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Home , Futurama, Futurama (season 5), Popular mathematics, Simon Singh, The Simpsons, The Simpsons (franchise)

Book Review Animating Popular : “ and Their Mathematical Secrets” Reviewed by Christopher Goff

and live-action films [1], [2], [18]; the ways in which The Simpsons and Their Mathematical Secrets characters with mathematical talent are portrayed (gender, race, age, and whether or not they are hyper- Bloomsbury, USA (October 2013) intelligent) can affect audience attitudes towards US$22.85, 272 pages mathematicians [16]; including popular culture ISBN: 978-14088-353-02 references in the mathematics classroom can alleviate math anxiety and provide an access point Your nonmathematical may have asked to engage students in deep mathematical thinking you about this book. Written by Simon Singh (who [14]; new theorems can come from television shows also wrote Fermat’s Enigma [22]) and published [6]; and finally, the publishing market can support by Bloomsbury (who also published the Harry Pot- a popular work such as the book under review ter books), The Simpsons and Their Mathematical here. Secrets is wrapped in a bright yellow jacket and The Simpsons was created by (of can probably be found in your nearest bookstore. comic fame) as a set of vignettes for Ostensibly about the mathematical references one The Show on the Fox Network. Its can find in The Simpsons, the longest-running success there led to a regular spot in the Fox lineup, scripted show in television history [21], the book where it has aired since the 1989–90 television also covers [7] and the mathematical season, garnering no fewer than ten Primetime credentials of the two shows’ writers. Through for Outstanding Animated Program. the lens of these programs, Singh glimpses the The consists of nuclear plant wider arena of mathematics and popular culture, safety technician Homer and his loving blue-haired describing several interesting ways in which the en- wife, Marge; their troublemaking son, Bart; their tertainment industry and the world of mathematics academically talented daughter, Lisa; and their can interact. infant daughter, Maggie. The emerging field of mathematics and popular Still more success led Fox to ask Groening to culture lies at the interface of these two seemingly create another animated show, resulting in the 1999 disparate areas and examines how each can shape premiere of the -fiction-themed Futurama, and be shaped by the other. As examples (though by in which pizza delivery boy Fry accidentally falls no means an exhaustive list): mathematical models into a cryogenic chamber on New Year’s Eve can be used to create special effects for animated 1999 and doesn’t unfreeze until a thousand years Christopher Goff is associate of mathematics later. In the future he befriends a named at the University of the Pacific. His email address is and obtains a job as a delivery boy for a [email protected]. distant relative of his, the rather old and nerdy DOI: http://dx.doi.org/10.1090/noti1199 . Futurama aired on Fox

40 Notices of the AMS Volume 62, Number 1 for four years, after which reruns were shown a perfect number (8128), and a narcissistic number on the for four more years. (8208). Underground popularity resurrected the show Likely constrained by the fact that he was writing for four direct-to-video movies and an eventual a popular book, Singh does not describe Greenwald return to series television on Central. The and Nestler’s (or others’) prior contributions to show won two Emmys for Outstanding Animated the field in much detail, though he does mention Program—one while at Fox and the other at Comedy them again in the acknowledgments and includes Central—before coming to an end in 2013. links to their definitive websites. For the academic Both The Simpsons and Futurama are immensely audience of these Notices, however, I will continue popular, having been seen by millions of viewers. to cite references in the area of mathematics and So, any mathematical references or jokes contained popular culture when they arise during the course in their episodes are transmitted to many more of this review. people than a typical instructor of mathematics can As do many mathematics books, The Simpsons ever hope to reach. As someone interested in the and Their Mathematical Secrets begins with a Chap- ways in which