Portrayals of mathematicians have become particularly common in many recent films, novels and stage productions. The prevalence of these images has made some mathematicians such as John Nash recognizable figures in popular culture. Prior to the succes s of a film based on Nash's life, A Beautiful Mind , released in 2001, the film Good Will Hunting  received two Academy Awards for its depiction of a young mathematical prodigy on the MIT campus in Boston. An independent, surrealistic film Pi [3 ] about a mathematical genius apparently on the brink of a new discovery made its way onto the screen in 1998. Recent books dealing with mathematics and mathematicians include a 1998 biography of John Forbes Nash, Jr. , and the novels The Wild Numbers , translated from Dutch into English in 1999, and Uncle Petros and Goldbach's Conjecture , by Apostolo s Doxiadis, first published in Greek, with an English translation in 2000. Doxiadis seems influenced by the views of G. H. Hardy, whom he cites in the first pages of his novel, on the esthetic nature of mathematics, presented in A Mathematician's Apology , in 1940. "Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever that means" [13, p. 81]. Renowned playwright Tom Stoppard incorporated mathematics into Arcadia , the story of a 13-year-old mathematical prodigy, first performed at the National Theatre in London in 1995. Mathematics also occupies the Broadway stage in David Auburn's play, Proof . After an initial off-Broadway run at the Manhattan Theatre Club, the play moved to New York City's Walter Kerr Theater in 2000. Proof, which currently stars Jennifer Jason Leigh in the leading role created by Mary-Louise Parker, has earned th e Joseph Kesselring Prize, the Pulitzer Prize, the Drama Desk Award, and the Tony Award for Best Play of 2001. Although according to his own account, Auburn did not set out to write a play devoted entirely to mathematics, his work will provide us with a framework for examining the current representations of mathematicians in the mass media. Has the new visibility of mathematics and mathematicians on stage and screen had an impact on the popular image of mathematics in American culture? Is it producing a more profound understanding in the general public of the nature of mathematics, or is it merely reinforcing certain stereotypes of elitism and gender? These are some of the questions we will try to come to grips with here. Mathematicians On Screen
The accomplishments of John Forbes Nash, Jr. have been absorbed by the impressed upon the public consciousness by the recent Academy Award winning film, A Beautiful Mind. While the author of the screenplay, Akiva Goldsman, has been criticized for omitti ng crucial aspects of Nash's life, the film has certainly highlighted the complex life and work of John Nash. The New York Times, for instance, recently published an article explaining Nash's prize-winning contribution to game theory, the Nash equilibriu m. "You've seen the movie," runs the headline - "Now just exactly what was is it that John Nash had on his beautiful mind" [32, p. C2]? Another New York Times article described Nash as "a newly minted pop legend" [15, p. E28] whose film portrayal has pr ompted television documentaries, such as "A Brilliant Madness" , which attempts to clarify the puzzling nature of Nash's public persona. In a television interview with Nash and his wife on 60 Minutes, host Mike Wallace mentioned reports of a "smear c ampaign" in the run-up to the Academy awards, [26, p. 4D] referring to allegations of anti-Semitism and bisexuality, emerging from the subterranean infighting in the run-up to the Academy Awards.
Despite the controversy surrounding the accuracy of John Nash's character in A Beautiful Mind, the film highlights the ground-breaking work of a mathematician who overcame schizophrenia, going on to win the Nobel Prize for Economics in 1994, sustaine d for decades primarily by the care of his (ex-)wife, but also by his associates in the mathematics community, acting as an extended family to which the couple could turn for support [7, p. 456].
In the film, Good Will Hunting (1997), written by Matt Damon and Ben Affleck, Damon plays the lead character, Will Hunting. Will, who never attended college and works as a janitor at MIT, exhibits a wealth of historical and mathematical knowledge. "He can also solve difficult mathematical problems with an ease that makes MIT's richer more educated students envious of him" . After a professor discovers Will's vast mathematical ability, he bargains with him to meet on a weekly basis for mathematical sessions; Will's side of the bargain requires him to enter therapy as well; battles with the law, a symptom of mental conflicts, trouble Will's character in the film.
A more extreme image of a mathematician is conveyed by the independent film, Pi, the story of Max Cohen, a mathematician on the edge of insanity. The film exploits chaos theory, the idea that small occurrences can lead to large disruptions in the world.
"Everything around us is comprised of patterns, and Max is trying to find one in the largest production of ordered chaos: the stock market" . Like David Auburn, who did not set out to write a play specifically about mathematics, director Darren Aro nofsky combines mathematics with Kabbalistic allusions, to challenge common perceptions of reality in Max's attempts to crack the code.
