Proof

“Those days are lost. You threw them away. And you’ll never know what else you threw away with them – the work you lost, the ideas you didn’t have, discoveries you never made because you were moping in your bed at four in the afternoon.” 

The Robert who Catherine imagines in the first scene chides her for wasting time. This is especially poignant given the limited time that Robert had to enjoy mental acuity and life in general. Although Catherine has, in fact, written a groundbreaking proof, she continues to feel the pressure of time that her father emphasized. 

“My father wouldn’t want anything moved and I don’t want anything to leave this house.” 

Catherine protects her father’s notebooks and home in line with Robert’s wishes, despite the fact that they are irrational. When Claire arrives, it becomes clear that the house cannot remain unchanged as a museum to Robert. Catherine’s instinct is to keep everything closed off, which would be impractical should Hal find something publishable in Robert’s notebooks. When Catherine shows him her proof, it becomes clear that she can’t protect her own work from bringing public attention.

“I don’t believe a mind like his can just shut down.” 

Hal’s refusal to believe that Robert could have truly been incapable of work stems from his own anxieties. If a genius like Robert can lose his brilliance, how can Hal, already a lackluster mathematician, hope to fare any better? The mind relies on the brain, which is mortal and fallible.

“After my mother died it was just me here. I tried to keep him happy no matter what idiotic project he was doing. He used to read all day. He kept demanding more and more books. I took them out of the library by the carload. We had hundreds upstairs. Then I realized he wasn’t reading: he believed aliens were sending him messages through the Dewey decimal numbers on the library books. He was trying to work out the code.” 

As Catherine describes, Robert’s work patterns continued to mimic those from when he was healthy. However, his disease caused him to see connections in what was random and to imagine conspiracies around those connections. This raises the question as to whether his brilliance was not part of the earliest stages of his illness.

“Hair is dead. […] It’s dead tissue. You can’t make it ‘healthy.’” 

Catherine’s comment to Claire about hair highlights the fact that Claire has come to offer her help too late. Robert is dead, and Catherine has already built up resentments toward her sister for leaving her to care for him alone. Just as hair cannot be made healthy, their relationship cannot be repaired. 

“Yes but I didn’t actually want them to come. But they did come and they started acting like they owned the place, pushing me around, calling me ‘girly,’ smirking at me, laughing: they were assholes.” 

Catherine is particularly sensitive to condescension and is clearly accustomed to having men treat her like a child. She allows Hal to make comments about her supposedly limited mathematical abilities without defending herself. When she calls the police, they refuse to take her word for it when she says that she no longer needs help. Instead, they condescend to her as if she is a little girl, causing Catherine to snap.

“They think math’s a young man’s game. Speed keeps them racing, makes them feel sharp. There’s this fear that your creativity peaks around twenty-three and it’s all downhill from there. Once you hit fifty it’s over. You might as well teach high school.” 

As Hal describes, anxieties about aging and losing one’s mental edge are rampant in academia. This perpetuates the idea that breakthroughs are somehow locked in any mathematician’s mind, and that one must access those breakthroughs before they are locked forever. In fact, most academics will not become immortal for changing the face of math. Most will teach and raise up the next generation of mathematicians. 

“Really original work – it’s all young guys.”

As Hal explains, most of the new ideas come from those who are starting their careers. This phenomenon, however, is likely not a race against the clock but due to the fact that newer scholars who are fresh from school will have just learned the most recent techniques. Catherine points out that his statement leaves out the women, adding that it’s true that most mathematicians are men.

“It’s not about big ideas. It’s work. You’ve got to chip away at a problem.” 

Although Catherine is talking about math problems, her assessment carries over into the other problems she is facing. Her father has just died, and she suddenly has options for her life. Claire would like her to make the huge decision of selling the house and leaving Chicago, but Catherine says that she needs time to figure out what is next. In the end, she starts by explaining her proof to Hal, one step at a time.

“My stupid friends left–it was only eleven o’clock!–they all had to get home and pay their babysitters or bake bread or something.”

Claire has lost touch with her Chicago friends, as she notes to Catherine that the party after the funeral might be the only time she can see them. While Claire does not seem to attach the same significance to time and aging as her father and sister, she is dismayed to discover that her friends have aged and changed while she was absent. If they have reached a different stage of their lives, that means that Claire has reached the same age and is possibly on the cusp of that next stage as she plans to get married and settle down.

“Honey, now that Dad’s gone it doesn’t make sense. It’s in bad shape. It costs a fortune to heat. It’s time to let it go. Mitch agrees, it’s a very smart move.” 

Claire describes the faults of the house but letting go of the house also means letting go of their father. It’s no longer practical to hold onto either one but letting go is a huge step. Claire (and Mitch) don’t seem to fully comprehend the emotional toll that taking the next step will have on Catherine. Claire’s decision is another example of the disconnect she’s had with her family over the years.

“It means that during a time when everyone thought your dad was crazy… or barely functioning… he was doing some of the most important mathematics in the world. If it checks out, it means you publish instantly. It means newspapers all over the world are going to want to talk to the person who found this notebook.” 

Hal, having looked at Catherine’s notebook, holds onto the idea that Robert’s mind did not actually fail, at least not fully. Since Robert was in his fifties and severely mentally ill at the time of his death, this gives Hal hope for making his own academic contributions, even as he ages. Hal is also shedding light on something that has, until now, been hidden. By showing him the proof, Catherine opens herself up to becoming a more public figure.