popular culture and mathematics ter Zero, in which Singh outlines some of the many interact, I am thrilled that a large publisher and ways that academia has interacted with the show. a well-known author are shedding more light on of philosophy, psychology, and religion some interesting examples of the interplay of have written about how ideas in their disciplines mathematics and popular culture. arise in various plots and subplots revolving around But the professional mathematical community the Simpson family. Even President George H. W. is not Singh’s target audience. Indeed, little in this Bush famously criticized the Simpsons as antithet- book will be new to mathematicians who both ical to the wholesome all-American Waltons. The observe and critique popular culture, especially writers responded satirically (via Bart), “Hey, we’re those who are familiar with the work of scholars just like . We’re praying for an end to in this field. In particular, Dr. Sarah J. Greenwald the Depression, too” [p. 2]. and Dr. Andrew Nestler have been publishing Singh rightly shines his spotlight on some of the specifically on The Simpsons and Futurama for writers themselves and their personal mathemat- over ten years and have created and maintained ical accomplishments. Since I also refer to these extensive websites [15], [19], [12]. I too have writers, I will list them by name: J. Stewart Burns (BS, long been interested in this area, ever since mathematics, Harvard; MS, mathematics, Berkeley); I began giving conference presentations about David S. Cohen (BS, , Harvard; MS, com- mathematics and the movies in 2004. Shortly puter science, Berkeley); (BS, mathematics, thereafter, Greenwald and I coedited a special Harvard); (BS and PhD, applied mathe- issue of the journal PRIMUS [9] that focused on matics, Harvard); and Jeff Westbrook (BS, physics, mathematics and popular culture. We have had Harvard, and PhD, , Princeton). another collaboration since then [4]. Singh includes quotations in which some writers Singh interviewed Greenwald and Nestler for point out the similarities between mathematics his book, and he quotes them throughout Chap- and humor: Burns says that a mathematical puzzle ter 8. He also includes an interesting anecdote and a joke share a structure, and Cohen about how the two mathematicians were implicitly likens the task of telling a complex story in a short responsible for adding mathematical content to amount of time to solving a big logic puzzle. For an episode of The Simpsons. After Greenwald was more information about the writers, see [12], and interviewed for NPR’s Science Friday in 2005, some for possible classroom uses of their interviews, see of the writers heard the program. Intrigued that [11]. mathematicians were using material from the show In Chapter 3, titled “Homer’s Last Theorem,” in their classrooms, they invited Greenwald and Singh mentions some connections between these Nestler to Fox Studios for a table-read, a key step in writers and the story of ’s proof the process of writing any television script. After of Fermat’s Last Theorem, the topic of Singh’s the mathematicians had left, however, the writers 1997 book, Fermat’s Enigma [22]. In particular, realized that the baseball-themed episode, titled when Wiles spent a brief time at Harvard, Jean “Marge and Homer Turn a Couple Play” (2006), attended some of his lectures, and when Cohen contained no jokes of a mathematical . So was a graduate student at Berkeley, he attended they added three possible attendance numbers at a some lectures of Ken Ribet. Singh mentions these baseball game as a freeze-frame gag, that is, a joke connections while discussing a near-miss solution that goes by so quickly that in order to see it fully, to Fermat’s equation that appears as a background viewers have to record the show and pause the freeze-frame gag on ’s chalkboard playback. Unbeknownst to most of the audience, in the episode “The Wizard of Evergreen Terrace” the three numbers were a Mersenne prime (8191), (1998), namely, 398712 + 436512 = 447212. Cohen

