The Mathematician as Hero in Audio-Visual Media Roslynn Haynes and Raymond Haynes Compared with fiction, audio-visual media both enhance opportunities and impose constraints on the representation of scientist characters. This is true both in depicting the inner life of scientists and in presenting credibly what they actually do when ‘doing science’. Mathematics is arguably the most non-visual and non-verbal of sciences, as the science lacks even the visual apparatus of chemistry. In addition, mathematical symbols and formulae are the most arcane to non-scientists. Thus, the problem for film-makers is the question of how to engage and maintain audience interest while presenting the mathematicians’ experience faithfully and avoiding ‘information dump’. In this article, we focus on the depiction of mathematicians in film, television, and recorded TED talks and the success (or otherwise) of their representation. “All we know about the world we know through the mass media.” Niklas Luhmann The Reality of the Mass Media (2000: 1) The stereotypical mathematician of film, an unfashionably dressed and socially inept guardian of abstruse and boring knowledge, has never been a likely candidate for movie stardom and box-office success. So why, since the 1990s, has there been a steady stream of successful films featuring mathematicians as the main characters? 1 Two pivotal events in the history of mathematics may have sparked this interest in maths and the people who dedicate their lives to it. Stephen Hawking’s A Brief History of Time was published on April Fool’s Day 1988 and sold out the first edition in a few days. Improbably for a book about theoretical physics based largely on mathematics, it rocketed 1 Wikipedia lists 45 films about mathematicians since 1992 (List of Films about Mathematicians, 2022). AAA - Arbeiten aus Anglistik und Amerikanistik Band 47 · Heft 2 Gunter Narr Verlag Tübingen DOI 10.24053/ AAA-2022-0011 Roslynn Haynes and Raymond Haynes 190 to the top of the best-seller lists, was translated into more than 35 languages, and has now sold more than ten million copies world-wide. Its success reflected a combination of fascination with the big questions it posed about the origins of the universe, and the interest generated by Hawking’s well-known motor neuron condition and his witty persona. These aspects were preserved in the biographical film of the same name, along with interviews with Hawking’s family, friends and colleagues, and computer graphics to illustrate his complex ideas. In 1994, the British mathematician Andrew Wiles made media headlines with his proof of Fermat’s Last Theorem, for which he received the prestigious Abel medal in 2016. Prior to this, few non-mathematicians would have heard of Fermat’s Last Theorem, 2 but the publicity suggested that maths was not just a matter of cut-and-dried answers; rather, it was an intellectual discipline of such difficulty that a problem might wait threeand-a-half centuries for a solution, even though, in the interim, many mathematicians had pursued it through a lifetime of dedication, obsession, and frustration. The level of public interest was maintained by Simon Singh’s television documentary “Fermat’s Last Theorem” (1996), made for the BBC’s Horizon series. 3 Singh saw the potential of Wiles’s story in terms of the classic myth of the hero’s quest: the young man achieving hero status by completing a near-impossible task - as Theseus, Jason, Hercules, and the legendary protagonists of many cultures had done. In Singh’s words: There is a brilliant genius from the past who solves an apparently impossible problem. He dies without revealing the solution. It becomes buried treasure, and every subsequent mathematician goes in search of it. There are heroes, villains, rivals, rich prizes, a duel at dawn, a suicide […,] but after 300 years the problem remains intact […]. Undaunted, however, a young boy promises to devote the rest of his life to solving this notorious problem. After thirty years he suddenly identifies a strategy that might work. For seven years he works in secret. He reveals his proof only to learn that he has made a mistake. He hides away again, humiliated and ashamed, but he returns a year later, this time triumphant. The problem has been solved. His journey is over. (Singh n.d.) In Singh’s documentary, which proceeds like a detective story following clue after clue, Wiles speaks of his experience of doing maths in Gothic 2 Fermat’s Last Theorem is stated in the form: The equation xn + yn = zn has no solutions in integers if n >2. It was formulated by Pierre de Fermat in a handwritten note in Latin in the margin of a book in 1637: “I have a truly marvellous proof of this, which this margin is too narrow to contain”, he wrote (qtd. in Manin/ Panchishkin 2005: 341). After spending their life trying unsuccessfully to solve this theorem, some mathematicians have doubted whether Fermat really did have a demonstration of the proposition. 3 In the United States, the documentary was shown under the title The Proof on NOVA in 1997. The Mathematician as Hero in Audio-Visual Media 191 terms, as “entering a dark mansion” (Singh 1996). With considerable emotion, he describes his breakthrough in terms of “this incredible revelation” (Singh 1996), but it is clear that this ‘revelation’ is not a bolt from the blue but emerges from years of dedication to solving the problem rationally. An analysis of the films and television programs that have appeared since these events indicates that, in audio-visual media, maths has been presented in two contrasting scenarios: a) Maths as magic, mystery, and madness, associated exclusively and inexplicably with the figure of the genius and mysterious powers, such as the esoteric Kabbala of Jewish mysticism, or inspiration derived from the imagination that was central to nineteenth-century Romanticism. In its modern form, maths is portrayed as a sudden rush of intuitive understanding, rather than the result of intellectual effort. Because of its unexplained nature, maths is often associated with obsession, schizophrenia, or mental illness (e.g. A Beautiful Mind [2001] and Proof [2005]) or with religious revelation (e.g. Pi [1998] and The Man Who Knew Infinity [2015]), an unexplained talent (e.g. Good Will Hunting [1997] and The Gifted [2017]) or autistic spectrum disorder (e.g. X+Y [2014] and Beautiful Young Minds [2007]). The majority of these films conclude with the genius figure either abandoning a potential career in maths altogether (e.g. Pi) - in the case of young prodigies, opting to embrace a life of emotion, joy, and relationships (e.g. Good Will Hunting and X+Y) - or, rarely, seeking a compromise (e.g. The Gifted). b) Maths as the product of reasoning and sustained