-renowned figure in mathematics, he?s been absent form the field for years, but now he?s evidently inspired and hard at work on a proof. Catherine, a fine math student, has cared for him as dementia ’ his long night of the living dead ? has taken hold. She hopes beyond all reason that her revered father, who had made his name in Britain at the age of 22, is back. That would set her free.

The film, which also features the excellent British character actor Roshan Seth as Professor Bhandari, was co-scripted by Rebecca Miller ’ Arthur?s daughter. Completed in late 2004 and one of the main entries at the recent Venice and Toronto film festivals, it tries to bring the arena of mathematics and its inhabitants to life. Set at the University of Chicago, it talks a good game, but doesn?t show enough of mathematicians in action.

*Proof isn?t just a movie about mathematics; it?s a mathematical movie. The scenes may as well have been laid out by diagram: Let?s put a touching father-daughter moment here, a startling revelation there, and use interstitial flashbacks to cube the total emotional-resonance quotient. *
’Stephanie Zacharek
Salon

But the film is not really about mathematics anyway. That?s just a backdrop, window dressing, so to speak. The filmmakers have chosen mathematics as the metaphor through which to make their points, including a few about the field itself. There?s the impression that mathematics is dominated by a few geniuses. That real mathematicians must show their talent early before they flame out. And that mathematics is too incomprehensible to show on the screen. Thus all we get is a bit of clichÃ©d ?mathematics.?

We do, however, see a lot of mathematical books and journals ’ some of them from the Mathematical Association of America! Who are the people involved with this stuff? They are young wizards, we?re informed, striving for greatness. The world of rarefied mathematics, apparently, requires genius and its substantiation. If you can?t maintain the lofty mathematics ’ exemplified by a proof so original that it causes your colleagues? heads to spin ’ you might as well head for the hills. The young mathematicians have only a bit of time: the clock is ticking. There are those in the mathematics community who believe this but others, like Catherine, disagree. So implies the new film from director John Madden.

Then again, Robert may be the exception to this rule. Although he?s suffering from dementia, he just might have come up with a major mathematical proof late in life that will set the math world ablaze and restore him to his former glory. Or is this mysterious ?proof,? which Catherine has uncovered, not really his? Has she perhaps inherited her father?s genius? Does the future hold promise or peril for her? Is she her father?s daughter in more ways than one?

Self-centered young graduate mathematics student Hal (Jake Gyllenhaal) represents the young mathematicians. He teaches, he coaches young hockey players, he plays drums in a band. He?s no geek. When we first meet Hal, he?s wearing glasses. That?s the last time he can see clearly, so to speak. After that, sans spectacles, he grows stubble and is in it for the glory. Getting close to Catherine, he offers her a way out of her emotional bind. He?s fond of saying, ?There?s nothing wrong with you.?

So the film comes down to proofs of love and trust in other ways. Catherine?s proof is of her commitment and love for her father, the sacrifices she makes for him as his life ends ’ and of her career choices. It?s also about proof of Hal?s trust and love for her, and hers for him. However, her father?s final years have been a nightmare for her. She had to make sacrifices socially and educationally. She couldn?t pursue her work because her father couldn?t manage without her.

We do see that Catherine is depressed and in mourning even while her father is alive but in decline. Her sister Claire (Hope Davis), is a rather clear-headed New Yorker, although she is portrayed as materialistic and hyperorganized. Having perhaps inherited these characteristics of her father, she has already given up on him. There?s never a scene between her and Robert. Claire arrives in Chicago to try to get her sister, who appears to her to be in need of psychiatric help, out of there. Catherine, a masochist of a sort, will have none of Claire or her ideas.

What?s perhaps most notable in the 100-minute film for MAA members is that the MAA contributed several hundred journals and books to the producers of this film so that they could recreate the ambience of a real mathematician?s office. Look, therefore, for some of the real mathematics in the film: the *American Mathematical Monthly, the College Mathematics Journal*, and *Mathematics Magazine*.

**Melanie Wood**

You should see the movie *Proof* ’ but not just because you are a mathematician. Feel free to take along non-mathematician friends or recommend it to your relatives. *Proof *is an emotionally compelling drama, which manages to present a fresh story without resorting to the laughingly preposterous premises that are the recent formula for an original plot. Gywneth Paltrow drives the show with her convincing portrayal of Catherine, the daughter of mathematician Robert (Anthony Hopkins) who has gone crazy in his later years and requires the constant attention of his daughter. At the start of the movie, Robert has just died, and his other daughter Claire (Hope Davis) flies in for the funeral and to take care of Catherine. Claire?s overbearing manner is not the only annoyance Catherine also faces. Hal (Jake Gyllenhaal), a former student of Robert?s, wants to go through over a hundred notebooks left by Robert to see if there is any new mathematics in them. Catherine is grieving and struggling to cope with her father?s death and what this means for her own life.

