Historical Context
Sophie Germain
Sophie Germain, the French mathematician greatly admired by Catherine in Proof, was born to a middle-class family in Paris in 1776. Her interest in mathematics sparked at the age of thirteen. During the French Revolution, she was confined to her home and used her father's library to teach herself mathematics. Her family attempted to dissuade her, believing that mathematics was unsuitable for a girl. However, Sophie remained determined. She acquired lecture notes from the École Polytechnique, an institution established in 1794 to train mathematicians and scientists but which did not admit women. Fascinated by the work of J. L. Lagrange, she submitted a paper to him under the male pseudonym Antoine-August Le Blanc, a supposed former student of the academy. Lagrange, impressed by the paper, sought to meet its author. Despite his initial surprise at discovering a young female mathematician, he agreed to mentor her. This mentorship allowed Germain to enter a previously exclusive circle of mathematicians and scientists.
In 1804, Germain began corresponding with the German mathematician Carl Friedrich Gauss, as Catherine recounts to Hal in Proof. Gauss, one of the most brilliant mathematicians of all time, received her work in number theory. It took three years for Gauss to realize that the talented young correspondent he had been mentoring was a woman. Twelve years later, Germain wrote to the mathematician Legendre, presenting her most significant contributions to number theory. In 1816, the French Academy of Sciences awarded her a prize for her mathematical explanation of the vibration of elastic surfaces. Germain's continued work in this field represented another lasting contribution to mathematical theory. She passed away in 1831, before she could accept an honorary degree from the University of Göttingen, which Gauss had persuaded the university to award her. Germain's contributions to mathematics were particularly remarkable given that, like Catherine in Proof, she lacked formal academic training.
Trends on Broadway
When Proof premiered in 2000, it joined a series of plays inspired by intellectual fields like mathematics and physics. These playwrights aimed to offer the audience not only an engaging evening but also thought-provoking content. This trend was initiated by British playwright Tom Stoppard. His play Hapgood (1988; revised 1994) used the complexities and paradoxes of quantum physics as metaphors for the espionage world during the Cold War. In 1994, Stoppard wrote Arcadia, another play that immersed audiences in quantum physics and chaos theory. Like Proof, Arcadia features a young woman with an exceptional understanding of mathematical theory. Additionally, it references a nineteenth-century woman who significantly influenced mathematical theory, not Sophie Germain, but Ada Byron, Lady Lovelace. Ada, the poet Lord Byron's daughter, collaborated with mathematician Charles Babbage on developing the theory for a new calculating machine. Her mathematical plan is now regarded as the first computer program.
Other plays that incorporated quantum physics include Michael Frayn’s Copenhagen (2000), a complex examination of a 1941 meeting between physicists Werner Heisenberg and Niels Bohr, and Hypatia by Mac Wellman, which explores the life and death of Hypatia, a fifth-century mathematician and philosopher. According to Bruce Weber, in his New York Times article "Science Finding a Home Onstage," this contemporary trend of writing plays with scientific themes:
This flourishing use of science as narrative material and scientific concepts as stage metaphors provides evidence that science is re-entering the realm of popular culture, not just in imaginative, futuristic fiction but also in other mainstream and alternative forms: from historical reconstruction and theoretical abstraction to fluffy romance and contemporary realism.
Style and Technique
In the realm of literature, style and technique play an essential role in shaping a narrative's impact and engagement. Mastery of exposition and the element of surprise are two...
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such techniques that can profoundly influence a reader's or viewer's experience. This article delves into how these techniques are skillfully employed to weave a compelling narrative, as illustrated by the playwright's adept use of both in the discussed play.
Exposition: Building Foundations
The exposition serves as the backbone of any narrative, setting the stage with essential details that ground the audience in the story's universe. In this play, the exposition is handled with remarkable efficiency and finesse. Within the initial eight pages, a wealth of information is conveyed, setting the emotional and intellectual tone of the piece. Through the dialogue between Robert and Catherine, the audience quickly discerns the complex father-daughter relationship, infused with both affection and frustration. We learn of Robert’s past as a brilliant mathematician whose prowess peaked in his twenties, now overshadowed by mental illness. Simultaneously, Catherine’s character is revealed as a deeply introspective and isolated individual, grappling with her own psychological fears and a strained connection with her sister. All these layers unfold through a mere few hundred lines of dialogue, showcasing the playwright's skill in painting a vivid, intricate picture in such brevity.
