Mathematics in movies

Summary: Mathematics and mathematicians often appear in movies, helping to shape the public’s image of mathematics

Mathematics has been showcased in a number of movies. Often, the lives of mathematicians, both real and fictional, have been dramatized for use in film. Mathematics in movies can reveal, reflect, and shape how society views mathematics. Images of nerds and geniuses are very common in movies, and the mathematical powers of geniuses are sometimes equated with mental illness. There are also examples in which talented women deny their mathematical ability. Some of the films that focus heavily on the lives of mathematicians include A Beautiful Mind (2001), Good Will Hunting (1997), Pi (1998), Proof (2005), I.Q. (1994), Infinity (1996), and Agora (2009). Other movies, such as 21 (2008), Contact (1997), Cube (1997), Jurassic Park (1993), Fermat’s Room (2007), and Mean Girls (2004), use mathematics as the basis of key plot points. Some films, such as Stand and Deliver (1988), dramatize the teaching of mathematics. There are also numerous documentaries, including n is a Number: A Portrait of Paul Erdös (1993) and Julia Robinson and Hilbert’s Tenth Problem (2008). Such films are often the public’s only connection to mathematics. As such, it important to point out how accurately these films communicate these ideas.

Mathematics and Character Development

A Beautiful Mind is a 2001 film directed by Ron Howard based on the life of Nobel Prize–winner John Nash. The film chronicles the life of Nash (Russell Crowe) beginning with his graduate studies at Princeton. While there, Nash discovers the principle of governing dynamics, a central principle in game theory and modern economics. The film simplifies the principle by showing an attractive blonde woman and her four friends entering a bar. If Nash’s friends all flirt with the blonde, they impede each other. Further, her friends will also spurn the would-be suitors, as they do not want to be the second choice. Hence, the best strategy for Nash’s friends is to avoid the blonde and instead approach her friends. The film later shows Nash’s romance with Alicia Larde (Jennifer Connelly) and his problems because of schizophrenia. The film omits many details of Nash’s life, including both his previous marriage and his divorce from and later remarriage to Alicia. Nonetheless, the film received four Academy Awards, including Best Picture and Best Director.

Good Will Hunting is a 1997 film directed by Gus Van Sant starring Matt Damon and Robin Williams. In this film, Will Hunting (Damon) is a janitor working at MIT. One night, he solves a difficult mathematics problem left on a chalkboard in the hall. When none of the students admit to solving the problem, Professor Lambeau (Stellan Skarsgard) places a second problem on the chalkboard, which Will promptly solves. Unfortunately, Will is plagued by antisocial behavior, causing him to be arrested after a fight in a bar. Lambeau has Will released into his custody provided that Will works with him on mathematics and Will sees a therapist (Williams). While the film does present what appear to be well-posed problems in graph theory and combinatorics, it is unlikely the solution to such difficult problems could be placed on a single chalkboard in a short amount of time. The film won two Academy Awards.

The 1998 film Pi was directed by Darren Aronofsky. In Pi, Max Cohen (Sean Gullette) is a number theorist who believes in three basic principles: mathematics is the language of the universe; the universe can be understood through numbers; and if one graphs these numbers correctly, patterns will emerge. In particular, he studies the stock market looking for patterns. If one were able to find patterns in the stock market, one could accurately predict the future. After a conversation with Lenny Meyer (Ben Shenkman) a Hasidic Jew, Cohen begins to do research on the numbers in the Torah. Meyer tells Cohen that the Torah is composed entirely of numbers, and there are relationships between the numbers. Thus, Cohen searches for a pattern in the Torah in the hope of revealing the true name of God. There has been mathematical research on finding patterns to the stock market. However, the level presented in this film is impractical. For instance, there are literally thousands of variables involved in the stock market. A slight change in any of these variables can lead to a large change in the market.

The 2005 movie Proof was directed by John Madden, based on the play by David Auburn. In Proof, Gweneth Paltrow plays Catherine, a woman who has been looking after her father (Anthony Hopkins). Her father was a brilliant mathematician who later became incapacitated because of mental illness. During this time, he wrote numerous notebooks full of his delusional ramblings. After his death, his former student Hal (Jake Gyllenhaal) finds one of these notebooks containing what appears to be an important result. While Catherine claims the result is hers, some question both her authorship and her sanity. Catherine’s father seems based in part on real life mathematician Kurt Gödel. Like her father, Gödel was an important mathematician who descended into insanity, writing endlessly. Like most research professions, it is important to establish priority. However, the film does not accurately depict suitable ways to establish priority, such as presenting at research conferences or publishing a preliminary technical report.

Romance and Mathematicians

Two films, I.Q. (1994) and Infinity (1996), focus more on the romantic sides of mathematicians lives. In I.Q., Albert Einstein (Walter Matthau) and his friends help local mechanic Ed Walters (Tim Robbins) to romance Einstein’s niece, Catherine Boyd (Meg Ryan), a doctoral candidate in mathematics. In order to accomplish this, Einstein makes it appear that Ed is a genius in physics. In typical romantic comedy fashion, Catherine falls for Ed, only to discover the deception. The film takes many liberties in portraying the personalities of Einstein and his friends. Further, the film does not discuss the science of Einstein or his colleagues.

Science and Mathematics Themes

Infinity is a 1996 film based on the books Surely You’re Joking, Mr. Feynman, and What Do You Care What Other People Think by Richard Feynman. Feynman (Matthew Broderick) was a Nobel Prize-winning physicist who worked at Los Alamos and later investigated the Challenger shuttle disaster. Like I.Q., the film does nothing to discuss Feynman’s scientific discoveries. Instead, the film focuses on the romance of Feynman and his first wife Arline (Patricia Arquette). In one of the film’s more memorable scenes, Feynman impresses Arline with his ability to do mental computations faster than a shop owner with an abacus. Such anecdotes form the cornerstones of Feynman’s biographies, however, they are largely omitted in the film.

