Beautiful Mathematics In Movies

Almost every math teachers love using movie clips about math in their classrooms to enhance content and engage their students. This listing is a sample of the types of movies that math people found useful.

The movie is fantastic and quite good mathematically. It is a bit like the play by the Swiss writer Friedrich Dürrenmatt who wrote Die Physiker similarly discussing scientific ethics questions. A mysterious bodyguard is listening to all of the conversations (which is a bit strange, given that everything is so top secret). In Dürrenmatts’ play, there is a psychiatrist Mathilde von Zahnd who eavesdrops on the conversation. In the Travelling Salesman movie, there is also a bit of cold war atmosphere, similarly as in the 1962 play of Duerrenmatt, when NATO and WTO were the players.

A detail: Stephen Cook and Leonid Levin formulated the P=NP problem. The mathematicians Michael Garey and David S Johnson were mentioned, who worked on the Traveling Salesman Problem and wrote Computers and intractability.

A simple insurance equation is appearing in the movie “Fight Club”, which is probably on everybody’s list of top 100 films. Brad Pitt and Edward Norton are both excellent (and forming an equivalence class of people here).

The movie “Goodwill hunting” features some beautiful problems in graph theory and linear algebra. Here is an exhibit from 2003 with a handout[PDF]. A low-resolution clip had been included in 2006 in the math in movie collection here and here. After working a bit on Bowen-Lanford zeta functions Mathtable talk [PDF], the clip was also mentioned in the paper. There are various reasons why I like these problems. First of all, it features the Bowen-Lanford Zeta function, named after Oscar Lanford III, who was my Ph.D. advisor. These Bowen-Lanford Zeta functions appeared naturally in the context of connection calculus, which is part of Quantum calculus. Indeed, and that only emerged on Block island is that the Green function values, the diagonal entries of (L-z)-1xx can be expressed than in terms of the Euler characteristic of the unit sphere in the graph. Very exciting. Here is the clip showing the two problems.

A perfect triangle appears.

This R rated movie from the creators of South Park is so over the top and full of bad taste and juvenile jokes that it is truly genius. It is quite a valuable parody as it illustrates the freedom we have to laugh about and offend national feelings, terrorism, culture, intelligence, stereotypes, politicians, or actors. There is hardly anything that is off limit in this puppet show. There is no need for a sequel as the real politics these days come very close.

There are two short math scenes in that movie. By the way, a film which is highly recommended. One knows Seann William Scott, of course from movies like American Pie (Stiffler), Oldschool (a brief scene as a farmer with the tranquilizer gun), or the MTV music awards (the spoof of the matrix is excellent, a shitload of stifles). Here, in this a bit darker but uplifting comedy, he brings great performance, similar to that of Steve Carell’s exceptional performance in Little Miss Sunshine as one associated Carell, of course, with the “Office.” The math scene which appears in “Just before I go” is a flashback. The scene is highly staged. Different kids have books from different areas (there seems to be an ancient history book on the table). The math problems are given as homework (questions 1–12) on the green board are hilariously un-imaginative.

A few simple computations and fraction computations are appearing in the classic Treasure of the Sierra Madre with Humphrey Bogard.

I wouldn’t say I like horror movies without a happy end, but there is a beautiful end scene of a rather depressing film. It does not contain math, but I believe the end is very much math inspired. It looks a bit like iterated function system generated. The closest software which does that is Apophysis.

This is a bit of a larger resolution version of this entry in the Math in the movie collection. It is prompted by the recent discovery of a solution to the Diophantine equation x³ + y³ + z³ = 42, which is x=-80538738812075974; y=80435758145817515; z=12602123297335631; x³+y³+z³ = 42 found by Andrew Booker from the University of Bristol and Andrew Sutherland. There are still quite a few such computational challenges ahead. We don’t know an answer to x³ + y³ + z³ = k for k=114,165,390,579,627,633,732,795,906,921,975 yet. (Source). But of course, nothing is as cool as finding the answer to k=42. We have to find out what the ultimate question is.

In the movie “Avengers End Game (2019),” there is a beautiful scene about the Moebius strip. It is interesting as what is said there could all be made perfect sense. The Moebius strip can be realized as a finite abstract simplicial complex. That defines matrices for which one can look at eigenvalues. The individual simplices can be thought of as “particles.” Now, I proved once that for the matrix L, which is defined to be L(x,y)=1 if simplices x and y intersect and L(x,y)=0 else, the eigenvalues can be associated with the individual simplices. The number of positive eigenvalues minus the number of negative eigenvalues is the Euler characteristic. One can, therefore, hear the Euler characteristic. But more, one can ``hear the individual simplices or particles”. See also this blog entry.