mental application, the antithesis of mysticism. This reaffirms the ancient Greek insistence on rigorous proof, involving a series of arguments based on logical deductions leading to an inescapable conclusion; but it is also associated with the cult of reason that characterised the European Enlightenment. Central to this scenario is a belief that reason (epitomised in mathematical equations) reduces apparent chaos to order. In the modern context, the formal steps of the proof are usually carried out by computers solving complex algebraic equations devised by a mathematical genius, as in The Imitation Game (2014), Enigma (2001), A Brief History of Time (1991), Fermat’s Last Theorem, and Hidden Figures (2016). In this second group of films, the hero figures complete their quest and triumph in the world of maths (e.g. Hidden Figures and The Man Who Knew Infinity), though this success may be tempered by other limitations - physical (e.g. A Brief History of Time), psychological (e.g. A Beautiful Mind), social (e.g. The Big Bang Theory [CBS, 2007-2019]), or by personal tragedy with social repercussions (e.g. The Imitation Game). Roslynn Haynes and Raymond Haynes 192 Representing Maths in Audio-Visual Media Compared with fiction, specifically the science novel, 4 audio-visual media both enhance opportunities for, and impose constraints on, the communication of mathematical facts and theories and the depiction of the inner life of mathematicians - what they actually experience and feel when ‘doing science’. Maths is the most non-visual and non-verbal of the sciences; it is an almost wholly cerebral pursuit (although, as we shall see below, its applications are not). Its symbols and formulae are even more arcane to non-scientists than the jargon regularly used in other sciences and, more strategically, it lacks the visual interest of a chemistry laboratory or a biology field station. The problem for the film-maker therefore is how to engage and maintain audience involvement, faithfully presenting the experience of mathematicians while avoiding the disconnect of the too-obvious ‘information dump’. In this article, we focus on the depiction in audio-visual media of mathematicians, the success or otherwise of their representation, the level of science communication achieved, and the significance that the audience is likely to attribute to their work. We explore how successfully various audio-visual media can: a) communicate mathematical concepts and theories to a general audience; b) escape the stereotyping that has characterised film scientists from the beginning and present mathematician characters as interesting, even charismatic; c) avoid the ‘information dump’; d) explore the effects of discrimination arising from race, gender, class, religion, physical disability, sexual orientation, or family expectations on the lives of mathematicians, both real and fictional; e) convey the motivations, obsessions, and the intellectual and moral struggles of mathematicians; and f) examine how real-life mathematicians have used audio-visual media to educate and inspire audiences. As case studies, we draw mainly on the films A Beautiful Mind, The Man Who Knew Infinity, The Imitation Game, A Brief History of Time, and Hidden Figures, scenes from the television sitcom The Big Bang Theory, maths documentaries and TED talks given by mathematicians, but we also refer to other films and documentaries where appropriate. 4 ‘Science novel’ is a term used to describe realistic fiction which has as its theme some aspect of science, and in which a major character is a scientist. It is not to be confused with science fiction or science fantasy. For a study of modern examples, see, for example, Farzin et al. (2021). The Mathematician as Hero in Audio-Visual Media 193 a) Communicating Mathematical Concepts and Theories to a General Audience The language of maths is numbers and equations, but these are regarded as a major disincentive to non-specialist readers and film audiences. When Stephen Hawking submitted an equation-riddled first draft of A Brief History of Time to Cambridge University Press, the then-science editor, Simon Mitton, advised him that for every equation in the book the readership would be halved. Thereupon Hawking removed all but one equation, E=mc 2 , which was so well-known as to be non-threatening, and later attributed the phenomenal success of the book to Mitton’s advice (Falk 2018). Film-makers usually regard equations as merely background props. Even when correct, their purpose is not to explain the maths or even to be understood by the audience, but rather to indicate that this character is indeed a mathematician with a level of intellect far above the average. The focus is on the mathematician character, writing (usually illegible) equations on multiple sheets of paper, blackboards, whiteboards, or, extraordinarily, on windows. Even though the era of solving maths problems on the back of an envelope has long passed, film mathematicians are rarely shown using computers, possibly because they obscure and dehumanise the process of solving the problem and have become too ordinary in our everyday experience. Written equations, by contrast, can more immediately suggest obsession, frustration, perplexity, genius, or, in the case of Proof, authenticity of authorship through handwriting. In The Man Who Knew Infinity, Srinivasa Ramanujan is at first regarded with grave suspicion by G.H. Hardy and his colleagues at Cambridge because he does not conform to the Western culture of mathematical proof through a paper trail of equations that lead to an incontrovertible solution. On Hardy’s insistence, Ramanujan undertakes the rigorous procedures required to substantiate his intuitive answers. We see him at the desk in his chilly Cambridge room frantically covering reams of paper with equations, dropping them to the floor in frustration until he can present his mentor with an acceptable, conventional proof for what he, alone, knows. In Good Will Hunting, the young, untrained janitor’s ability to complete a hitherto unsolved equation left on a college blackboard by a lecturer marks him as a unique intellect and railroads him against his will into an academic education. In A Beautiful Mind, John Nash writes abstruse equations in chalk on a window (Illustration 1). This improbable procedure has a filmic purpose: it enables the audience to view simultaneously the complexity of the Roslynn Haynes and Raymond Haynes 194 problem Nash is working on and the perplexity apparent on his face seen through the glass as he does so. Illustration 1. John Nash’s writing on a window allows viewers to simultaneously see the equations and Nash’s mimics. Screenshot from A Beautiful Mind © Universal Pictures, 2011. The