Agora is a 2009 Spanish drama that presents a semi-fictionalized account of the life of Hypatia of Alexandria. This film has elicited a variety of reactions among members of the mathematics community, including concerns about its focus on certain aspects of her personality and private life as well as her mathematical investigations and achievements.

The 2008 film 21 is based on the book Bringing Down the House by Ben Mezrich. In this film, Ben Campbell (Jim Sturgess) and the mathematics club (Kate Bosworth, et al.) are coached by Professor Micky Rosa (Kevin Spacey) to count cards in blackjack. Using simple counting techniques and signals, they act as a team to bring in the big player when the deck begins to favor the player. By doing so, they are able to bring in much greater returns than an individual counting cards on their own. Unfortunately, their success is hampered by a security chief (Lawrence Fishburne) who begins to realize their system.

Jurassic Park is a 1993 movie directed by Steven Spielberg starring Sam Neill, Laura Dern, Jeff Goldblum, and Richard Attenborough. Jurassic Park was constructed by John Hammond (Attenborough) to feature genetically recreated dinosaurs. To gain support for the park, he recruits paleontologists (Neill and Dern) as well as mathematician Ian Malcolm (Goldblum). Malcolm specializes in chaos theory, preferring to be called a “chaotician.” Chaos theory deals with unpredictability in a complex system. The film accurately illustrates this phenomenon with an experiment involving placing drops of water on the back of a still hand. Despite the best attempts to achieve predictable results by placing the drops of water at the same place, subtle differences on the hand will cause the drops to roll off in different places. Malcolm argues that, despite the best intentions of the engineers and geneticists, Hammond and his associates do not have control of Jurassic Park. For instance, they do not predict the actions of a saboteur or that the dinosaurs would begin to breed. These oversights lead to the failure of the park. Jeff Goldblum returns as Ian Malcolm in the 1997 sequel The Lost World: Jurassic Park.

Prime Numbers

The search for extraterrestrial intelligence is the basis of the 1997 film Contact, based on the book by Carl Sagan. In this film, Dr. Eleanor Arroway (Jodie Foster) discovers a signal that appears to be from the star Vega using the telescope array in New Mexico. The signal consists of a long string of prime numbers. Prime numbers are positive numbers divisible only by themselves and the number 1. Moreover, the prime numbers are not associated with any random natural phenomenon. Hence, the broadcast of the primes from an extraterrestrial source suggests the work of an alien intelligence. As various layers of the message are decoded, her team discovers the plans for a machine that will hopefully transport one individual to meet these aliens. The film won the Hugo Award for Best Dramatic Presentation.

The 1997 psychological thriller Cube also uses prime numbers as a key plot point. In Cube, a group of five individuals (Nicole de Boer, David Hewlett, et al.) find themselves in a cube-shaped room. The room they are in is surrounded on all six sides by other cube-shaped rooms. They quickly discover that many of the rooms contain deadly traps. One of the group is a mathematician and realizes that if the rooms are labeled with prime numbers, then the room is trapped. They also discover that the numbers give the position of the room within the larger cube structure. Finding an autistic savant in the maze allows them to factor the numbers more quickly and thus navigate the cube structure.

The 2007 Spanish film Fermat’s Room uses a famous conjecture about prime numbers as a catalyst. The Goldbach Conjecture states that every even number greater than two can be expressed as the sum of two primes. Despite being conjectured in 1742, this problem has remained unsolved as of 2010. A young mathematician known only as “Galois” claims that he has a proof of the Goldbach Conjecture to impress a young woman called Olivia. They are soon invited to dinner by the enigmatic Fermat along with a middle-aged mathematician, Pascal, and an older mathematician, Hilbert. Coincidently, Hilbert has been working on Goldbach for 30 years. When their host, Fermat, leaves, they soon find themselves locked in the room. They are presented with riddles one after another. If they are unable to solve the riddles within their time limit, the walls of the room close in until they solve the riddle. While the names of the characters are based on famous mathematicians and the Goldbach Conjecture is presented accurately, the riddles in the film are quite elementary.

Social Life and Mathematics

In the 2004 movie Mean Girls, the main character, high school student Cady Heron, struggles to balance her mathematical talent with social pressures and attempts to be popular. She pretends to struggle at mathematics in her calculus class in order to impress a boy she likes.

Finally, the 1988 movie Stand and Deliver illustrates the difficulty of teaching mathematics in an inner-city school. Jaime Escalante (Edward James Olmos) teaches basic arithmetic in a Los Angeles high school. He senses that his students are capable of more, and using props, humor, and examples from their lives, he motivates them to learn calculus. At the end of their senior year, his students all pass the AP calculus exam.

Some producers hire mathematical consultants to ensure the accuracy of the content. It is likely that mathematics and mathematicians, both real and fictional, will continue to remain sources of dramatic material in feature films. Mathematicians also analyze these representations in the classroom and in publications, such as the media column in the Association for Women in Mathematics Newsletter.

Bibliography

Farley, Jonathan. “Moment of Proof.” Notices of the American Mathematical Society 53, no. 3 (2006).

Greenwald, Sarah J., and Jill E. Thomley. “Mathematically Talented Women in Film and Television.” Association for Women in Mathematics Newsletter 38, no. 1 (2009).

Polster, B., and M. Ross. “Mathematics Goes to the Movies.” http://www.qedcat.com/moviemath/index.html.

Reinhold, Arnold. “Math in the Movies.” Math Horizons 4 (April 1997).