January 2015 Notices of the AMS 41 42 Edo -ao ubr ie,tesmo h two the of sum the (i.e., “Erd˝os-Bacon number” rtrWsbokhsa r˝snme f3 as 3, of Erd˝os number an has Westbrook Writer eeterltvl o r˝sBcnnmesof Erd˝os-Bacon numbers low relatively the were cdm wr-inrClnFrhsErd˝os-Bacon Firth’s Colin Award-winner Academy ota’ s6 huhntlse ySnh Danica Singh, by listed not Though 6. Natalie is Award-winner Portman’s Academy while 7, is number book. the in mentions Singh stars Hollywood the West- me to seen, Surprising already 6. of Erd˝os-Bacon have is brook’s number measure we world As rough the mathematics. and a of Hollywood both as to used links someone’s be can numbers) tongue-in-cheek the Thus circles. prominence Hollywood suggest in number Bacon one’s one’s community, does for so mathematical proxy the one’s a to that as connectedness way used same be the In can Erd˝os 3. number of have number to Bacon happens a Westbrook and on graph, Bacon Kevin costar from the distance “Bacon his actor’s or An her is business. number” movie the of employed playfully fans is by metric similar A Cohen. does graph. coauthor Erd˝os the Paul on from is someone removed the far to how audience indicates his which Erd˝os introduces number, Singh 5, Chapter industry. In entertainment the mathe- and the community matics between connections close relatively to [5]. results algorithm general computational more new obtain a a in giving it paper acknowledged Elkies near-miss Noam this aired, after example years 37]. of [p. couple a jokes” Interestingly, function bodily those I’ve writing when been days those out cancels glorify mathematics—it to discussion—particularly of to opportunity level the the get raise Cohen we “…when As book, online. the to in generated says thrilled it was that buzz he the and read falsity, its reveal not first glance, at would, a calculators most as that mathematics knowing prank, of bit this inserted intentionally

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Graham, Ron Nestler as and such speak, others inviting to or several audiences how interested to of speaking story the tells study Singh to In 9, television. continued Chapter for writing they while that even mathematics was me terested the at Reznick Illinois. Bruce of Appar- to University minimal. belongs 3, not lowest, is the this ently that but 4, of Erd˝os-Baconnumber an Erd˝os has that himself out points Wing nesesdbtentesoiso h writers the of stories the between Interspersed in- that writers the about aspect more One Futurama lohsa r˝sBcnnme f6 Singh 6. Erd˝os-Bacon of an number has also ) eectdysae i odfortune good his shared excitedly He . n xliste o general a for them explains and h odrYears Wonder The iceeApplied Discrete 62 and h Simpsons The Number , h West The 1 In Chapter 1, Singh describes the first official stereotypically “female” approach to mathematics episode of The Simpsons to air, “” instruction (“How do numbers make you feel?”), (1990). In it, Bart writes his name on the completed Lisa disguises herself as a boy, sneaks into the aptitude test belonging to the class nerd, Martin boys’ class, and thrives so much that she ultimately Prince. Bart is thus “recognized” as gifted and receives the award for Outstanding Achievement placed into a different school, where the teacher in the Field of Mathematics. She unveils her true r 3 identity, proving that girls can do math too, at writes y = on the board and says, “…if you 3 which point Bart claims that she succeeded only determine the rate of change correctly, I think because she was acting like a boy. you will be pleasantly surprised.” All the students This episode was the first to rely heavily on except Bart solve the problem and begin to chuckle. mathematics and its instruction as the main the- The teacher works out the problem on the board matic material rather than as tangential references 2 and writes the answer dy = r dr as “r dr r,” or freeze-frame gags. In the end, the writers ex- saying, “har-de-har-har”. plicitly side-stepped the question of why girls are Unlike other examples, Singh avoids explaining underrepresented in mathematics by cutting Lisa the mathematics behind this one, other than a off mid-sentence and replacing her with Martin footnote reminding some readers how to differen- Prince playing the flute. Singh goes on to describe n tiate r with respect to r. In a 2004 article [14], similarities between and Sophie Greenwald and Nestler explain how they used Germain (1776–1831), who had to use a male pseu- this very scene as part of an assignment in a donym to obtain Lagrange’s lecture notes from first-semester course. They describe how the newly opened École Polytechnique. Greenwald it can help students