A Beautiful Mind, Good Will Hunting and Pi present three distinct images of mathematicians. Even so, these figures are all men and each suffers from one form of instability or another. Other movies featuring mathematicians include Antonia's Line (19 96) , directed by Marleen Gorris, Sneakers (1992) , directed by Phil Alden Robinson, and An Unmarried Woman (1978) , directed by Paul Mazursky. These films illustrate ways that the cinema can exploit, and possibly amplify, the public's inter est in mathematics. At the same time, we believe that it behooves media executives to consider the effects of the images that they produce for public consumption.
G. H. Hardy categorizes mathematics as either 'real' or 'trivial' in A Mathematician's Apology, a title that no doubt refers to the tradition inaugurated by the Socratic Apology. Hardy discusses the notion of triviality of mathematics in terms of a che ss problem while taking 'real' mathematics to consist of the results of gifted individuals who prove new and significant theorems. Moreover, Hardy compares the work of 'real' mathematicians to that of a painter or poet. "A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas" [13, p. 84]. Rather than shapes, colors or words, a mathematician constructs patterns through ideas; the permanence of these ideas distinguishes mathematics from other fields of study. This view appears to fascinate directors, playwrights and authors who have chosen to focus on the nature of mathematics and the characteristic behavior of individual mathematicians in their creative pursuits. Prior to Sylvia Nasar's biography of John Nash, A Beautiful Mind, a number of books had appeared relating to the cryptographic effort which resulted in the decription of the principal German military codes, such as Seizing the Enigma: The Race to Break the German U-Boat Codes, 1939-1943 in 1993 . Like Nasar's book, which inspired a movie, the biography of the British mathematician and code breaker Alan Turing became a play, appropriately titled Enigma. As Joel Spencer, a mathematics professor at New York University, remarked in the context of Proof, "What was once considered hopelessly geeky is suddenly au courant" [30, p. 165]. Hardy's esthetic view of mathematics is connected with his view that only the best mathematicians matter, and he also holds that young men are the ones responsible for 'real' mathematics. "No mathematician should ever allow himself to forget that mathematics, more than any other art of science, is a young man's game" [13, p. 70]. Hardy urges the reader to appreciate the beauty of mathematics, specifically the 'real' mathematics of young men. The elitist tone of A Mathematician's Apology is reflected by many of the contemporary images of mathematicians striving, generally alone, to complete a complex proof or solve a difficult problem. According to the review by Fernando Q. Gouvea of Philibert Schogt's novel The Wild Numbers, Schogt places his story on a human level by describing a critical moment in the life of a more typical mathematician, Isaac Swift. Gouvea, a professor of mathemat ics at Colby College in Maine and editor of MAA Online and FOCUS for the Mathematical Association of America, analyzes Isaac's life story in terms of what he calls the "Hardy myth," that the best mathematics is the so-called 'real' or serious mathematics. The plot of the novel concerns Isaac's solution to the fictional Beauregard's "wild number problem," which is put into question after an apparently demented student, much occupied with the same problem, accuses Swift of plagiarism. "One can read this book as an attempt to ask how one can live under such conditions, an attempt to get beyond the Hardy myth to a more humane (and more true) view of what being a mathematician is all about" . Mathematics is a relatively new focal point for the mass media, and this portrait of a "mediocre mathematician," as Swift describes himself, could inspire a more realistic assessment of the field of mathematics in general. Schogt illustrates the "Hardy myth" by presenting a character who seeks to accomplish something beyond his basic responsibilities as a university algebra teacher. The solution to the "wild number problem" would be the catalyst for upward mathematical mobility. In the novel Uncle Petros and Goldbach's Conjecture, the task at hand is proving the infamous (and nonfictional) Goldbach's conjecture. Uncle Petros was formerly a respected professor of mathematics, a fact unknown to his nephew, and devoted his life to solving this elusive conjecture, before curiously disappearing into the Greek countryside. After his nephew uncovers Uncle Petros's past career, he encourages the retired mathematician to return to the pursuit of Goldbach's conjecture. In the novel, th e main character embraces Hardy's notion of 'real' mathematics in the form of Goldbach's conjecture. There is also great concern for the old man's sanity, a common thread in many portrayals of individual mathematicians. The exposition of mathematics by serious mathematicians is hardly a new phenomenon. A typical example is Hermann Weyl's Symmetry (1952) . Nonmathematicians have also reached toward mathematics for a variety of reasons: as examples we cite The Confu sions of Young Tvrless (1906) , by Robert Musil, which makes use of mathematics for dramatic effect, and Flatland: A Romance of Many Dimensions (1884) by Edwin Abbott , which plays with the mathematical ideas themselves. It is the weaving of mathematical subject matter into more accessible literature, not necessarily written by mathematicians, that bears most closely on the role of mathematics in popular culture. Mathematicians On Stage
The issues of elitism and gender that shape many representations of mathematicians in the mass media are clearly exhibited in David Auburn's Proof. The play tells the story of a young woman, Catherine, who tends her mentally ill mathematician-father in the years leading up to his death. The conflict in the play concerns whether Catherine could have been capable, as she claims, of devising a complicated proof which appears to be the work of her late father. In the closing scene, Catherine as explains t he steps of the proof to Hal, a young professor of mathematics, and a former pupil of her father, we see her finally, clearly, as a mathematician.