long-running American TV sitcom The Big Bang Theory centres on the lives of four nerdy, young scientists: Sheldon (a theoretical physicist who considers himself intellectually far superior to everyone except Stephen Hawking), Leonard (an experimental physicist), Rajesh (an astrophysicist), and Howard (an aerospace engineer). Sheldon and Leonard share an apartment in which whiteboards covered with formulae and equations that change throughout the series suggest that they are working on advanced maths problems and models. However, mathematically astute viewers would realise that the equations displayed are not new research, but undergraduate level and sometimes wrong, 5 indicating the limitations of Sheldon’s self-proclaimed genius. These limitations are further exposed in the episode “Hawking Excitation” (2012), in which Sheldon finally meets the real Stephen Hawking, to whom he has sent his thesis on the Higgs boson, an idea “that came to [Sheldon] in the shower one morning” (Lorre et al. 2012). Hawking, who plays himself in the episode, sets Sheldon up with, “You clearly have a brilliant mind”, before demolishing him by saying, “Too bad it’s wrong. You made an arithmetic mistake on page two. It was quite a boner” (Lorre et al. 2012). Similarly, in the episode “The Pirate Solution” (2009), Sheldon grudgingly allows Raj to work for him on a pro- 5 For example, in “The Hamburger Postulate” (season 1, episode 5; 2007), Leslie corrects one of Sheldon’s equations. The Mathematician as Hero in Audio-Visual Media 195 ject exploring string theory from gamma-ray dark matter. Sheldon has covered a whiteboard with mathematical formulae, trying to design an experiment to look for annihilation spectra resulting from dark matter collisions in space. They both stare at the whiteboard, thinking hard, until Raj pronounces that one of Sheldon’s equations is incorrect (Lorre et al. 2009b). Throughout the series, the aspiring scientists debate current theories, mathematical models and experiments, and agonise over their failure either to solve the problems they set themselves or to advance in their respective careers. They discuss real issues that confront scientists - the politics of funding, job acquisition and security, the difficulty of getting published - and through the lens of comedy and social ineptitude, expose unsuspecting viewers to real, often up-to-the-minute, scientific discoveries. In all these cases, the actual maths concepts and theories are little more than window-dressing, designed to assure viewers that important science is ‘happening’ here. The references to maths do not communicate any significant scientific knowledge to the audience, although they do indicate the insecurity, the loneliness, and the intellectual risks of a career in mathematics (e.g. A Beautiful Mind, Proof, and X+Y). A significant exception is A Brief History of Time, in which Hawking explains to a non-specialist audience current thinking in cosmology about the origin of the universe, black holes, and time. His introductory lure is a series of intriguing questions: “Which came first: the chicken or the egg? ” “Where did the universe come from and where is it going? ” “Why can we remember the past but not the future? ” (Morris 1991). Although the goal is to provide an overview of the subject, Hawking also explains some complex maths concepts, and while viewers may not receive take-home answers to the big questions, he retains audience interest because of his witty, and necessarily slow, presentation. 6 b) Escaping Traditional Stereotypes Cinema has had a long tradition of employing a limited range of visual stereotypes for scientists because they tapped readily into the audience’s pre-conceived image of what a scientist should look like and presented an immediate cue to recognise this character as a scientist. In the case of mathematicians, this was supplemented by stereotypical behaviour involving social ineptitude, lack of conversation, and a demand for an isolated space to work undisturbed on mathematical problems. However, the 1990s ushered in a major change in films about mathematicians by abandoning obvious caricatures in favour of exploring their behaviour and psychology (cf. Frayling 2005). 6 Following a tracheotomy, Stephen Hawking spoke using a voice synthesiser, which produced slow, flat, robotic drawl. Roslynn Haynes and Raymond Haynes 196 In Lab Coats in Hollywood, David Kirby recounts how “to maintain a high level of realism, studios frequently call on science consultants to help actors portray ‘scientists’” (2011: 67). Much of this involves knowing how to act like a scientist. In the case of mathematicians, this frequently involves writing lengthy and abstruse equations with the speed and confidence of familiarity. For A Beautiful Mind, Dave Bayer served as both science consultant and ‘hand double’ for Russell Crowe (who played Nash): it was Bayer’s hand that fluidly wrote the equations in the film. For The Day the Earth Stood Still (2008), Seth Shostak wrote out the required maths equations in pencil for Keanu Reeves to trace over in chalk during filming (cf. Kirby 2011: 69-71). Even so, the film had to be speeded up to make Reeves appear more confident. Because mathematicians have no identifying workspaces or clothing, devising visually convincing locations is more difficult - hence the emphasis on writing math symbols on blackboards or whiteboards to indicate that ‘real maths’ is being done, and reproducing the language that mathematicians might actually use when discussing theories. In most cases, the jargon of science is boring and incomprehensible to non-specialists, but this is part of its purpose: it connotes ‘scientific knowledge’, which is what gives science its authority over those excluded from such knowledge and the characters who use it an aura of unique intellectual power. However, while needing to convey authenticity, filmmakers must avoid boring their audiences and thereby alienating them from the maths characters. Psychologically, mathematicians are often presented as being on the autism spectrum, a not unreasonable connection. The BBC documentary Beautiful Young Minds (2007) tracked the selection process and training of the U.K. team to compete in the 2006 International Mathematical Olympiad (IMO), as well as the actual event in Slovenia. Many of the young mathematicians featured in the film had a form of autism, which the documentary clearly linked to mathematical ability. Morgan Matthews, who directed Beautiful Young Minds, went on to direct the British fictional drama X+Y, released in the U.S. as A Brilliant Young Mind. It follows sixteen-year-old Nathan Ellis, a maths prodigy diagnosed with autism, who is being prepared to compete for a place in the IMO. Having