review material before an also wrote about this episode, right before it aired. exam and how it can even alleviate math anxiety In an interview she and Nestler conducted with in the classroom. writer Westbrook in August 2005, he describes Greenwald and Nestler continue in the same the then-upcoming episode and how the writers paper to discuss the non- segment “Homer3” “didn’t want to toe any ideologically obvious line (1995), in which Homer enters a futuristic three- either way” [10]. So while the writers did focus dimensional world (as opposed to the presumably on the controversial debate about gender and lower-dimensional nature of the Simpson universe) mathematics, they tiptoed around it in the end. to escape an evening with his sisters-in-law. Class- Singh devotes the final four chapters to Fu- room use of this vignette, an homage to a classic turama, also created by Matt Groening. David S. episode of , can spark a variety Cohen became head writer “David X. Cohen” (the of interesting debates around two- and three- name David S. Cohen having already been taken dimensional and can initiate student when television writers became unionized) and thinking about the shape of four-dimensional space ramped the quantity and quality of jokes [14]. Singh devotes his Chapter 13 to “Homer3,” involving mathematics, physics, and computer where he explains several of the freeze-frame jokes programming, such as the regular hexagonal cross- that the writers have inserted into the background, section of Madison Cube Garden and Bender’s from statements like “P = NP” to Euler’s equation, serial number of 1729. Singh describes these in “eπi = −1.” detail, including the Ramanujan-Hardy story, and In addition to providing explanations of various even explains Möbius strips and Klein bottles, mathematical tidbits, Singh also describes other which also show up on the Futurama screen. For ways that popular culture has the potential to more about these jokes and other examples of comment on the mathematical community. The sums of cubes in the show, as well as possible character Lisa Simpson, for example, is a bright classroom uses, see [8], [11]. young girl with obvious intellectual prowess in In the last chapter, Singh describes something all disciplines, including science and mathematics. truly novel: the “Futurama Theorem.” In the However, Lisa often experiences prejudice, either episode “ of Benda” (2010), many of for being female or for being smart. The two come the characters use one of Professor Farnsworth’s together in “Girls Just Want to Have Sums” (2006), inventions, the Mind-switcher, to switch their brain which Singh focuses on in Chapter 7. This episode into another character’s body. Unfortunately, once put the issue of women and mathematics front the machine switches two minds, it will not work and center and treated it with the writers’ usual again on the same two. After several different satirical panache. In the episode, exchanges, the characters wonder how they can makes tone-deaf comments about how girls are bad get their minds back into their own bodies. at mathematics (à la Larry Summers), prompting Keeler, while trying to complete the writing of him to be replaced and the school to be split the episode, cast the problem in the language of along gender lines. Frustrated by her new teacher’s distinct transpositions and proved that in order to

January 2015 Notices of the AMS 43 guarantee a way to return everyone’s mind back [5] Noam Elkies, Rational points near curves and small to her or his original body, at most two more nonzero |x3−y2| via lattice reduction, 4th International individuals need to be included who have not Symposium, ANTS-IV (Leiden, The Netherlands, July 2000), Lecture Notes in Computer Science, Vol. 1838, previously swapped with anyone. In the episode, (Wieb Bosma, ed.), Springer, Berlin-Heidelberg, 2000, recurring characters “Sweet” Clyde Dixon and pp. 33–63. Ethan “Bubblegum” Tate (from the Globetrotter [6] Ron Evans, Lihua Huang, and Tuan Nguyen, Keeler’s Homeworld and known for their mathematical, theorem and products of distinct transpositions, The scientific, and basketball-playing talents) write American Mathematical Monthly 121 (2014), no. 2, 136– 144. Keeler’s proof of the theorem on a glowing green [7] Futurama – Series, Official Site, blackboard and explain it to the professor, who is ComedyCentral.com. in