In the movie “Ocean 8 (2018)”, one can see some 3D scanning technology. This article in 3Dprintingindustry has some scoop on the feasibility. There are various challenges: scanning an object from one side only (not from the back), printing this relatively complex necklace which has moving parts so that it does not fall apart. Having seen in a project with Liz some of the challenges for straightforward objects, even when producing scans and printing with professional printing services, it is an interesting question of how long in the future that part of the story in Ocean 8 becomes feasible. All the Ocean movies, of course, are ludicrous in their design but still fun to watch. The film shows a Makerbot Replicator Z18 3D Printer that can be seen here. But that 6500 dollar printer still produces a lot of supporting material. The movie is showing the David statue printed in “zirconium” was a fake. Even a top of the line printer can not do that as quickly. Even pro services that print with 100 times more expensive machines need manual cleaning out. Zirconium can not yet be printed as described. One can do metal or raisin.

The movie “The Time Machine” features some black and green boards with mathematical formulas.

It is a beautiful metaphor: the Rubik cube fighting back. The following scene of the Bond movie Skyfall from 2012 also features some nice Linux terminals. It looks a bit like my computer screens. There are some “htop” processing terminals and, of course, the good ol Hex editor. It is a Hacker cliche. We would all poke around in the binaries of games in the 80ies. For example, to change the dialogues appearing in the game. And then there are cool graph animations.

Catch 22 logic is a paradox coined by Joseph Heller in the 1961 novel of that name: to get out of combat duty, one has to be crazy. But whoever applies to get out of combat is not crazy, so, can not get out of combat duty.

Like in the classic Groundhog Day, there are a few people trapped in a time look. There are a few parallels to groundhog day: it is also a good comedy, decent acting, and then, there is some quantum mechanics! To get out of the time loop, Sarah takes a few EdX classes, including some quantum mechanics. She figures out that going into the wormhole with an explosive belt can bring you out of the loop. Similarly, in Groundhog Day, the time loop stuff does not make a lot of sense anyway. At least it is fun entertainment.

There are some pretty good math components in this one, like prime factorizations, “Dreisatz” (linear equations of one variable), detecting the fine structure constant or coordinates in a signal, some linear algebra like eigenvalues and eigenvectors or trivial solutions to a system of linear equations. Also, the myth that mathematical or scientific discoveries come at a young age comes up several times. There is a bit more in it.

In the Oscar-winning movie “Encounters of the Third Kind” (1977) directed by Steven Spielberg, there is some simple math appearing. First, a scene with fractions (what is 60/3 ?). The view is hilarious, notice the smile of the kid, when the train smashes the wagon. Then some numbers 104 44 30 40 36 10, which turn out to be coordinated. According to this page, the coordinates (40–36–10N, 104–44–30W) aren’t close to the Devils Tower but a farm paddock in Colorado 444 km south from the Devils Tower monument. The north latitude should have been 44–35–25N; the longitude should have been 104–42–54W.

A scene from the movie Contagion 2011 which is is much in demand these days.

The graph of a function h(t) expressing the height of a balloon is a common theme in a single variable calculus course. The movie “The Aeronauts” is a bit of a free adaptation of the record flight of James Glaisher, who in 1862 broke the world record for altitude in flight. It is a nicely told story with good action scenes. And then there are some graphs.

The Prichard Scale of Understanding Poetry is a simple formula that measures the greatness of a poem. It is a simple taxonomy. In the P-I plane of a Poem, one can measure the greatness with the formula:

Greatness = Perfection * Importance

This formula appears in the movie “Dead Poets Society” from 1989. The film won an Oscar for best screenplay in 1990.

The movie The Red Violin is remarkable for many reasons: it is a great story, nicely told, and has good violin solo parts. The story is about a mysterious red violin. It is a bit of a detective story as more and more about the history of the red violin emerges. Who will get it in the end? The monks in the Austrian alps, the Gypsy violonist girl, the representative of the Pope foundation, the professional violinist Mr Ruselsky, the Chinese investor who listened to the instrument, then possessed by Xiang Pei in Shanghai as a kid when it had been forbidden to own a violin, or the investigator played by Samuel Jackson who tracks the story for the auction house?

The classic movie Dr. Zhivago features a tiny bit of math. The scene is just a few seconds before Yuri sees Lara the first time. The sound of the Balalaika always accompanies the moments when Lara is close. The movie has grown to one of the greatest of all times. It was one of the first movies I have seen in a movie theatre (as a kid) and had been affected a lot by the scene in which Yuri would see Lara the last time falling dead onto the street without her noticing.

The Sum of Arithmetic Series Formula in All Quiet on the Western Front

In the movie “All quiet on the Western front” from 1930 (which is an adaptation of the 1929 novel by Erich Maria Remarque), there is a scene where a soldier at the front mentions the sum of arithmetic series formula. The soldier says “S = A + NL/2” and finds it beautiful.