lost his father (the only person able to communicate with him) in a car accident, Nathan is unable to relate emotionally to anyone until, at a two-week maths camp in Taiwan, he meets Chinese maths student Zhang Mei, who helps him adjust to these new surroundings and encourages him to fight through his fears. Nathan and Mei both qualify for the IMO to be held in Cambridge. However, Mei’s uncle finds her in Nathan’s room and forces her to leave the competition. Nathan now realises he loves Mei and the first question on the paper triggers memories of his father. At this pivotal moment of his mathematical career, he must decide whether to stay and pursue his dream or identify with his father and Mei. He rushes from the exam room, and his mother drives him to the station The Mathematician as Hero in Audio-Visual Media 197 to be re-united with Mei. Despite directors’ determined attempts to ‘get the science right’, A Brilliant Young Mind, and a number of similar films, capitulate to a Romantic rejection of maths and its intense intellectual demands in favour of a life attuned to nature and relationships. The plot of Pi follows a similar trajectory. Pi is a psychological thriller focussing on Max Cohen, a numbers theorist, who is obsessed with finding patterns in numbers and who suffers constantly from debilitating headaches, hallucinations, extreme paranoia and schizoid personality disorder. One day his computer, called Euclid, produces a 216-digit number and then crashes. This number is of interest to a group of Hasidic Jews, who believe it is a means to interpret the Torah as a code from God, and also to a Wall Street firm, which sees it as a means to manipulate the stock market. Despite pressure to reveal the number, Max refuses and, driven insane, destroys part of Euclid, burns the paper with the number on it and trepans himself with an improvised cranial drill to obliterate all memory of the number. Abandoning maths entirely, he sits in a park, enjoying Nature, a capitulation to Romantic values. Likewise, Good Will Hunting traces the journey of a youth with a geniuslevel IQ who, as a result of having been severely abused as a child, has been in trouble with the police and has a probationary job as a janitor at MIT. Finding a difficult maths problem left unsolved on a blackboard in a corridor, he amuses himself by solving it, covering the blackboard with complex equations. On finding the problem solved, the astonished professor is determined to discover who the unknown genius is and then to ensure he receives an education to reach his potential. Will resists this plan but agrees to see a therapist as an alternative to a gaol sentence. However, at the end of the counselling sessions, he turns down the challenging, intellectual jobs offered to him and instead drives to California, hoping to find a more fulfilling life with his former girlfriend. Similar suspicions about the limitations of a life dedicated to maths are explored in Gifted, the story of a child prodigy, Mary, whose mother, a brilliant mathematician, committed suicide as a result of the extreme stress she underwent when trying to solve one of the Millennium Prize problems. 7 Mary’s mother appointed her brother Frank as guardian of Mary, with a request to raise her daughter in a normal lifestyle. However, Mary’s mathematical gifts are discovered at primary school and there is pressure on Frank to send her to a special school. Mary’s grandmother challenges Frank’s custody and attempts to channel Mary into an academic career. The film ends in a compromise: Mary continues to live with Frank and attend school with her age peers while taking college-level courses outside school hours. 7 In 2000, the Clay Mathematics Institute of New Hampshire released seven maths problems of extreme difficulty with a reward of U.S.-$1,000,000 for each correct answer. To date only one has been solved. Roslynn Haynes and Raymond Haynes 198 While Will and Mary are fictional characters, A Beautiful Mind is closer to reality, being based on Sylvia Nasar’s biography of mathematician and Nobel Prize laureate John Forbes Nash. Nash suffered for decades from schizophrenia and hallucinations, which produced bizarre behaviour. In the film, Nash believes he has been recruited by a representative of the Defense Department to thwart a Soviet plot by looking for hidden patterns in magazines and newspapers and posting his results in a secret mailbox. The film tracks Nash’s struggles, supported by his wife, to relinquish his belief in this alternative reality, to which he is obsessively dedicated. While there is no specific link between Nash’s condition and his mathematical brilliance, the film implies that a life with more social interactions would be less prone to such hallucinations and self-destructive behaviour. Proof makes a more direct connection between mental illness and brilliance in maths. As Robert, a highly-regarded mathematician, descended into dementia before his death, his daughter Catherine, also a gifted mathematician, completed the proof of a complex equation that her father was struggling to solve. She herself is fearful that she has inherited her father’s mental illness as well as his mathematical genius. After his death, she suffers hallucinations that her father is still alive and struggles to combat both her sister’s assertion that she is mentally unsound and the university department’s disbelief that she was capable of completing the proof discovered amongst her father’s papers. However, this film ends more optimistically with the qualified hope that Catherine may eventually develop her potential as a mathematician at the University of Chicago. Notably, despite their social and psychological problems, all these characters are presented empathetically. Unlike the stereotypical mad scientist of fiction, who was portrayed objectively as either threatening or a figure of fun (cf. Haynes 2017: ch. 12 and ch. 3), viewers see the worlds from the characters’ perspectives. Indeed, until late in A Beautiful Mind, viewers likely believe in Nash’s alternative reality, while the opening scenes of Proof suggest that Catherine is actually talking to her father in real life. Only later do viewers learn that he has already died. c) Avoiding the ‘Information Dump’ Film-makers face a major problem when trying to introduce scientific concepts and technical information while, at the same time, maintaining audience engagement. The most direct and concise means of disseminating information is the lecture, but artistically this is the most dangerous form in terms of retaining audience interest and is rarely used in fiction films. However, this approach is the flagship of TED talks, where experts, including mathematicians, speak passionately