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From time to time, I come across some unusual mathematical terms. I know something about strange attractors. I also know what Witch of Agnesi is. However, what prompted me to write this question is that I was really perplexed when I read the other day about monstrous moonshine, and this is so far my favorite, out of similar terms.

Some others:

Are there more such unusual terms in mathematics?

Jan 17 update: for fun, word cloud of all terms mentioned here so far:

enter image description here

and another, more readable:

enter image description here

KingLogic
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VividD
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    I've always been tickled by 'Fuzzy Logic.' – Peter Woolfitt Jan 13 '15 at 17:30
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    The `Golden ratio' $\phi$. – pshmath0 Jan 13 '15 at 17:37
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    It may say more about me than about math, but if I need to give a strange sounding math term, then perverse sheaves is my go-to-answer. – Jyrki Lahtonen Jan 13 '15 at 17:48
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    Shouldn't this be CW? – Asaf Karagila Jan 13 '15 at 18:22
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    Klein's bottle – Miguelgondu Jan 13 '15 at 18:25
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    @jyrki That one is even worse in Danish due to the choice someone made at some point to translate sheaf as kneppe, rather than neg (which would mean the same but not be slang for a certain verb). – Tobias Kildetoft Jan 13 '15 at 19:10
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    I tried to downvote, but don't have the required rep yet. Lists of things don't fit well in the Q & A format. Flagging this as a poll. – RubberDuck Jan 13 '15 at 19:57
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    I'm surprised that no-one has linked to XKCD yet. – KSmarts Jan 13 '15 at 20:17
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    I think it would be a good idea to ask for references for all the terms. There are links in many articles, but not all. – flawr Jan 13 '15 at 21:21
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    @RubberDuck If you like this, see the big-list tag. – Cascabel Jan 13 '15 at 23:12
  • @Jefromi if y'all are all right with this and want to go down that road, so be it. – RubberDuck Jan 13 '15 at 23:24
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    @RubberDuck Just pointing you at it, didn't say I agreed. (I'm not a regular user here, just a sometimes-lurker. I'm mainly active on cooking, where this kind of thing would get nuked from orbit.) – Cascabel Jan 13 '15 at 23:24
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    Threesomes, Degenerates, and Love Triangles -> http://arxiv.org/abs/1404.0799 – Mmmh mmh Jan 14 '15 at 11:25
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    @JyrkiLahtonen: the best part being, of course, that they are neither perverse, nor sheaves. –  Jan 14 '15 at 16:15
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    Wait, you want someone to compile a list of all the "unusual" terms in mathematics? Do you believe that someone like that even exists? – Asaf Karagila Jan 15 '15 at 18:01
  • I never said "all", @AsafKaragila. I just have impression that the origin of terms is not explained in many answers (and that can be very interesting part), and also I think there is a need for a list that covers larger but reasonable number of terms. – VividD Jan 15 '15 at 18:05
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    So you want people to write a few sentences describing the history of the terminology, if one even exists, for each suggested term, and you want someone to do it for a lot of terms in a single post? – Asaf Karagila Jan 15 '15 at 18:12
  • Yes, both. All in reasonable limits, of course. The presentation is also important, not only number of terms etc. @AsafKaragila – VividD Jan 15 '15 at 18:15
  • For now, @DenDenDo's answer wins. – VividD Jan 15 '15 at 18:16
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    I think that you are forgetting that a lot of these terms are rather advance (otherwise, you would have known most of them, and wouldn't have asked this question). This makes things awkward, I don't know many terms from geometry or group theory or graph theory that might be considered "unusual"; and I doubt that many analysts, or category theorists, are aware of the examples I provided (whose history is unbeknown to me). Do you get my point? – Asaf Karagila Jan 15 '15 at 18:19
  • I do, but it is an interesting topic, and someone good at presenting can compile an attractive easy-to-read answer. – VividD Jan 15 '15 at 18:24
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    “The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.” what. – k.stm Jan 15 '15 at 19:21
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    Including anything with "Tits" isn't fair. It's not a funny word in Belgium, and it's the guy's NAME! – Matt Samuel Jan 18 '15 at 00:16
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    I do not like that type of humor too, but what can you do? It is funny for some people, and it is not MEANT to be an insult to anybody. I think great majority of us visiting this site have enough intellectual tolerance to live with such things... So, my advice is not to be overly sensitive, @MattSamuel. – VividD Jan 18 '15 at 07:45
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    Just found another one: a Killing form – Miguelgondu Jan 25 '15 at 17:18

39 Answers39

45

I've always liked 'abstract nonsense'.