Theatrical Surprise: Twists and Revelations
One of the hallmarks of engaging storytelling is the strategic use of surprises that keep the audience on their toes. In this play, the playwright demonstrates mastery over this technique, delivering unexpected revelations that shift the narrative’s trajectory. A pivotal moment arises midway through the first scene when Robert admits his insanity, only to reveal that he speaks from beyond the grave. This revelation not only shocks but injects a layer of dark humor into the narrative, demonstrating how surprises can balance the play's inherent intensity and sadness. The technique is further employed in various scenes, introducing new information that alters character dynamics and plot direction. For instance, the end of the first scene sees Hal exposing his true motive for attempting to abscond with a notebook, while act 1, scene 3, uncovers a prior meeting between Hal and Catherine, adding depth to their interactions. The pièce de résistance of this technique is delivered at the climax of act 1, when Catherine boldly asserts authorship of a mathematical proof, a claim that dramatically reshapes the audience’s understanding of her character and intellect.
Through effective use of exposition and surprise, the playwright crafts a narrative that is both engaging and thought-provoking. These techniques not only enrich the storytelling but also ensure that the audience remains invested in the unfolding drama. Such mastery of style and technique highlights the power of nuanced dialogue and unexpected turns in creating a memorable theatrical experience.
Adaptations
Proof was adapted into a film scheduled for release in the United States in 2005. The screenplay was written by David Auburn and Rebecca Miller. Directed by John Madden, the film features Anthony Hopkins as Robert, Hope Davis as Claire, Jake Gyllenhaal as Hal, and Gwyneth Paltrow as Catherine. Paltrow reprises her role as Catherine, which she originally performed on stage in London’s West End.
Bibliography
Sources
Auburn, David, Proof, Faber and Faber, 2001.
Barbour, David, ‘‘Proof Positive’’ in Entertainment Design, Vol. 43, November 2000, p. 19.
Brustein, Robert, Review of Proof, in the New Republic, November 13, 2000, pp. 28–29.
Clark, John, ‘‘So Smart It Hurts,’’ in Los Angeles Times, December 16, 2001.
Foster, John Evan, Review of Proof, in Theatre Journal, Vol. 53, No. 3, October 2001, Performance Review Sec., pp. 503–04.
Gussow, Mel, ‘‘With Math, a Playwright Explores a Family in Stress,’’ in the New York Times, May 29, 2000, Sec. E, Col. 2, p. 1.
Hoffler, Robert, Review of Proof, in Variety, Vol. 380, No. 11, October 30, 2000, p. 34.
Melton, Robert W., Review of Proof, in Library Journal, April 1, 2001, p. 100.
Nasar, Sylvia, A Beautiful Mind, Simon & Schuster, 1998.
Poincaré, Henri, ‘‘Mathematical Creation,’’ in The Creative Process: A Symposium, edited by Brewster Ghiselin, New American Library, 1960, p. 40.
Rockmore, Daniel, ‘‘Uncertainty Is Certain in Mathematics and Life,’’ in the Chronicle of Higher Education, June 23, 2000, Opinion & Arts Sec., p. 89.
Weber, Bruce, Review of Proof, in New York Times, May 24, 2000, p. B3.
———, Review of Proof, in New York Times, October 27, 2001. ———, ‘‘Science Finding a Home Onstage,’’ in New York Times, June 2, 2000, p. B1.
Further Reading
Billington, Michael, Review of Proof, in Guardian, May 16, 2002. This review of the British production of Proof at London’s Donmar Warehouse censures the playwright for not explaining what the crucial mathematical theory is. Billington calls this the weak point of the play.
Feingold, Michael, Review of Proof, in Village Voice, June 6, 2000. A review that is generous in its praise. Feingold points out that Auburn has no interest in explaining the finer points of mathematics; it is simply a given that for three of the four characters, mathematics is something they love, and the play is more of a love story than anything else—love of mathematics, love of father and daughter, and the growing love of Hal and Catherine.
Heilpern, John, Review of Proof, in New York Observer, June 19, 2000, p. 5. A laudatory review that praises the play’s evocation of love between father and daughter, the fragility of life, and the discovery of love. The only flaw Heilpern sees is that the mystery of who wrote the proof is too easily resolved.
Parker, Christian, ‘‘A Conversation with David Auburn,’’ in Dramatist Magazine, December 10, 2001. In this interview, Auburn talks about how he became interested in writing plays and how his career developed.