about their subjects. The very successful format of TED talks includes a large initial injection of humour, visuals, immense enthusiasm expressed through the voice and manner of The Mathematician as Hero in Audio-Visual Media 199 the lecturers, personal accounts of the excitement of breakthrough moments, absence of jargon and an explanation of why this research matters for individuals and society. French mathematician and Fields medallist Cédric Villani gave a model TED talk with the provocative title “What’s So Sexy about Mathematics? ” With a hair style reminiscent of the Romantic poets, a flowing cravat, and outsized jewelled spider brooch, his flamboyant appearance aroused immediate attention, but his mission was to inspire his audience with the beauty, usefulness, and truth of maths: “Math is exciting because it is about reasoning; it is about imagination; and it is about finding the truth” (Villani 2016). He insists, however, that “beautiful mathematical explanations are not only for our pleasure” (Villani 2016); they are also eminently useful. Using a Galton board, he demonstrates the universality of the bell-shaped Gauss curve for numerous everyday events: choosing the most important eye-witnesses to an event, selecting the most relevant Google pages to consult for research, proving that our world is composed of atoms, and much more. He also includes an account of his personal frustration at not being able to solve a problem in plasma physics. Having worked late into the night with no success, he fell asleep and woke with a voice in his head telling him the steps which would establish the missing part of the proof. However, instead of attributing this ‘voice’ to intuition or to a mysterious revelation (as Ramanujan does in The Man Who Knew Infinity; see below), Villani ascribes it to reason - his brain continuing to work on the problem during sleep. Other TED talks illustrate scientific concepts by analogy with everyday events, for example demonstrating the relevance of maths to basketball, love, the stock market, infinity, and discovery (see, for example, Maheswaran 2015, Antonsen 2015, and Woo 2019). These lecturers successfully model a way to make maths interesting and relevant, using examples that appeal to general interest, analogy, visuals, and humour, while exuding a passion for presenting the relevance of maths in everyday situations. TED talks are designed for a self-selected audience already interested in the subject. In a fiction film, on the other hand, lectures of more than a few minutes are considered sudden death to audience engagement. When they do occur, they are compressed and used for a purpose other than to disseminate information: to indicate the character of the lecturer, the response of the audience, antagonism between the lecturer and a member of the audience, or acclaim for the speaker. The same is true for lengthy soliloquies by an individual mathematician and exchanges, however dramatic, between mathematicians. One of the more prominent exceptions are the ‘lectures’ that Sheldon gives in The Big Bang Theory. They are rambling, boring, and usually irrelevant but succeed in the context of the sitcom just because their inappropriateness or other characters’ inability to see their relevance is comic. For example, in the episode “The Tangerine Factor” (2008), Sheldon attempts to explain to their neighbour Penny Schrödinger’s hypothetical proposition Roslynn Haynes and Raymond Haynes 200 that a cat locked in a box with a vial of poison which might explode at any (unknown) time would, until the box is opened, be theoretically both alive and dead. 8 Understandably, Penny cannot see any relevance to her question as to whether or not she should go out with Leonard. In the episode “The Gorilla Experiment” (2009), Sheldon reluctantly agrees to teach Penny “a little physics” to impress Leonard (Lorre et al. 2009a). Beginning with the Greek word ‘physika’, he threatens to meander through the twentysix-hundred-year history of physics, from ancient Greece to what Leonard is researching, without clarifying anything about the subject. However, Penny does memorise several impressive sentences and unfortunately blurts out Sheldon’s opinion that Leonard’s experiment “is qualitatively no different than the experiment already conducted in the Netherlands[, which has] already conclusively demonstrated the electric analogue of the Aharonov-Bohm quantum interference effect” (Lorre et al. 2009a). For all their exaggerated nerdiness and oblivion to social cues, a modern version of the stupid virtuoso of the Restoration stage and the absentminded professor of twentieth-century comic films such as ‘Doc’ Brown of the Back to the Future movies (1985-1990) and Professor Kelp/ Klump of the Nutty Professor movies (1963, 1996, 2000), 9 the characters of The Big Bang Theory do deliver a surprising amount of up-to-the-moment scientific discoveries, disguised and made audience-friendly through comedy. They debate problems in physics and maths, presenting actual theories and models on their whiteboards, and some episodes incorporated appearances by real scientists who were fans of the series, including Stephen Hawking and astrophysicists George Smoot and Neil deGrasse Tyson. d) The Effects of Social Discrimination on the Lives of Mathematicians Where the scientist is the main character of a film, other interests, usually unrelated to science, are introduced to ‘dilute’ the technical aspects and create a sense of a life outside maths. Like the mythical heroes, these protagonists, whether real or fictional, are almost always presented as being discriminated against on the grounds of some personal or societal issue, which they must overcome in order to succeed in their quest: race, gender, class, religion, physical disability, sexual orientation, and/ or family obligations. Ramanujan, the gifted Indian mathematician of The Man Who Knew Infinity, arrives in Cambridge, where he confronts not only the inimical climate and a meat-based culinary culture abhorrent to his Hindu regimen, but prejudice against his colour, race, religion, and culture, as well as the pressures and expectations of his mother and wife in India. The extreme 8 Schrödinger’s Cat is a recurring topic in The Big Bang Theory, also featured in “The Codpiece Topology” (2008) and “The Russian Rocket Reaction” (2011). 