Auburn, who makes much of the scarcity of great female mathematicians [16, p. 333], recognizes the abilities of female mathematicians through the central plot device of his play. That is, he exploits gender issues for psychological effect, throwing the character of Hal off within the play, and also throwing the audience off the scent by this and other devices. At the same time Auburn bases the character of Robert, Catherine's father, on John Nash, with regard to his brilliant yet fatally unstable per so na. This deliberate choice on the part of the playwright illustrates the potential for stereotypes to arise along with various images of mathematicians in popular culture. The mathemtatician Rob Kirby has stated that "some very edgy personalities are dr awn to it [math] as a way to find order in the world" [Kirby p. 334].
In Proof, the audience is confronted with many popular attitudes toward mathematics and mathematicians, including some which have been prominent recently in the mass media. Catherine's character seeks to overcome gender bias; her father is modeled on Jo hn Nash, not only in personality but in the timing of his career and to a degree in his accomplishments; the perplexing proof itself is reminiscent of the elitist and esthetic tendencies set forth in Hardy's A Mathematician's Apology; and there are freque nt references to "geeks", "nerds", and the like. This combination upholds a key function in the study of popular perceptions of mathematics and mathematicians. Popular views of Mathematicians In January 2001, Susan Picker and John Berry conducted a study of 476 12 and 13 year-olds in the United States, Britain, Finland, Germany and Romania . The study revealed a strongly negative stereotype of the mathematical profession among such adoles cents. "For children, images tend to be gatekeepers, and kids who would prefer an active social life don't want to end up being lonely geeks," [23, cited in 8]. While their study provides considerable insight into young people's perceptions of mathematics and mathematicians, it does not examine the possible impact of the recent upsurge of interest in mathematics on the part of the mass media. "Even better, the i mage that has captured the public imagination is that of a mathematician working intensely and usually alone on the most difficult and abstract problems" [30, p. 165]. As American culture absorbs a new and more varied set of images of mathematics and mat hematicians, one may wonder whether these representations will produce more positive perceptions of the mathematical profession among young people. Professor Berry of Plymouth University in England, who ran the study in question, pointed out that in addition to the negative image of "a scruffy person, probably with pencils in his shirt pocket, holes in his clothes, and equations written on his arms [ 8]," many of the children interviewed assumed mathematicians were male. Looking at contemporary images in the media, one finds the story of Nobel Prize winner, John Forbes Nash, Jr. in A Beautiful Mind. Matt Damon plays the featured male mathematician i n Good Will Hunting. Other pieces of mass media previously mentioned have featured a male mathematician as well. In Proof, however, the main character is a young, accomplished female mathematician. If the larger goal is to incorporate mathematics into the public consciousness, one must recognize all the aspects of artistic work. The increase of mathematical interest in the mass media acts as a double-edged sword, illuminating the aesthetic nature o f mathematics and mathematicians, while reinforcing specific stereotypes of mathematicians presumed in John Berry's study of young people. For Hardy, beauty and seriousness go hand-in-hand when it comes to mathematics. It is on this basis that one can e valuate the representations of mathematics over the course of recent years. In Lynne Butler's review of A Beautiful Mind, for instance, she looks beyond the supposed flaws in Goldsman's screenplay to "gain an intelligent appreciation of a movie that transcends stereotypes of mathematical genius and mental illness" [6, p. 456]. B utler encourages the public to appreciate this film's compelling and important story and not to criticize the movie for omitting or misrepresenting specific aspects of Nash's life. A Beautiful Mind illustrates Nash's ability to see the beauty in mathemat ics everywhere. "Their [Nash and his wife, Alicia] love grows from a shared appreciation of the beauty to be found in pattern and color" [6, p. 456]. The beauty and seriousness of Nash's mathematical patterns is precisely what Hardy called for in A Math ematician's Apology. It is also manifest in the drama, Proof, which, like A Beautiful Mind, tells "a story inspired [in part] by Nash's life that is suspenseful without a car chase or a homicide" [6, p. 456]. The elements of beauty and seriousness that contribute to Hardy's definition of the esthetic value of mathematics enable one to evaluate the connection between mathematics and popular culture in the modern world. A Mathematician's Apology thereby serves as a standard by which one can measure the beauty in these "patterns" of mathematical representations. Moreover, Hardy's elitist view of mathematics is applicable to many images of mathematics and mathematicians throughout the mass media. Proof: A Symposium In "Geek Chic,"  Joel Spencer describes a symposium that was held at New York University in October 2001, in response to the success of David Auburn's play Proof, and a general sense that mathematics was receiving unprecedented attention on the part o f the media, and, presumably, the