A Futurama Math Interview with Dr. Ken Keeler

On February 29, 2008, I was thrilled that Ken Keeler responded to my questions in writing. Ken Keeler graduated summa cum laude with a bachelor's degree in applied mathematics from Harvard University in 1983. He received his master's degree in electrical engineering from Stanford, and in 1990, he received his Ph.D. in applied math from Harvard University. The title of his doctoral thesis was Map Representations and Optimal Encoding for Image Segmentation. He also published the following article with Jeff Westbrook: Short Encodings of Planar Graphs and Maps. Discrete Appl. Math. 58 (1995), no. 3, 239--252. He worked at Bell Labs before switching careers to write for David Letterman. After moving to Hollywood he wrote for both The Simpsons and Futurama and has won Writer's Guild and Emmy Awards for his work.

Sarah: What influences led you to study applied mathematics? Did you have support from both family and society?

Ken: The main influence was my father, who was a doctor but he was as interested in mathematics as I think it's possible for a non-mathematician to be. Whenever we ate in restaurants he made it a family game to check the primality of the bill. He only got through first-year calculus, but I remember I once asked him what the sum of the first n squares was and he was able to derive the formula in a few minutes [n3/3 + n 2/2 + n/6]. What still surprises me is that he didn't do it by a geometrical argument (like the way you usually derive the sum of the first n integers) or an inductive argument [see, for example, John Graham-Cumming's Blog Post or I Like Math: Sum of the first n squares]. He assumed the formula was a cubic polynomial with unknown coefficients, then found the coefficients by solving the system of four linear equations generated by computing the first four sums of squares. (And he solved them by hand, without determinants.) When I asked him how he knew the formula would be a cubic polynomial, he said "What else would it be?"
        Other influences: of course there's Mr. Spock. Also, most of my friends in high school were interested in math and science - I know there's a cart-and-horse issue there, but the point is that there was a lot of positive reinforcement. Also I gradually got really sick of subjective subjects like the fine arts where "studying" means making inherently unprovable claims and then making your arguments as clever and persuasive as possible. I don't mean I don't like the fine arts; I just don't like theories about them.
        As far as societal support: my graduate education was paid for by research grants, so in that sense, there was a fair amount. Otherwise, I don't really know how society feels about its applied mathematicians.

Sarah: What kind of barriers did you face?

Ken: After I got my doctorate it was remarkably hard to get a job. The number of available research positions for new doctorates in applied math and EE was an order of magnitude smaller than the number of applicants. I did in fact get a pretty good job at Bell Labs, but had the supply-and-demand picture not looked so bleak, I probably wouldn't have become a comedy writer.
        The other barrier I remember was the Stanford Electrical Engineering Department. I took the PhD qualifying exam while I was getting a Master's there, which was in the form of a few separate ten-minute oral exams by professors chosen by lottery. One of them asked me to design an oscillator circuit, which I guess I didn't do too well, and the department wasn't quite happy enough with the results to promise me I could continue. A couple of individual professors encouraged me to find a problem in their area and they'd try and help me stay, but I was pretty angry, because it seems like a pretty crazy standard for picking your doctoral candidates. Still, maybe they were right. How the hell should I know?

Sarah: How does your mathematical mind work? Do you have a photographic memory, are you really good with numbers, visualization?

Ken: My memory isn't photographic, but it tends to be pretty good. For the first 30 years of my life, I'd say it was very good at the things that help mathematicians. I'm better than average, I think, at remembering who came up with any given joke in a script if I was present when it was pitched, and - weirdly - I can often remember where they and I were sitting at the time. Which you would think would be some sort of visualization skill, but I don't think I'm any better than average at visualizing mathematics.

Sarah: Describe the process of how you do mathematics. Lots of people have different styles of how they do mathematics, so what was the style that worked for you?

Ken: I get a suspicion that a result should be true, or that a given method might lead to a desired result, and then throw lots of trial and error at it.