9 For an analysis of the stupid virtuoso, see Haynes (2017: 41-54). The Mathematician as Hero in Audio-Visual Media 201 contrast between G.H. Hardy, doyen of Cambridge mathematicians, and his Indian protégé is exemplified in their opposite assumptions about deriving solutions to maths problems. For Hardy, proofs are validated only by a chain of algebraic equations; Ramanujan, on the other hand, is convinced that he ‘knows’ a solution because the goddess Lashki has written it on his tongue. During World War I, he is attacked by English soldiers who deride him for failing to enlist, and Hardy’s attempts to have him accepted as a member of the Royal Society are at first rejected on grounds of race. The three African American women on whom the biographical film Hidden Figures centreswere gifted mathematicians who worked at NASA during the Space Race of the 1960s. 10 As the film emphasises, their contributions were crucial to the launching of astronaut John Glenn into orbit. But it is their struggle against gender, class, and racial discrimination (Illustration 2), rather than the maths solutions they produce, that sustains the drama (and sometimes humour) of the film and makes their eventual recognition meaningful for the audience. Illustration 2. While Katherine Johnson repeatedly solves complex mathematical problems, her and her fellow African American scientists’ struggles against racism and misogyny drive the plot. Screenshots from Hidden Figures © Twentieth Century Fox, 2016. The Imitation Game is based on the biography of Alan Turing, the cryptanalyst who designed a machine to decipher the Enigma code messages used by German Intelligence during the Second World War, thereby providing the British with prior knowledge of planned Nazi attacks. However, the main focus of the film is not the maths involved or even the suspense about cracking the Enigma code, but Turing’s difficult and reserved personality, the hostile interactions between members of the code-breaker team at 10 Katherine Johnson was a mathematician who calculated the flight trajectories for Project Mercury and other NASA missions; Dorothy Vaughan was a NASA supervisor and mathematician; and Mary Jackson was an engineer. Roslynn Haynes and Raymond Haynes 202 Bletchley Park, the revelation of Turing’s homosexuality, the social consequences of this, and the threats to his personal liberty at a time when homosexuality was a criminal offence in Britain. 11 In A Beautiful Mind, the focus is on the torment arising from Nash’s paranoid schizophrenia, delusions and hallucinations, the strain on his family, and his eventual triumph over his disability. Good Will Hunting explores class differences and the progressive revelations through psychoanalysis of both Will and his therapist. Gifted revolves around the battle between the diverse expectations of Mary’s uncle and her grandmother for her education and, by implication, a debate about what constitutes the good life. In A Brief History of Time, although Hawking contrives to deliver his theories of the universe, presented through creative graphics, the main interest of the film for general audiences is Hawking’s way of dealing with the onset of motor neuron disease, his immobility, and his dependence on computergenerated speech alongside commentary from family, friends, and colleagues. e) Motivations, Obsessions, and Moral Struggles of Mathematicians For actors to appear realistic as mathematicians, they need to do more than speak and act credibly in the role. They need to express the level of motivation required to spend years of frustration pursuing a theoretical problem, often to the detriment of personal relationships. That motivation is an intense desire to understand how the universe ‘works’, how all the diverse phenomena that we observe and experience can be reduced to the elegant, non-negotiable terms of an equation that gathers chaos into order. In Cédric Villani’s words, “Hidden truths permeate our world; they’re inaccessible to our senses, but math allows us to go beyond our intuition to uncover their mysteries” (2016). It is the possibility of discovering these laws governing the universe that drives mathematicians, and film directors and actors need to understand and express this. Ironically, the sub-plots that are introduced to make a film more entertaining for an audience often detract from this central purpose. In A Beautiful Mind, Nash’s fascination with number theory is subsumed in his delusion that his activities are helping to combat an espionage ring. It is his colleagues who see the far-reaching significance of his real contribution to maths and games theory. In The Imitation Game, a similar short-term aim, to further the war effort, obscures references to Turing’s more enduring work in artificial intelligence. In The Man Who Knew Infinity, Ramanujan’s initial fascination with maths problems, while still a clerk in India, is wellportrayed by implication. It drives him to overcome the many barriers to his departure for Cambridge: his mother’s religious prohibitions, his wife’s distress, the poverty they will endure without his income, the culture shock 11 Turing was given a posthumous royal pardon by Queen Elizabeth II in 2013. The Mathematician as Hero in Audio-Visual Media 203 of arriving in an indifferent environment with incompatible expectations, and mores. However, once in Cambridge, it seems that the driving force is to conform to Hardy’s requirements rather than the joy of maths itself. In Proof, it appears that Catherine’s dedication to her father and the wish to complete the proof that he himself is no longer able to derive are her motivation, rather than her own engagement with the subject. Unlike physicists and chemists, who have been implicated in the development of destructive weapons and deleterious substances, mathematicians have enjoyed a relatively benign reputation because their work seems to be of no immediate practical importance and hence no threat to society or individuals. This view is challenged in the first season of the American docudrama Genius (2017), which traces Albert Einstein’s life from his early years as a struggling patent clerk to his status as an internationally renowned theoretical physicist, whose mathematical work was the basis for the development of atomic weapons. His life is presented as a series of conflicting obligations beginning with his stormy relationship with a brilliant fellow student, Mileva Marić, whom he marries but who continues to resent the fact that her own potential career is halted in deference to his. Their poverty while Albert pursues his theories of relativity is alleviated when he secures an academic position, but his marriage is again threatened by the growing appreciation of his work by luminaries such as Marie Curie, leaving Mileva housebound with the children. He then has an affair with his cousin Elsa, who demands that he divorce his wife. With the increasing Nazi offensive, he is under pressure to assist his fellow Jews, even while his academic colleagues press him to join the German war effort. Fleeing to the United States, he still tries to save German Jews from the holocaust. When the atomic bomb is dropped on Hiroshima, ending World War II, Einstein, a life-long pacifist, suffers intense guilt for his role in urging President Franklin D. Roosevelt to develop the atomic bomb and spends the rest of his life trying to halt the Cold War. 12 In a lecture to students at Caltech, he said that science was often inclined to do more harm than good (Isaacson 2007: 374). Genius is one of the very few audio-visual examples that engages with the conflicting roles and allegiances of a scientist - intellectual, personal, political, and religious. It suggests that Einstein’s multi-faceted work came at the cost of other obligations. Two fictional films also deal with ethical struggles of mathematicians. One is the intellectual thriller Travelling Salesman (2012), in which four mathematicians are hired by the U.S. government to solve the elusive P versus NP problem, potentially the most powerful tool in computer science. 