To quote wikipedia:

Note that referring to an argument as "abstract nonsense" is not supposed to be a derogatory expression, and is actually often a compliment regarding the generality and sophistication of the argument.

Caleb Stanford
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Dasherman
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34

Complex theorems often use simple, illustrative names.
Ham Sandwich Theorem
No Free Lunch Theorem
Ugly Duckling Theorem

Some are named by the scenario they are describing
Birthday Attack
Doomsday Argument

Other by the accompanying real-life events
Happy Ending Problem

and finally the top 10 Dirty Mathematics from Spikedmath (slightly edited to take up less space) enter image description here
A Survey on Cox Rings
Cox-Zucker machine

DenDenDo
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    Good examples. However, /ˈlɑːtɛx/ is not (should not be) pronounced Lay-tech, that's just typical americanisation of syllables. The fault is with the original poster of the image but it bothers me :) – orion Jan 15 '15 at 10:14
  • @orion How do you pronounce it? –  Jan 16 '15 at 04:00
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    You have the IPA above ("Lah-tech" is you want, where "tech" rhymes with Scottish "loch"). That's how the entire world says it (pronouncing "a" as "eye" is english-only thing), and that's how it was originally intended. However, due to constant ignorance and abuse, the alternative used above is usually stated as acceptable. The last syllable is also constantly pronounced wrongly, but that's another matter. – orion Jan 16 '15 at 08:03
  • Because X Makes Anything Cool – DenDenDo Jan 16 '15 at 10:17
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    @DenDenDo I believe that the X in $\LaTeX$ is actually supposed to be a chi, but I'm not 100% sure. – apnorton Jan 18 '15 at 05:02
  • @anorton, you are right: https://en.m.wikipedia.org/wiki/Tau_Epsilon_Chi#Pronouncing_and_writing_.22TeX.22 . – LSpice Jan 18 '15 at 16:17
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    Call me naive, but why is #7 dirty?! – rschwieb Jan 19 '15 at 11:31
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    @rschwieb I think it's intended to sound like "impotent"? – user170231 Sep 18 '15 at 16:46
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    I know this is comment thread necromancy, but... @orion: Per Lamport, /ˈleɪtɛx/ is perfectly acceptable, as is /ˈlɑːtɛx/. "One of the hardest things about LaTeX is deciding how to pronounce it.This is also one of the few things I'm not going to tell you about LaTeX, since pronunciation is best determined by usage, not fiat. TeX is usually pronounced teck, making lah-teck, and lay-teck the logical choices; but language is not always logical, so lay-tecks is also possible." Not simply a crude Americanism, despite your insinuations. :-) – Brian Tung Sep 27 '19 at 16:18
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Hairy Ball Theorem

No Hair Theorem

Arnold's Cat Map (this kills the cat)

No Ghost Theorem

The condom/glove problem (do NOT do this)

Buridan's Ass Paradox

Alex R.
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31

I've always been fond the term pointless topology.

Devin Murray
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23

While the pronunciation is French, there is the Tits Group.

There's also the Dragon family of fractal curves. Also, related to Cantor dust is the Menger sponge. Actually, fractals give a lot of fun ones, such as Douady rabbit (and related "fat rabbit"), Mandelbulb, Pythagoras Tree, the Flowsnake, and the Minkowski Sausage.

In recreational mathematics, with some applications to number theory, numbers can be happy or sad/unhappy; evil or odious; economical, equidigital, or wasteful; or lucky. Edit: They can also be solitary or friendly, which made me think of XKCD.

Computability theory has Busy Beavers.