Sarah: Do you have any general comments about what mathematics is or where you think mathematics comes from, philosophically?

Ken: I try not to form opinions on those topics, but I can't rid myself of the sense - not the certainty but the sense - that mathematics is completely independent of the physical universe. Which makes it sound kind of grand, but on the other hand, I've heard it suggested that some - or many - mathematicians regard math as God. I don't even know what meaning to attach to the notion of "regarding math as God", but I don't think any mathematicians I know feel that way.

Sarah: What were/are your favorite mathematically related experiences?

Ken: The most instructive, if not the favorite, happened during my senior year in high school. My English teacher came in one day and announced that "if you have 23 people in a room, two of them will have the same birthday." Now, his statement is obviously both moronic and false; as I'm sure everybody reading this knows, what he meant was that the probability is greater than one-half (under basic assumptions) [for more information, see Ivars Peterson's MathTrek - Birthday Surprises], but his claim was that it was certain. So I raised my hand and attempted gently to correct him: something along the lines of "Uh, Mr. Platz, that's not exactly true-"
        At which point he cut me off: "Oh, yeah? Let's see." And he began to go around the room getting the other kids' birthdays. And I knew immediately what was going to happen, and I was right: I sat there in agony waiting and there were -- of course -- two kids with the same birthday, so I was the one who came off looking like an idiot.
        The lesson here is that many people - many well-educated people - are idiots. And that many more simply look like idiots.
        ("Mr. Platz" was not his real name. It was "Mr. Schwartz".)

Sarah: Does a PhD in applied mathematics help you as a writer? If so, how? Are there any similarities between the creative process of writing and the creative process of mathematics?

Ken: Mathematical training makes you good at following logical structure, and I think that's a plus in any field. In writing, it helps you to see the steps you need to lay out to make a story hang together. I also think studying hard math problems teaches you how to just disconnect from your current approach sometimes and force yourself to come up with a radically new one. This is kind of an effective method of coming up with jokes when you're stuck; I guess maybe it helps you achieve the element of surprise. And the way a mathematician will exhaustively explore the consequences of an assumption or a result is kind of similar to the way multipart jokes are occasionally built up; you've started down a road and you want to see how far it'll take you.

Sarah: Were you responsible for any of the mathematical references on The Simpsons?

Ken: I don't think so. I did get some things in that had a sort of interesting scientific idea behind them. There's an episode where Homer's out wandering randomly and Marge has to track him down and she finds him in a lighthouse off the coast, and when he asks her how she found him she explains that she knew he'd be near the ocean because "Springfield slopes down that way" [El Viaje Misterioso de Nuestro Homer [3F24]]. I guess you could argue this is really a joke about local optimization algorithms.

Sarah: In Futurama, Bender's serial number is 1729, and in previous interviews you have joked that this historically significant integer (to mathematicians) was worth your six years of graduate school. How did this reference arise?

Ken: We needed a number for plot reasons, and David Cohen asked if I could think of an interesting one, and the Hardy-Ramanujan sum-of-two-cubes story leapt to mind [For more information, see Taxicab Number - from Wolfram MathWorld]. Afterwards David sort of went to town with the idea whenever we needed a serial number.

[In the episode Xmas Story [2ACV04], Bender the robot receives a card from the machine that built him wishing "Son #1729" a Merry Xmas. 1729 also appears in many episodes as the hull of the space ship called the Nimbus and as the reference number of the universe populated by "bobble head" characters in the episode The Farnsworth Parabox [4ACV15]. The sum of two cubes arises again in The Lesser of Two Evils [2ACV06] as Bender and Flexo's serial numbers (see Dr. Sarah's Sum of Two Cubes Activity Sheet). Recently, both Fry's taxicab and Al Gore's taxicab have interesting numbers in Bender's Big Score Taxicab 87539319 is an actual cab (as well as the smallest number that can be written as the sum of two cubes in three different ways), while Al Gore' Hybraxi taxi is numbered 543895, which is mathematically related to Gore in a different way.]