12 Einstein and other American scientists believed that Nazi Germany was further advanced towards developing atomic bombs than was actually the case. Later Einstein said that, believing this, he had had no other option than to support the development of atomic bombs, but that it was, according to Linus Pauling’s diary, his “one great mistake” (Livio 2013: 233). Roslynn Haynes and Raymond Haynes 204 If solved, it could break through encryption protection and permit hackers to access bank accounts, personal correspondence, and government secrets and annihilate enemies. A Department of Defense official offers them U.S.- $10 million for the algorithm, but one mathematician rejects the offer and is forced to reveal a dark truth about his portion of the solution. They must all struggle with the ethical consequences of what had formerly seemed an intellectual game. In the Spanish psycho-thriller Fermat’s Room (2007), four mathematicians, one a woman, assuming the names of famous dead mathematicians (Pascal, Galois, Hilbert and sixteenth-century philosopher Oliva Sabuco), are lured to a warehouse at the invitation of a person who calls himself Fermat. Here, they are required to answer maths problems within a limited period. Each time they exceed the deadline, the walls move inward, threatening to crush them. As they try to discover which of them is responsible, they finally realise that their mutual hostility over who solved Fermat’s Last Theorem is of no consequence. ‘Pascal’ scatters the pages of ‘Hilbert’s proof’ in the river because “the world is the same with or without the proof” (Piedrahita & Sopeña 2007). f) The Use of Audio-Visual Media by Real-Life Mathematicians We have noted already the very different styles that Simon Singh, Stephen Hawking, and Cédric Villani have used in audio-visual media to educate a non-specialist public about maths. Other examples developed to popularise maths to a wider audience include three documentaries presented by Marcus du Sautoy, Professor of Mathematics at Oxford: The Story of Maths (2008) narrates seminal moments and people in the history of mathematical thought and how it affects the world today; The Secret Rules of Modern Living: Algorithms (2015) deals with the question of what algorithms are, how they work, and how we are unsuspectingly relying on them every day; and The Code (2011) explores the mathematical code underlying all life on Earth and the universe itself, governing everything from lunar eclipses to criminal behaviour. These three documentaries follow a similar pattern - an historical account of the development of maths, centring on specific moments and people, some familiar to a general audience, and a liberal number of references to contemporary practices and experiences to emphasise the necessity of maths to our understanding of the world. Other notable documentaries concentrate on aesthetic and philosophical implications of maths. Fractals: The Colours of Infinity (1995), presented by Arthur C. Clarke, covers the discovery of the Mandelbrot Set and its significance for maths, exploring the beauty of the ubiquitous fractals and the new ideas that have emerged from Mandelbrot’s elegant equation. In The Great Math Mystery (2015), astrophysicist Mario Livio investigates whether maths is human-made or a natural part of the universe. The signature of maths is everywhere from the whirlpool of a galaxy to the spiral The Mathematician as Hero in Audio-Visual Media 205 at the centre of a sunflower, to the swirl of a nautilus shell. Maths is also essential for radio transmissions, successful landings on Mars, and the prediction of the Higgs boson. This raises the unresolved philosophical question of whether mathematics is invention or discovery, or both. Conclusion The period from the 1990s to the present has seen an unprecedented number of films, documentaries, and YouTube talks featuring maths and mathematicians. The earlier, longstanding stereotype of the mathematician as a colourless and socially awkward introvert, lacking interest in, or from, nonmathematicians, might appear to have been superseded, insofar as mathematicians have become the main characters of a significant number of films, documentaries, and even sitcoms. Indeed, our survey suggests that film directors now see the potential for presenting mathematicians as interesting characters, who are not necessarily figures of fun, but rather rounded characters with interesting personae. Their psychological and social problems, so far from reducing them to ridicule, are presented empathically, and become a necessary part of their heroic role in overcoming them. Nevertheless, in many of the cases discussed above, mathematicians are still portrayed as socially introverted because they are confronted with schizophrenia, mental illness, or autistic spectrum disorder (as in the case of A Beautiful Mind, Proof, X+Y and Beautiful Young Minds), or are so obsessively involved in their intellectual quest that they have no time or wish to engage in social events. However, instead of being treated dismissively, these characteristics are now presented as a major interest, not only of the characters themselves, but also in the impact they have on the family or friends of the mathematician (A Beautiful Mind, Gifted). The logistical problems involved in balancing a realistic presentation of obscure mathematical information with a credible private life, while entertaining a lay audience and securing adequate box-office success are considerable. It is therefore not surprising that most directors have veered towards presenting these characters as involved in personal, even heroic, quests. Exploring the social and human struggles over which mathematicians must triumph to succeed in their passionate quest indicates to a wider public the extent to