So, "Are there more such unusual terms in mathematics?" Yes.

KSmarts
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  • As a colleague of mine likes to point out, changing the pronunciation from 'tits' to 'teats' just substitutes a different name for the same thing(s), so it's not clear that it makes it less risqué. – LSpice Dec 11 '18 at 22:08
20

I always wanted to get a room at the Hilbert Hotel.

I also love working with annihilators....

Eleven-Eleven
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    All of our rooms are occupied... How long will you be staying? – KSmarts Jan 13 '15 at 20:07
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    That's a shame because I have an infinite amount of millionaire friends who wanted to dine at the restaurant.... – Eleven-Eleven Jan 13 '15 at 20:12
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    @Eleven-Eleven Countable or uncountable? Are they drinking beer? Do they know their limits? – flawr Jan 13 '15 at 21:32
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    @flawr, well, countable of course. Actually, the first mathematician will order a pint of beer, the second will order a half a pint, the third will order a quarter of a pint...so if the bartender is smart,.... – Eleven-Eleven Jan 14 '15 at 13:49
20

A Killing field is not as bloody as it sounds; it's actually a certain type of vector field named after Wilhelm Killing.

MartianInvader
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  • And the Killing form https://en.m.wikipedia.org/wiki/Killing_form , named after the same gentleman. – LSpice Jan 18 '15 at 16:19
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Here's my favorite: cleavage (SFW).

Brian Fitzpatrick
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The function $$f(x)=\left\{\begin{array}{rcl}\frac{1}{q}&:&x\in\mathbb{Q}\text{ and }x=\frac{p}{q}\text{ in lowest terms}\\0&:&x\notin \mathbb{Q}\end{array}\right.$$ is called (among other things) the Stars over Babylon.

Alexander Gruber
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While categories are often called "Cats", in set theory we have mice and weasels.

(We also have morasses, which sound pretty weird, but one look at the definition and you see that the name is very accurate in describing the object.)

I recently sat in a lecture where someone defined a "piste" (ski slope).

Asaf Karagila
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The Chicken McNugget Theorem.

Lopsy
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12

The monster group
A group with $808017424794512875886459904961710757005754368000000000$ elements.

Lehs
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12

The Hairy Ball theorem and forgetful functors make me giggle!

crypton480
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11

Diagram chasing is rather fun.

user134824
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  • Adding a link for those who were not aware of this term: https://en.wikipedia.org/wiki/Commutative_diagram#Diagram_chasing – flawr Jan 13 '15 at 21:30
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The concept of a Syzygy always tickled me, as do Zero-Knowledge Proofs. Of course I'd be remiss were I not to mention Gropes.

senshin
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Ballunix
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10

Alien Ring Structure - from Mochizuki's papers on inter-universal Teichmuller theory.

Christian LaPointe
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9

Would you like to zigzag inside the random forest of some beautiful tropical geometry? But keep an eye on voracious ant colonies!

Tropical cubic curve

(The image shows a tropical cubic curve, stolen from Wikipedia.)

azimut
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8

Exotic spheres (differentiable manifolds which are homeomorphic but not diffeomorphic to an $n$-sphere).

The Alexander horned sphere (this shows the Jordan–Schönflies theorem doesn't hold in $3$ dimensions).

Peter Woolfitt
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Devil's staircase

Blancmange function

martin
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8

Not exactly math, but physics is close enough. There are higher derivative of velocity called jerk, jounce, snap, crackle and pop.

And there's also screw theory.

orion
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Although the term may not really be in common use: A paper about "Generalized staircases: Recurrence and symmetry" refers to a figure showing a certain surface at page 10, and calls it

"The eierlegende Wollmilchsau surface"

The term eierlegende Wollmilchsau literally means "egg-laying wool-milk-sow", and refers to any (usually imaginary) thing that "can do everything" or "has many positive properties". In this case, the surface has many properties that usually are not found in this combination in other surfaces.

Marco13
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Some examples could be:

jinawee
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The famous "pons asinorum" (Euclid's Elements, Book I, prop. 5), which literally means "bridge of asses (donkeys)" in Latin.

