# Futurama Math Sum of Two Cubes Activity Sheet

Ken Keeler has a PhD in applied math from Harvard. When he was finishing up, there were very few jobs, so he applied to both academic and TV writing jobs. After a year at Bell Labs, he decided to try TV writing. In a gotfuturama.com (CGEF) interview, when he was asked about his many years at school, Ken Keeler joked that a Futurama reference to 1729 was worth six years of grad school:

Ken Keeler: ...I felt like if I didn't try writing now, I'd regret it the rest of my life. So after a year at Bell Labs, I went to Letterman. I've regretted it the rest of my life.
CGEF: Did it ever pay off to go through all these years of education?
Ken Keeler: Well, sure. For example, Bender's serial number is 1729, a historically significant integer to mathematicians everywhere; that "joke" alone is worth six years of grad school, I'd say.

Keeler refers to the episode Xmas Story [2ACV04] written by David X. Cohen in which Bender the robot receives a card from the machine that built him wishing "Son #1729" a Merry Christmas. Answer the following questions on a separate sheet of paper.

Question 1 Use an effective web search to find out what Ken Keeler means when he says that 1729 is "a historically significant integer to mathematicians everywhere." Your answer should include information about the mathematicians Ramanujan and Hardy and a calculation statement about the number 1729.

Question 2 Verify that the related computation statement holds, but do not prove that it is the smallest such number. Show work. Next discuss a general proof method or technique one could use to show that 1729 is the smallest such number but do not prove the statement.

Ken Keeler says that, "We didn't have the agenda of putting a mathematical reference in there, other than that we needed a number for plot reasons. We could have picked one at random, but there was no reason not to make it an interesting one, and that's how many of these references found their way in." The number 1729 also appears in many episodes of Futurama on 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 comes up again in the episode The Lesser of Two Evils [2ACV06]. Read the following and look for David X. Cohen's calculation hint.

Professor Farnsworth: This is Flexo
Hermes: Sweet llamas of the Bahamas! Except for that stylish beard, he look just like Bender!
Flexo: No duh dreadlock, we're both bending units.
Bender: Hey brobot, what's your serial number?
Flexo: 3370318.
Bender: No way! Mine's 2716057.
[They both laugh. Then Fry laughs, but stops and looks confused.]
Fry: I don't get it.
Bender: We're both expressible as the sum of two cubes.
Flexo: Woooh!
[DVD audio commentary begins]
Matt Groening: Now whose joke was that?
David X. Cohen: Well I imagine that either me, Ken Keeler, or Jeff Westbrook, the staff mathematicians, had something to do with it, I forget who - that's true though.
Matt Groening: Wait a second, so let me see, one of you made it up and two laughed uproariously...
David X. Cohen: But I invite the zealous viewer to check that claim. It is true and there's a little trick to it so it's not as easy to figure out as it seems.
Matt Groening: Really?
David X. Cohen: Yes. It's mathematically accurate, all integers, but it's a little tricky. [The Lesser of Two Evils [2ACV06]]

Question 3 Express each of Bender and Flexo's identification numbers as the sum of two cubes. Use a successful web search to help you, and then use a computer algebra system or calculator to verify that each number is indeed expressible as the sum of the cubes of the numbers you found.

Question 4 In David X. Cohen's calculation hint (see his comments above) what did he mean when he said that "it's a little tricky"? Specifically, what kind of numbers do mathematicians usually look for when they express numbers as the sum of two cubes, and which serial number was "a little tricky" in this sense?

Question 5 Search the web to find recent results about the sum of two cubes (within the last five years) and summarize what you found.

In an interview with frontwheeldrive.com, David X. Cohen said that they try to put in as much science as possible with the hope of making die-hard fans out of those that appreciate it. Thanks to the cleverness and mathematical backgrounds of the writers, Futurama can be especially fun to watch. And David X. Cohen was correct in my case. Researching math in Futurama for an article I was asked to write did indeed make a die-hard fan out of me.

Also see Klein's Beer: Futurama Comedy and Writers in the Classroom, PRIMUS, Volume XVII, Number 1, March 2007, pp. 52-66.

Dr. Sarah J. Greenwald

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