which maths matters. For real-life mathematicians, however, there can be a danger in becoming too popular in audio-visual media. As well as appearing in The Big Bang Theory and Star Trek, 13 Stephen Hawking, at his own request, made four 13 In the Star Trek: The Next Generation episode “Descent” (season 6, episode 26; 1993), Data plays a game of poker with holograms of Newton, Einstein, and Hawking, who plays himself. Roslynn Haynes and Raymond Haynes 206 guest appearances in the high-rating, American animated series The Simpsons (1989-), of which he was an enthusiastic fan. Beginning with the episode “They Saved Lisa’s Brain” (1999), in which he delivers the memorable line, “Your theory of a doughnut-shaped universe intrigues me, Homer. I may have to steal it” (Groening, Brooks & Simon 1999), he later made three more appearances, 14 which he apparently enjoyed, but later regretted for the surprising reason that “[p]eople think I’m a Simpsons character” (Hawking & Cox 2010). Ironically, this brilliant physicist was quoted as feeling that he was “sometimes not properly recognised for his contribution to our understanding of the universe” (Hutchison 2010), a statement corroborated by Sherman Young, who has noted that most people know Hawking from his appearances in The Simpsons, rather than from anything he has written (2007: 12). It would seem that in appearing too ‘human’ and too ‘ordinary’, mathematicians may lose that mystique and power arising from their unique knowledge that has set scientists apart from the time of the alchemists (cf. Haynes 2003). Bibliography Antonsen, Roger (2016). Math Is the Hidden Secret to Understanding the World. [Video Clip]. TED. 18 Nov. https: / / www.ted.com/ talks/ roger_antonsen_math _is_the_hidden_secret_to_understanding_the_world. [Aug. 2022]. Briggs, David (dir.) (2015). The Secret Rules of Modern Living: Algorithms. [Film]. London: BBC. Brown, Matt (dir.) (2015). The Man Who Knew Infinity. [Film]. Burbank, CA: Warner Bros. Cooter, Stephen & Michael Lachmann (dirs.) (2011). The Code. [Television Mini- Series]. London: BBC. du Sautoy, Marcus (writ.) (2008). The Story of Maths. [Television Mini-Series]. London: BBC. Falk, Dan (2018). A Brief History of Time Changed Our Perception of Physics, and Science. Slate. 14 Mar. https: / / slate.com/ technology/ 2018/ 03/ how-a-brief-history-of-time-changed-our-perception-of-physics-and-science.html. [Jul. 20-22]. Farzin, Sina et al. (eds.) (2021). Under the Literary Microscope: Science and Society in Contemporary Fiction. University Park: Penn State UP. Frayling, Christopher (2005). Mad, Bad and Dangerous. London: Reaktion. Hawking, Stephen & Brian Cox (2010). Gods of Science: Stephen Hawking and Brian Cox Discuss Mind Over Matter. The Guardian. 10 Sept. https: / / www.theguardian.com/ science/ 2010/ sep/ 11/ science-stephen-hawking-briancox. [Aug. 2022]. Haynes, Roslynn (2017). From Madman to Crime Fighter: The Scientist in Western Culture. Baltimore, MD: Johns Hopkins UP. Haynes, Roslynn (2003). From Alchemy to Artificial Intelligence: Stereotypes of the Scientist in Western Literature. Public Understanding of Science 12 (3). 243-253. 14 “Don’t Fear the Roofer” (season 16, episode 16; 2005), “Stop or my Dog Will Shoot” (season 18, episode 20; 2007), and “Elementary School Musical” (season 22, episode 1; 2010). The Mathematician as Hero in Audio-Visual Media 207 Howard, Ron (dir.) (2001). A Beautiful Mind. [Film]. Universal City, CA: Universal Pictures. Hutchison, Peter (2010). Stephen Hawking ‘Mistaken for a Simpsons Character’. The Telegraph. 10 Sept. https: / / www.telegraph.co.uk/ news/ science/ stephen-hawking/ 7995554/ Stephen-Hawking-mistaken-for-a-Simpsons-character.html. [Aug. 2022]. Isaacson, Walter (2007). Einstein: His Life and Universe. New York: Simon and Schuster. Kirby, David (2011). Lab Coats in Hollywood: Science, Scientists and Cinema. Cambridge, MA: MIT P. Lanzone, Timothy (dir.) (2012). Travelling Salesman. [Film]. Philadelphia, PA: Fretboard Pictures. Lesmoir-Gordon, Nigel (dir.) (1994). Fractals: The Colours of Infinity. [Film]. Bedford: Gordon Films. List of Mathematicians in Film (2022). Wikipedia. 21 Jun. https: / / en.wikipedia.org/ wiki/ List_of_films_about_mathematicians. [Aug. 2022]. Livio, Mario (2013). Brilliant Blunders from Darwin to Einstein: Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe. New York: Simon and Schuster. Lorre, Chuck et al. (writ.) (2012). The Hawking Excitation. The Big Bang Theory. [Television Series]. Season 5, Episode 21. New York: CBS. Lorre, Chuck et al. (writ.) (2009a). The Gorilla Experiment. The Big Bang Theory. [Television Series]. Season 3, Episode 10. New York: CBS. Lorre, Chuck et al. (writ.) (2009b). The Pirate Solution. The Big Bang Theory. [Television Series]. Season 3, Episode 4. New York: CBS. Lorre, Chuck et al. (writ.) (2008). The Tangerine Factor. The Big Bang Theory. [Television Series]. Season 1, Episode 17. New York: CBS. Maheswaran, Rajiv (2015). The Math Behind Basketball’s Wildest Moves. [Video Clip]. TED. 6 July. https: / / www.ted.com/ talks/ rajiv_maheswaran_the_math_behind_basketball_s_wildest_moves. [Aug. 2022]. Manin, Yuri Ivanovic & Alexei A. Panchishkin (2005). Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories. Berlin: Springer. Matthews, Morgan (dir.) (2014). X+Y. [Film]. Höfen: Koch Media. Matthews, Morgan (dir.) (2007). Beautiful Young Minds. [Film]. London: BBC. Melfi, Theodore (dir.) (2016). Hidden Figures. [Film]. Century City, CA: Twentieth Century Fox. Morris, Errol (dir.) (1991). A Brief History of Time. [Film]. Camarillo, CA: Triton Films. Piedrahita, Luis & Rodrigo Sopeña (dirs.) (2007). Fermat’s Room. [Film]. London: Revolver Entertainment. Pink, Noah et al. (writ.) (2017). Genius: Einstein. [Television Series]. New York: National Geographic. Singh, Simon (n.d.). Fermat’s Last Theorem: The TV Documentary. Simon Singh’s Website. https: / / simonsingh.net/ books/ fermats-last-theorem/ fermats-last-theorem-the-tv-documentary/ . [Aug. 2022]. Singh, Simon (dir.) (1996). Fermat’s Last Theorem. Horizon. [Television Series]. Season 32, Episode 9. London: BBC. Van Sant, Gus (dir.) (1997). Good Will Hunting. [Film]. Los Angeles, CA: Miramax. Villani, Cédric (2016). What’s So Sexy about Math? [Video Clip]. TED. 6 Jun. https: / / www.ted.com/ talks/ cedric_villani_what_s_so_sexy_about_math. [Aug. 2022]. Roslynn Haynes and Raymond Haynes 208 Woo, Eddie (2019). How Math Is Our Real Sixth Sense. [Video Clip]. TED. 24 Jul. https: / / www.ted.com/ talks/ eddie_woo_how_math_is_our_real_sixth_sense. [Aug. 2022]. Young, Sherman (2007). The Book is Dead: Long Live the Book. Sydney: U of New South Wales P. Roslynn Haynes University of New South Wales Raymond Haynes Astronomical Society of Australia