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Foolproof: a Sampling of Mathematical Folk Humor, Volume Foolproof: A Sampling of Mathematical Folk Humor Paul Renteln and Alan Dundes n the discipline known as folkloristics [D1] (the on mathematical culture in general, and even a study of folklore), a folk is defined as any clue as to the nature of mathematical thinking. group whatsoever that shares at least one As the readership of the Notices is principally common linking factor. The factor could be na- professional mathematicians, we do not feel it is Itionality, ethnicity, religion, or occupation. necessary to explain all the data we present. Most Members of a profession would also qualify as a readers will already be familiar with many if not folk group. Hence, mathematicians constitute a all of the examples given here. That is to be ex- folk. And, like all folk groups, mathematicians have pected. All folklore exists in multiple forms and their own folk speech (slang), proverbs, limericks, demonstrates variation. There are often many ver- and jokes, among other forms of folklore. It is pre- sions of a classic joke or legend. The same absent- cisely the folklore of a group that defines that minded professor joke, for example, may be at- group. So, mathematicians as a group share a com- tached to various historical individuals, for mon core of mathematical folklore. Some of this example, Norbert Wiener and John von Neumann. folklore tends to be quite esoteric and intelligible So it is likely that each reader will recognize a par- only to members of the group. Outsiders not pos- ticular item even though he or she might have 1 sessing the requisite mathematical vocabulary and heard it (orally) in a slightly different form. knowledge rarely know such esoteric material, and Making Fun of Mathematics even if they did they would probably not under- Many English-language mathematical jokes are stand it. But there is also exoteric mathematical based on word play involving standard mathe- folklore that is known to a limited number of out- matical concepts and terminology. In fact, many of siders, for example, physicists, chemists, and en- the jokes involve food items, which may be a re- gineers. Much of this exoteric folklore consists of flection of the fact that some mathematical con- classic jokes contrasting members of different but cepts are hard to digest, or difficult to swallow: related academic disciplines. We intend to offer a brief sampling of both esoteric and exoteric math- Q: What’s purple and commutes? ematical folklore, concentrating on humorous gen- A: An abelian grape. res such as jokes. We are persuaded that these data not only serve as a basis for identity among 1Many of the following texts come from oral tradition, mathematicians but also provide a unique window but we have also borrowed freely from various Internet websites, including Paul Renteln is professor and chair of the Department of http://www.xs4all.nl/~jcdverha/scijokes; Physics at California State University, San Bernardino, http://www.math.utah.edu/~cherk/mathjokes.html; and visiting associate in the Department of Mathematics http://www.workjoke.com/projoke22.htm; at the California Institute of Technology. His email address http://users.ox.ac.uk/~invar/links/jokes.html; is [email protected]. and Alan Dundes is professor of anthropology and folklore at the University of California, Berkeley. His email address http://outreach.math.wisc.edu/local/ is [email protected]. miscellany/MathJokes.htm. 24 NOTICES OF THE AMS VOLUME 52, NUMBER 1 There are several other variants of this joke: Q: What is green and homeomorphic to the open unit interval? Q: What’s purple, commutes, and is worshipped by A: The real lime. a limited number of people? A: A finitely-venerated abelian grape. Q: What’s yellow, linear, normed, and complete? A: A Bananach space. Q: What is lavender and commutes? A: An abelian semigrape. Q: What do you call a young eigensheep? A: A lamb, duh! Q: What is purple and all of its offspring have been committed to institutions? Q: What’s the value of a contour integral around A: A simple grape: it has no normal subgrapes. Western Europe? A: Zero, because all the Poles are in Eastern Europe. Q: What’s purple, round, and doesn’t get much for Christmas? Addendum: Actually, there ARE some Poles in West- 2 A: A finitely presented grape. ern Europe, but they are removable! Q: What’s an abelian group under addition, closed, Q: Why did the mathematician name his dog associative, distributive, and bears a curse? “Cauchy”? A: The Ring of the Nibelung. A: Because he left a residue at every pole. Q: What’s nutritious