general public. At "Proof: A Symposium," the first panel discussion was the most mathematical with its treatment of the nature of the proof. "Women and Proof" was the second panel, and "Images of Proof" was the final p anel, which consisted of various writers and actors. "The key to the success of "Proof: A Symposium" and similar ventures is to bring together people from inside and outside the mathematical community" [30, p. 165]. All the recent media attention on mathematics was felt to provide an excellent opportunity to convey the beauty of this subject to the masses; such forums and dialogues between mathematicians and non-mathematicians may clarify the significance of such ma ny representations, and illuminate the misconceptions that may arise as a result. Another forum for discussing the frequent marriages between mathematics and the humanities is conducted by Robert Osserman, mathematician and Special Projects Director at the Mathematical Sciences Research Institute. Osserman hosts a series of televised public events called "Conversations" with playwrights and cultural figures who use mathematics in their work. Gerald L. Alexanderson of the Mathematical Association of America highlighted the key moments of these dialogues in an article written for the M AA website . Osserman began his conversation with questions regarding Auburn's background. Auburn explains that he studied political philosophy at the University of Chicago, ending his formal mathematical education with calculus. Auburn moved to New York after gradu ation and wrote copy labels for a chemical company before enrolling at Julliard to study acting and writing. When asked whether he planned to write about a mathematician in his play Proof, Auburn informed the audience that he set out with an interest in whether mental illness, as well as talent, could be inherited. The mathematical connections, according to Auburn, came later . The issues of elitism and gender arise when Osserman and Auburn read passages from the play that touch on various perceptions of mathematicians - "that it is a young man's profession, that there is something that predisposes mathematicians to mental insta bility, and that only brilliant results count in mathematics" . Osserman also draws a parallel between Arcadia and Proof. "In both plays there is a very clever young woman who has remarkable insights into mathematics and is "mentored," in a way, by a slightly older man who is well-trained in mathematics but much less original in his thinking" . Osserman's upcoming conversation is with author Sylvia Nasar and Dave Bayer, a mathematical consultant to the film, A Beautiful Mind. Modern representations of mathematicians in the media both challenge and reinforce common perceptions uncovered in the study of young people referred to above . According to David Auburn, "More than one source reported a far higher incidence of menta l instability among writers and poets than among natural scientists" [16, p. 334]. Furthermore, one must appreciate mathematics as a whole, not just the 'real' mathematics that Hardy so highly praises. If mathematics is to continue as a major source of interest in the mass media, mathematicians will need to fight the barriers and inconsistencies that have plagued common understandings of the mathematical field; some recent examples, such as The Wild Numbers, work to dispel the "Hardy myth" by presenting the public with a more expansive view of mathematics. It is not sufficient to make mathematics a focus of attention in the mass media, for media attention necessitates responsibility. A variety of films, plays and novels have promoted the "patterns" Hardy sought to convey in A Mathematician's Apology. As l ong as mathematics plays a prominent role in the mass media, writers, directors and media executives should exercise a responsibility to design a comprehensive compilation of mathematicians for public consumption. Popular representations of mathematicians in the media can perhaps influence common perceptions of mathematics and mathematicians in the minds of young people. Images of mathematicians can exist far beyond the page of a book, a movie screen or the Broadw ay stage. This seems particularly apparent in the many articles written on the topic, as well as the recent symposium designed as a result of the new interest in mathematics and the popularity of the play, Proof. The various images of mathematicians in popular culture have therefore caught the attention of both mathematicians and non-mathematicians. Proof serves as an appropriate framework in the analysis of popular perceptions of mathematicians and mathematics, and not only because of its success on Broadway. Despite his initial intentions, Auburn's play touches upon the primary issues of elitism a nd gender that are found in many of the modern representations of mathematicians in the media. Auburn's work can be analyzed on its own, or used as a reference for analyzing other artistic works of mathematical content. Along these lines, this appears to be an appropriate time to conduct a college seminar on the history of algebra, with a similar goal of communicating a sense of mathematical understanding to a broader audience. The various images of mathematicians in th e media have expanded mathematical conversation beyond the serious mathematicians. Mathematicians and non-mathematicians alike can thus appreciate Hardy's passion for the aesthetics of mathematics in the form of permanent patterns that contribute to the changing visage of mathematics in popular culture.
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