Bender’s body at the time. [8] Tom Georgoulias, Sarah J. Greenwald, and Mark Evans, Huang, and Nguyen [6] recently extended Wichterich, Futurama πk: Mathematics in the year and optimized Keeler’s original result, probably 3000, Math Horizons (April 2004). marking the first instance where a mathematical [9] Christopher D. Goff and Sarah J. Greenwald (eds.), PRIMUS Special Issue: Current Work and Future Direc- theorem created for a has entered tions in Mathematics and Popular Culture, Vol. XVII (1) the peer-reviewed world of academe. Mathemati- January–March, Taylor & Francis, 2007. cians have long been inspired by problems that [10] Sarah J. Greenwald, Girls just want to have sums, arise in other fields, but it seems surprising that The Newsletter of the Association for Women in a writing conundrum on a television show could Mathematics 36 (2006), no. 2, 22–23. [11] , Klein’s beer: Futurama comedy and writers in lead to new mathematics. Perhaps mathematicians the classroom, PRIMUS XVII (2007), no. 1, 52–66. could benefit from the world of entertainment. [12] , Dr. Sarah’s Mathematical Backgrounds of the In “The Prisoner of Benda,” Keeler’s proof was Simpsons’ Writers. mathsci2.appstate.edu/~sjg/ probably seen by 2.6 million viewers when it aired simpsonsmath/degrees.html (May 31, 2014). [23], while the paper by Evans et al. was likely seen [13] , Dr. Sarah’s Mathematical Morsels from The Simpsons & Futurama. www.mathsci.appstate.edu/~ by fewer than 16,000 [20]. Maybe those writers are sjg/SimpsonsFuturamamath/MathClub (June 3, on to something. 2014). In sum, Singh writes engaging prose explaining [14] Sarah J. Greenwald and Andrew Nestler, r dr r: interesting mathematics to a general audience. He Engaging students with significant mathematical con- also succeeds in continuing the conversation about tent from The Simpsons, PRIMUS XIV (2004), no. 1, many of the connections between the mathematical 29–39. [15] , Mathematics and Mathematicians on The world and Hollywood, such as the pedagogical Simpsons, SimpsonsMath.com, mathsci2.appstate. uses of r dr r and a 3-D Homer, raising public edu/~sjg/simpsonsmath/ (May 31, 2014). awareness of the issue of women in mathematics, [16] Sarah J. Greenwald and Jill E. Thomley, Mathe- and the creation and proof of the Futurama matically talented women in Hollywood: Fred in Angel, Theorem. These examples epitomize the exciting PRIMUS XVII (2007), no. 1, 103–116. [17] Kenneth Keeler and Jeffery Westbrook, Short en- possibilities for interplay between mathematics and codings of planar graphs and maps, Discrete Applied popular culture. Though Futurama was canceled Mathematics 58 (1995), no. 3, 239–252. (again) in 2013, we can only hope that The [18] Math in the Movies, Mathematical Association Simpsons and its writers (and Singh) will continue to of America. www.maa.org/meetings/calendar- provide the world with high-quality mathematical events/math-in-the-movies (June 4, 2014). [19] Andrew Nestler, Andrew Nestler’s Guide to entertainment. Mathematics and Mathematicians on The Simpsons. homepage.smc.edu/nestler_andrew/SimpsonsMath. References htm (May 31, 2014). [1] Timothy P. Chartier, Using the Force: in [20] Bonnie Ponce, personal communication, June 1, 2014. the classroom, Problems, Resources, and Issues in Math- (Bonnie Ponce is the editorial assistant to The American ematics Undergraduate Studies (PRIMUS) XVII (2007), Mathematical Monthly). no. 1 (January–March), 8–23. [21] The Simpsons on FOX—Official Site. www. [2] Timothy P. Chartier and Dan B. Goldman, thesimpsons.com (June 4, 2014). Mathematical movie magic, Math Horizons (April 2004). [22] Simon Singh, Fermat’s Enigma: The Epic Quest to Solve [3] David S. Cohen and Manuel Blum, On the problem of the World’s Greatest Mathematical Problem, Walker and sorting burnt pancakes, Discrete Company, New York, 1997. 61 (July 28, 1995), no. 2, 105–120. [23] Dan Snierson, ‘Futurama’ to end seven-season run [4] Leigh H. Edwards, Christopher D. Goff, Sarah J. on Sept. 4—EXCLUSIVE (April 22, 2013). insidetv.ew. Greenwald, and Jill E. Thomley, Mathematics and com/2013/04/22/futurama-not-renewed-comedy- Television, Encyclopedia of Mathematics and Society central/ (June 1, 2014). (October 2011). [I would like to thank Dr. Edwards for helpful discussions about this review from a popular culture studies perspective.]

44 Notices of the AMS Volume 62, Number 1