33 pages • 1 hour read
Proof
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Themes
Lost Time
One of the anxieties shared by most of the characters in the play is the fear of losing or wasting time. This fear is centered on the idea that in the field of mathematics, most major contributions are made by men in their early twenties. For Robert, this issue, amplified as the onset of his illness, meant that he had a very limited number of lucid years in which to work.
In the first scene, when Catherine imagines speaking to her father after his death, he calls the days that she spent sleeping late or reading magazines “lost,” accusing, “You threw them away. And you’ll never know what 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” (9). Ironically, while Catherine was spending days in bed, she was spending her nights working on a major contribution to the field. For Catherine, the looming threat of a possible genetic illness makes time even more valuable.
Hal describes his older colleagues who use amphetamines to avoid slowing down because, “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” (34). Hal feels a similar pressure as his twenties come to a close, and he hasn’t produced anything memorable. Hal calls Catherine’s proof “historic,” pointing to the idea that contributions to the field are a matter of posterity. Robert earned posterity before his decline.
The idea of lost time connects not only with history remembering someone, but also with memory and the loss of memory. As Robert’s mind breaks down and then dies, it is erased. In the end, the idea of wasting time professionally is less important than wasting time personally. In his journal entry on Catherine’s birthday, Robert writes, “The years she has lost caring for me. I almost wrote ‘wasted.’ Yet her refusal to let me be institutionalized–her keeping me at home, caring for me herself, has certainly saved my life” (23). This sacrifice of time was therefore meaningful and not a waste.
Gender and Academia
When Hal calls math a “young man’s game” (34), he highlights the fact that the field is not only dominated by young people but also by men. Although he knows of “a woman at Stanford” (18), Hal can’t remember her name. For a woman in mathematics, receiving respect and consideration is an uphill battle. Catherine talks about Sophie Germain, an 18th century French mathematician who made major contributions, and Hal does not immediately recognize her name either.
During the French Revolution, Germain studied math while she was “trapped in her house” (18) due to the war outside and she “passed the time reading in her father’s study (18). After the war, she was not allowed to attend school because she was a woman. Germain used a man’s name to correspond with German mathematician Carl Friedrich Gauss and receive feedback on her proofs. Catherine learned about Germain from a book that her father gave her, likely as encouragement and inspiration for a young woman who was showing promise as a talented mathematician.
There are many parallels between Germain’s life in the late 1700s and Catherine’s in the late 1990s. Catherine is also stuck in her house, unable to leave her father by himself. She also receives her math education in her father’s study, both through Robert’s teaching and by teaching herself. Catherine is denied formal schooling because she was needed at home. When Catherine produced her own work, she did so under the guise of her father: She writes in one of his notebooks, in handwriting that is very similar to her father’s, and she keeps the notebook in her father’s desk drawer. When Catherine admits to Hal that she wrote the proof, his reaction is much poorer than Gauss’s response upon learning that Sophie Germain was a woman.
As Catherine quotes, Gauss recognized:
“A taste for the mysteries of numbers is excessively rare, but when a person of the sex which, according to our customs and prejudices, must 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 of courage, quite extraordinary talents, and superior genius” (36).
Conversely, Hal is condescending. Early in the play, he presumes that Catherine can’t understand enough to determine whether there’s anything to salvage from Robert’s notebooks, saying, “I know your dad taught you some basic stuff, but come on” (20). When Catherine tells him that she wrote the proof, Hal doesn’t believe that she could be skilled or educated enough. When he finally believes her, it’s because he believes the evidence rather than her word.
Math
Math is about logic, a system of pieces that work together seamlessly. Even higher math, which requires more creativity, boils down to fitting logical pieces together. A proof is a mathematical argument composed of axioms, or statements accepted to be true, that lead from one point to another.
Robert refers to his brain as machinery, which suggests a logical order. When a machine breaks down or malfunctions, any technician or mechanic can diagnose the problem and repair it. A broken machine can be rebuilt. Catherine describes her experience of working on the proof as similarly logical, explaining, “You’ve got to chip away at a problem” (37). She suggests that math isn’t about having major ideas but about putting in the time and the work.
But when the machinery of Robert’s brain breaks down, it is anything but simple and mechanical. His lucidity comes and goes inexplicably. He begins to see math and logic in everything, including situations that are not logical, such as the changing weather or the actions of students returning to school. The loss of logic and memory are incompatible with math. So too are the egos that make Hal and his colleagues focus more on their own posterity than on solving problems. Speed, or acting “young” by drinking all night, may help the older mathematicians feel as if they are not aging, but neither of these practices is particularly helpful for long-term mental acuity.
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