and commutes? Q: What is a topologist? A: An abelian soup. A: Someone who cannot distinguish between a doughnut and a coffee cup. Q: What’s hot, chunky, and acts on a polygon? A: Dihedral soup. Q: Why didn’t Newton discover group theory? A: Because he wasn’t Abel. Q: What’s sour, yellow, and equivalent to the Axiom of Choice? Q: What do you get if you cross an elephant and a A: Zorn’s Lemon. banana? A: |elephant|*|banana|*sin(theta). There are thousands of lemmas in mathemat- ics, so in principle the same word play would work on any one of them, yet this joke based on Zorn’s lemma continues to be popular. Why should this 2There are several shaggy dog stories based on wordplay be so? The reason for this becomes clearer when in complex analysis. For example: we recall that the Axiom of Choice can be used to A bunch of Polish scientists decided to flee their re- prove many counterintuitive results in set theory, pressive government by hijacking an airliner and forcing such as the Banach-Tarski paradox. This leads the pilot to fly them to a western country. They drove to some mathematicians to reject the Axiom of Choice. the airport, forced their way on board a large passenger Yet because it is so useful (and because it seems jet, and found there was no pilot on board. Terrified, they listened as the sirens got louder. Finally, one of the sci- so innocuous at first glance), many mathemati- entists suggested that since he was an experimentalist, cians accept it, but with strong reservations. They he would try to fly the aircraft. He sat down at the con- find it distasteful, or unpalatable, or, if you will, a trols and tried to figure them out. The sirens got louder bitter fruit. and louder. Armed men surrounded the jet. The would- Here is another one, even more revealing: be pilot’s friends cried out, “Please, please take off now!!! Hurry!!!” The experimentalist calmly replied, “Have pa- Q: What is brown, furry, runs to the sea, and is equiv- tience. I’m just a simple pole in a complex plane.” alent to the Axiom of Choice? A group of Polish tourists is flying on a small airplane A: Zorn’s lemming. through the Grand Canyon on a sightseeing tour. The tour guide announces: “On the right of the airplane, you can see the famous Bright Angle Falls.” The tourists leap out Lemmings are known to follow each other of their seats and crowd to the windows on the right side. blindly into the sea, where they drown. The impli- This causes a dynamic imbalance, and the plane violently cation of this version seems to be that mathe- rolls to the side and crashes into the canyon wall. All maticians who rely upon the Axiom of Choice are aboard are lost. The moral of this episode is: always keep all lemmings who blindly follow one another and your poles off the right side of the plane. who may all be headed for intellectual death. For a classification of shaggy dog stories, including ones with punch lines based on “an Axiom of Science”, see [B]. JANUARY 2005 NOTICES OF THE AMS 25 Q: What do you get if you cross a mosquito with a Q: What is gray and huge and has integer coeffi- mountain climber? cients? A: You can’t cross a vector with a scalar. A: An elephantine equation. or this variation Q: What is very old, used by farmers, and obeys the Q: What do you get when you cross a mountain goat fundamental theorem of arithmetic? and a mountain climber? A: An antique tractorization domain. A: Nothing—you can’t cross two scalars.3 Q: What is hallucinogenic and exists for every group Q: What is a compact city? with order divisible by pk? A: It’s a city that can be guarded by finitely many A: A psilocybin p-subgroup. nearsighted policemen.4 Q: What is often used by Canadians to help solve cer- Q: What’s a dilemma? tain differential equations? A: A lemma that produces two results. A: The Lacross transform. Q: What’s a polar bear? Q: What is clear and used by trendy sophisticated A: A rectangular bear after a coordinate transform. engineers to solve other differential equations? A: The Perrier transform. Q: What goes “Pieces of seven! Pieces of seven!” A: A parroty error. Q: Who knows everything there is to be known about vector analysis? Q: Why can’t you grow wheat in Z/6Z? A: The Oracle of del phi! A: It’s not a field. Q: Why can fish from the United States enter Cana- Q: What’s big, grey, and proves the uncountability dian waters without a passport? of the reals? A: This is permitted by the Law of Aquatic reci- A: Cantor’s diagonal elephant.5 procity! 3 Q: Why are topologists especially prone to malaria? For further discussion of cross breed riddles, see [AH].
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