Pascal's limaçon curve (French for snail).

Another mathematical term that I find peculiar is "totient" (as in the Euler $\phi$-function. Apparently, it was first introduced by J. J. Sylvester.

Kim Fierens
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There are topological spaces called hedgehog spaces. According to the linked Wikipedia article, a $K$-hedgehog space is sometimes said to have "spininess $K$."

And let's not forget the process of blowing up points on a plane.

Jesse Madnick
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    Talking about your research may get you in trouble: http://mathoverflow.net/a/53738/48859 – JiK Jan 16 '15 at 18:19
5

Graph Theory has its "snarks".

Blue
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Be sure to check out wikipedia's List of humorous units of measurement, with such gems as:

Helen of Troy (from the Iliad) is widely known as "the face that launched a thousand ships". Thus, 1 millihelen is the amount of beauty needed to launch a single ship.

A Kardashian is a unit of measure representing 72 days of marriage.

The beard-second is a unit of length inspired by the light-year, but used for extremely short distances such as those in integrated circuits. The beard-second is defined as the length an average beard grows in one second.

The Wheaton is a measurement of Twitter followers relative to celebrity Wil Wheaton. The measurement was standardized when Wil Wheaton achieved half a million Twitter followers, with the effect that Wil Wheaton now has 5.52 Wheatons himself (as of January 2015). As few Twitter users have millions of followers, the milliwheaton (500 followers) is more commonly used.

And also wikipedia's List of unusual units of measurement.

Community
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Ehryk
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    This isn't exactly mathematical, as units are characteristic to the natural sciences (i.e., physics) and math can/does do live without. – Nox Jan 15 '15 at 22:39
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    It's not exactly non-mathematical, either, as units are quite relevant to mathematics. – Ehryk Jan 15 '15 at 22:58
4

For the botanists here: I'd like to add Euclid's orchard and the opaque forest problem which is rather from the field of computer graphics, but still got some maths in it.

EDIT: And of course the Sexy Primes as well as wild and tame knots.

flawr
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4

The Wiener Sausage is what the nbhd's of a Brownian motion trace out.

One might argue things named after Norbert Wiener or Mark Kac are not unusual since they were relatively famous mathematicians. But its still funny.

Batman
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  • Sorry to be a party-pooper (ahem), but "Kac" is pronounced like "Katz". –  Jan 16 '15 at 10:33
  • Supposed to be pronounced like Katz. Doesn't mean people pronounce it that way in reality. =) – Batman Jan 16 '15 at 16:39
3

Here is one from sorting.

aghost
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3

I've always been fond of the spectral theorem.

lokodiz
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3

Telling a story on myself. When as a graduate student I first heard about noetherian rings (before I saw a definition) I wanted to know what an ether was, so I could think about a ring that didn't have any of them.

I later taught for a while at Bryn Mawr College, where a colleague used Emmy Noether's desk.

Ethan Bolker
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3

In the Banach space theory there is a property called local unconditional structure, which is l.u.st for short. Another property is the Dunford-Pettis property which is DP for short.

Norbert
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3

Soap Film Problem - this is actually another term for "minimal surface problems", since soap bubbles or other similar soap forms tend to minimize their surface.

Links here and here.

Also, Antoine's necklace.

VividD
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2

Game theory has a trembling hand, some cheap talk, and, collectively, an El Farol Bar problem.

Řídící
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1

Nice topology tool

janmarqz
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1

The Tietze Extension Theorem is always a good one, and Heine-Borel if the speaker doesn't have his German pronunciations down.

Jon
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1

I'm a big fan of Krylov Subspace Methods, which I remain convinced are actually ways of detecting cloaked Klingon birds of prey.

Emily
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1

The Sieve of Eratosthenes is an abstract thing given a mundane (concrete) name, not unlike the "snowflake".  And I've heard that the term googol was chosen specifically because it sound funny.

Scott - Слава Україні
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John H. Conway and Simon B. Kochen's free will theorem

Free will theorem

And some theorems/terms named after unusual mathematicians. For example

Xi Li
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