“Pasta, oh God, don’t even say the word ‘pasta.’ It sounds so hopeless, like surrender: ‘Pasta would be easy.’ Yes, yes it would. Pasta. It doesn’t mean anything. It’s just a euphemism people invented with they got sick of eating spaghetti.” 

Robert’s rant about pasta is about more than food. It’s about refusing to give in and take the easy path. After his death, Catherine faces the choice to go with her sister, where her life will be like pasta: safe, predictable, and unremarkable. She will be encouraged to be more like her sister and less like her father. 

“The fucking books are gone, I took them back myself. Why do you bring that garbage up?” 

During Robert’s lucid year, he stops collecting library books to find conspiracy theories and returns to advising students. However, when Catherine mentions the way he hoarded books, Robert becomes upset and embarrassed. He treats his mental illness as a personal failing rather than the unavoidable effects of his body failing.

“I’m not doing much right now. It does get harder. It’s a stereotype that happens to be true, unfortunately for me – unfortunately for you, for all of us.” 

Just as Robert begins to decline after his year of lucidity, he feels more clarity as if the work he is doing has potential. He reminds Catherine that her time to work is limited. Sadly, when Catherine reads the work that he is so excited about, it is nonsense. Despite his optimism that he is not finished, this moment proves that he is.

“Jesus, you fucking mathematicians: you don’t think. You don’t know what you’re doing. You stagger around creating these catastrophes and it’s people like me who end up flying in to clean them up.” 

There is irony in Claire claiming that mathematicians don’t think since thinking is the majority of what they do. Claire is pointing out the selfishness of those who, as Robert did, put their work above all else. Their ability to think logically does not necessarily extend to handling their personal lives or interacting with others in socially appropriate ways. Conversely, Claire is unempathetic for her sister’s predicament and assumes she’s mentally ill. Hal may have accused her of the same carelessness she’s describing. 

“I probably inherited about one one-thousandth of my father’s ability. It’s enough. Catherine got more. I’m not sure how much.” 

While Hal immediately doubts that Catherine could have written the proof, Claire knows that Catherine has inherited something from her father that she did not. With a tiny amount of Robert’s ability, Claire has a successful career that involves math. Having more of Robert’s genius is a double-edged sword. Catherine may have the potential to contribute groundbreaking work as an academic, but she also may have inherited his illness and the obsessiveness with which mathematicians pursue their research.

“Goddamnit, I’m working! I say ‘I’ – the machinery. The machinery is working. Catherine, it’s on full-blast. All the cylinders are firing, I’m on fire. That’s why I came out here, to cool off. I haven’t felt like this in years.” 

Robert repeatedly calls his brain “the machinery.” At this moment, when he believes that his brain is finally working clearly, he is sitting outside in freezing weather wearing just a t-shirt. Catherine has had to miss class because he did not pick up the phone. To Robert, the machinery seems to be working, but what he produces in this moment shows that he has become even more dysfunctional. 

“No! I’m back! I’m in touch with the source – the font, the – whatever the source of my creativity was all those years ago. I’m in contact with it again. I’m sitting on it. It’s a geyser and I’m shooting right up into the air on top of it.” 

Robert talks about his inspiration as if it comes from something outside of himself. In this, he is just a conduit and has been unable to access brilliant ideas. In actuality, his mental illness caused his mind to malfunction, finding connections that aren’t there rather than recognizing the ones that are.

“It’s not going to be easy. But the raw material is there. It’s like I’ve been driving in traffic and now the lanes are opening up before me and I can accelerate. I see whole landscapes–places for the work to go, new techniques, revolutionary possibilities. I’m going to get whole branches of the profession talking to each other.” 

Robert’s grand and delusional ideas show that the tragedy of his illness isn’t just that he cannot work. It’s that he feels like he can. Just as the graphomania caused him to produce over 100 notebooks full of writing, he has the delusion that he is creating something profound. 

“I was starting to imagine I was finished, Catherine. Really finished. Don’t get me wrong, I was grateful I could go to my office, have a life, but secretly I was terrified I’d never work again. Did you know that?” 

Ironically, Robert makes this statement just before Catherine reads what he has written and has to help him inside. This marks the end of his lucid year and the start of the decline from which he will not recover. At this moment, Robert will never work again, even as an advisor to graduate students. 

“I’m going to sit quietly on the plane to New York. And live quietly in a cute apartment. And answer Dr. Von Heimlich’s questions very politely. […] I would like to see a doctor called Dr. Von Heimlich: please find one. And I would like him to wear a monocle. And I’d like him to have a very soft, very well-upholstered couch, so that I’ll be perfectly comfortable while I’m blaming everything on you.” 

Catherine describes a frustrating life in which she behaves and does whatever Claire tells her to do. She blames Claire because Claire was not there to help her take care of her father or to sacrifice so that Catherine could go to school. Instead, Claire has swept into town after Robert’s death and taken charge, judging Catherine’s life and choices and trying to fix her. Ultimately, Claire is not fully to blame for Catherine’s problems, but lashing out at Claire makes her less keen to make Catherine move to New York.

“It didn’t feel ‘amazing’ or–what word did you use? […] It was just connecting the dots. Some nights I could connect three or four. Some nights they’d be really far apart, I’d have no idea how to get to the next one, if there was a next one.” 

Catherine talks about writing her proof and how she didn’t wake up one day with a brilliant idea but simply started chipping away at a problem. This suggests that perhaps a brilliant math mind might be misled into believing that breakthroughs come by inspiration rather than constant work and trial and error. It calls into question the nature of genius, and how much of it comes down to persistence.