Steven Hawking died today, on Pi day 2018. The New York times has an obituary. Here are three short clips from the movie:

The 10 problems: Unfortunately, we don’t know what the 10 problems were!

The Thesis Topic in The Theory of Everything: The lecture of Penrose.

The Idea: The idea that black holes can radiate.

In the movie “After the dark (2013),” some thought experiments are done. The entire movie deals with the concept of “value” and “purpose” as the main part of the movie runs through 3 “shelter” experiments where the participants (the class) have to make choices and decisions. The topic is exciting, but critics are right that it falls off or even nose dives towards the end. (One review put it nicely: “… appears to have been written by somebody who has spent a day browsing “philosophy” on Wikipedia and Reddit after smoking a joint.”) But the movie illustrates how shallow philosophy is without help from the hard sciences. The first part, where the film is strongest, the “infinite monkey paradox” and the “trolley paradox” thought experiments appear.

Fermat’s Room was a brilliant movie in 2007. Four mathematicians are trapped in a room where the walls slowly crush them.

Here is a short clip from the movie “Chaos Theory”.

Here are just a few short clips from the movie The man who knew infinity. They are the parts where some mathematics is involved. The opening scene shows some formulas.

A prime formula appears

A class room scene, where Ramanujan finds an explicit expression for a hyperelliptic integral.

Another classroom scene

About partitions

An asymptotic formula for partitions

In the movie Suicide Squad (2016), “Deadshot,” played by Will Smith does some trigonometry with his daughter. I think the movie is quite well done. It got torn apart a bit by critics, but it was a box office success. Thanks to Craig Smorynski for alerting that there is some math in that movie. A movie containing some math is, by definition, great. But I like it also as a nice diversion and action movie and because it has likable and often funny actors. Yes, the film is in parts a bit slow, but it is okay to write an exam on the side while watching it and unplug a bit.

Hardware has become a cult movie, featuring some Sci-Fi, AI, cyberpunk, horror elements. It is quite artistically done; the mood is set with the initial and final desert scenes in a red sky. There are some affinities to Bladerunner or Mad Max (Fury Road). There is a Mandelbrot scene in this movie, and that’s why it appears in the Math in the movie collection.

The movie features at some points crunching root permutation and a “Mersenne prime algorithm,” which makes “shadow tracking more difficult.” This movie from 2001 appears a bit ahead of its time, as Mersenne primes (while famously linked to largest known prime numbers) are not so much used in cryptology. But here is a paper from 2017 (published here) which honors this movie a bit.

A rather poetic movie. Just two short parts. One with some fluid dynamics pictures, the other about knowledge of Pain.

The Physician is a historical drama playing a party in 11 century England (London and other villages) and then, after traveling through Egypt in the town Isfahan of central Iran, which is then an intellectual hub. It tells the story of a scholar who works first as a kid in a mine, follows a traveling ``barber” to pursue study with the polymath Avicenna (Ibn Sina) played by Ben Kinsey. It shows the Islamic golden age and already some trouble appearing, mostly due to war and religion. Religion was similarly as in the west also a reason for doing science, as Mohammad told: “The scholar’s ink is holier than the martyr’s blood.” Astronomy was necessary for religious purposes and navigation. Mathematics also had sacred significance as well as for practical reasons like measurements or trade. The word ``algebra” comes from “al-jabr” restoring balance, mend broken bones, which fits into the medical theme displayed in this movie. While math does not explicitly appear, there is a scene where resonance is mentioned asn; then, there is the scene of the “music of the spheres.” Aristotle is mentioned a couple of times as he plays a vital role in medieval Islam.

The black comedy “Better off Dead (1985)” is too cartoonish for today’s taste. However, it is so much over the top and ridiculous and ludicrous that it can be considered funny again. Not because the jokes are good but because they are so predictable and over the top that it is still amusing. It is an early performance of John Cusack (who plays Lane Meyer in this movie and would perform much better later, like in the “Runaway Jury” and himself was very disappointed by how the movie came out). There is a hilarious scene in a math classroom, in which some ridiculous nonsensical homework problem comes up: the math teacher (played by Vincent Schiavelli, who is probably best known for playing the evil doctor in the James Bond movie ``tomorrow never dies”), starts as follows: “The three cardinal trapezoid hereto made orientable in our diagram, creating our geometric configurations which have no properties, but with the location.” The scene drags then on a bit too long for a comedy. In the end, students are very upset when the class is over. But they get consolidated by the fact tomorrow there is the other class and that they have to memorize pages 39 to 110. All the students (except Lane, of course, who thinks he would better be off dead) are delighted. All right!

I know that you need some words to talk. Here, reading will be perfect for you.

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