Taxicab 87539319 in Bender's Big Score


Sarah: Are there any numerical refences that didn't make it on television?

Ken: There's some episode - Raging Bender [2ACV08], I think - where we needed a name for a movie theater and I came up with the ℵ0-plex. Which was a straightforward enough joke, but then we spent awhile composing a speech where Bender used a diagonalization argument to prove that even with a countably infinite number of screens, the ℵ0-plex still wouldn't be big enough to show every Rocky movie ever made, or something like that. But we just couldn't make it short enough to keep in the script.

Raging Bender [2ACV08]


Sarah: What about other kinds of mathematical references that are not numerically based, like Madison Cube Garden in Futurama? How did this reference arise?

Hell is Other Robots [1ACV09]


Ken: I think David Cohen proposed the name and since he ran the show we didn't debate it much. But afterwards when it was being designed, Stu Burns and I spent an hour or two trying to figure out what the bleachers would look like. We convinced ourselves that if the building was a big cube with one of its main diagonals vertical, and if the bleachers rose up to a uniform height determined by a horizontal plane through the midpoint of that vertical, then from above they looked like a perfect hexagon. (More clearly: the intersection of (1) a cube and (2) a plane that is orthogonal to one of the cube's main diagonals and contains that diagonal's midpoint is a perfect hexagon.) But it took us awhile to prove it. In fact, Stu ended up actually building a cube out of paper and taking a cross section. It was that kind of environment - the others were happy to goof off if those of us with math backgrounds had something we wanted to talk about, and so there was lots of goofing off.

Sarah: Are there any mathematical references to look forward to in the upcoming Futurama releases (Bender's Game, The Beast with a Billion Backs, Into the Wild Green Yonder)?

Ken: I'm not sure. I wrote the first and fourth movies, but I didn't work on the rewrites so I'm not sure what's been changed. I don't recall any math in the fourth movie the last time I saw it. Lots of astronomy jokes though.

Sarah: How do you feel about the representations of mathematicians in Hollywood?

Ken: Oh, it's awful. Many of us are really bothered by the way that mathematicians are portrayed in movies and television. Good Will Hunting and A Beautiful Mind and NUMB3RS are the obvious examples. The biggest obstacle to portraying mathematicians and math accurately is that there's usually not enough on the line in math problems to interest a general audience, or at least the executives who decide whether to make movies are afraid there isn't. While we as mathematicians know that the nature of the problem itself is completely absorbing and fascinating, I don't know why it is hard to transfer that to the screen - it's a mystery to me. I spend a lot of time thinking about this problem, because it is the reason why, when people do have mathematics stories, they do what is always called "raising the stakes": they say, like, "Well let's make it more interesting by making the guy crazy, or maybe somebody is going to die if the guy doesn't solve the problem," and they end up making the story completely phony.

Sarah: What do you do when you get stuck? Do you keep plugging away, do you relax and go get coffee, in writing or in mathematics...

Ken: Generally, if I run into even the slightest difficulty I stop and goof off. The exception is if there's a deadline that's so close that I'm not sure the final product will be acceptable unless I keep at it. My distraction of choice is Scrabble, which I play on an old Palm against the machine. Its program isn't very good, so I almost always win, which puts me in a good frame of mind and I can go back to work.

Sarah: Do you have any words of advice to undergraduate majors?

Ken: (At last a chance to pontificate!) You may have heard people say humans are motivated only by fear and greed. My best advice, based on personal experience, is that if you're planning your life, don't do it while you're afraid. Don't be afraid you're no good at something you want to do, don't be afraid you won't make enough money at something you want to do. (Unless it's acting, in which case give up right now.)
        I have no constructive advice about what to do if you're greedy.

Sarah: Thanks so much!

Sarah Greenwald, Jeff Westbrook, and Ken Keeler at MSRI in 2005



Dr. Sarah J. Greenwald, Appalachian State University

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