*Against considerable odds and despite a shaky start, Proof proves itself in every area. Thanks largely to Paltrow?s beautifully unadorned performance, an exceptional portrait of psychological fragility that is honest, direct and devastating, this is a film that really has to be seen.*
Kenneth Turan
The Los Angeles Times

At first, the movie deals with the issues of grieving, insanity, caring for ill parents, and though it is engaging in these aspects, it might leave you wondering when they are going to get to the math (and might leave everyone else in the audience relieved!). A few early mathematical jokes will allow you to identify your compatriots in the audience, but mostly the mathematical issues come late in the movie. A proof is discovered in a notebook in Robert?s desk and raises a question of the authorship. Was the proof done by Robert when everyone thought he was insane and incapable of work? Or is it possible that his daughter Catherine, a talented mathematics student, but not even finished with her education, could be the author? (Warning: the rest of review gives the answer.)

*The drama of the sisters and Hal and the past-and-present father drags a bit because some of the time it seems to be not much more than elevated bickering. All in all, this is the sort of work that gets credit for more gravity than it genuinely possesses, merely because of its subject.*
Stanley Kauffmann
The New Republic

Before it was a movie, *Proof* was a Pulitzer Prize play, which ran on Broadway and won Tony Awards for Best Play, Best Actress, and Best Director. Of course, the movie medium changes a lot in the presentation, but there were two big changes in substance from the play that were both disappointing. In the play, it is made clear early on that Robert did not do lucid mathematics in his relapse from insanity, and in particular, that the proof must be Catherine?s. Knowing that the work is Catherine?s, we in the audience sympathize with this woman not only because her sister and new boyfriend don?t seem to trust her, but also because her mathematical work is not recognized.

The movie takes a different approach, presumably to maximize suspense or set up a big plot twist. We are led to believe that Robert was able to start working during his relapse, and moreover that he had a program for a proof of an important result. Catherine also starts her own mathematical work, and it is possible they are working together. In a break-down, Catherine even seems to claim that she has stolen the proof from her dad.

The movie does in the end make it almost clear that the proof is Catherine?s, except that one very mysterious scene is left unexplained. While watching a movie, Catherine tells her father of her progress on some result, and he makes a suggestion ’ apparently a good one, judging by her reaction. This scene not only contradicts the impression that Robert was not able to do mathematics after his mental problems began, but also raises questions. Even if Catherine worked out the details, if her father gave her suggestions, was it really her proof? Could he have given her really significant suggestions? Could he have outlined the whole thing? This leads the audience to disbelieve Catherine, and thus makes it harder for them to feel sympathy for her plight.

This change also means that the movie loses the chance to unequivocally portray a young woman as an excellent mathematician who thinks in new and creative ways.

The second major change from the play is that Catherine is portrayed as actually having mental problems (the play makes that questionable at best). She appears to be more disturbed than just by normal grief. The movie uses flashing colors and scenes and lights going by quickly in one scene to give an impression of insanity. While it is exciting for mathematics that there have been two recent major motion pictures portraying mathematicians, it is unfortunate that they both feature mathematicians with significant psychological problems.

One of the repeated themes of *Proof* is that mathematicians do their best work by the time they are 26, and by 27 it is all downhill. Many of my colleagues were a little depressed by the movie for this reason. The movie?s end underscores this idea since the important proof was in fact done by Catherine (before she turned 27), and not by her older father. Another interesting ?observation? made is mathematicians? inclination for serious partying and use of speed. I am not sure what that will do for recruitment into our field.

**Jacqueline Brannon Giles**

As I viewed the movie *Proof* I tried to strip myself of the tendency to compare and contrast it with other movies about mathematicians. I wanted to study the movie as a single unit of entertainment. The dedication and compassion of a young female mathematician (Catherine) who cared enough about an ailing, yet renowned older mathematician, was touching and heart warming. It was the intergenerational connecting and caring that impressed me.

*The point lies in a darker place ’ at the intersection of insanity and genius, and the inheritance of both. It asks if pathology can be separated from gift. It wonders if a wunderkind will fade past his 20s, or if the child of a madman is doomed to crack. And it talks about math like music. *
Amy Biancolli
The Houston Chronicle

Catherine?s birthday, possibly marking the beginning of her decline in capability, was also the day of her father?s burial. This highlighted both transition and continuity, for in the daughter?s struggle to aid her father she was inspired to do her best work. The death of the father spawned the birth of the daughter.

Catherine?s intimate interaction and constant contact with her father, who was also her mentor and her teacher, spurred on the genius in her. Nevertheless, she deposited her work in a drawer only to be shared after her affection for the young man (Hal) was acted on. Once she felt free to emote and share with Hal, she was willing to share the treasured mathematical thoughts in her notebook. It suggested to me that her development as a female preceded her full development as a mathematician.

A schism occurred because of distrust among the characters, yet there was a satisfying resolution at the end. The daughter, together with her father?s former student, went on to affirm and improve the mathematical work inspired by her father, who sincerely desired that his daughter would ?do? mathematics. While the movie leaves this somewhat undecided, I believe that the father?s hope was indeed actualized in the decision of the daughter to continue the legacy of ?writing and doing mathematics.? This could easily be a visionary statement for the senior mathematicians in our professional community; Out of the decline and death of our great mathematicians should come the birth and rise of the next generation of mathematicians.