Unusual mathematical terms

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:

• I've always been tickled by 'Fuzzy Logic.' Jan 13 '15 at 17:30
• The `Golden ratio' $\phi$. Jan 13 '15 at 17:37
• 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. Jan 13 '15 at 17:48
• Shouldn't this be CW? Jan 13 '15 at 18:22
• “The question is widely applicable to a large audience. A detailed canonical answer is required to address all the concerns.” what. Jan 15 '15 at 19:21

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.

• and don't forget "highly abstract nonsense"
– Alan
Jan 13 '15 at 19:20
• General abstract nonsense. Jan 14 '15 at 21:06
• Special abstract nonsense! Jan 15 '15 at 18:45
• I thought it was "generalized abstract nonsense". Jan 15 '15 at 19:03

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)
A Survey on Cox Rings
Cox-Zucker machine

• 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 :) Jan 15 '15 at 10:14
• 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. Jan 16 '15 at 8:03
• @DenDenDo I believe that the X in $\LaTeX$ is actually supposed to be a chi, but I'm not 100% sure. Jan 18 '15 at 5:02
• Call me naive, but why is #7 dirty?! Jan 19 '15 at 11:31
• 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. :-) Sep 27 '19 at 16:18

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)

• Is Buridan's Ass mathematical? I've heard of it, but never in the context of mathematics. Jan 13 '15 at 20:10
• Yes, see this paper by Leslie Lamport: research.microsoft.com/en-us/um/people/lamport/pubs/buridan.pdf Jan 13 '15 at 22:05
• Whoever came up with the solution to the condom problem has apparently never used a condom. Jan 14 '15 at 1:08
• When I once told someone of the hairy ball theorem he found it funny that it was discovered by someone named “Harry Ball”. Jan 15 '15 at 8:09
• no kill cat plz thankyou Jan 16 '15 at 3:25

I've always been fond the term pointless topology.

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.

• 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. Dec 11 '18 at 22:08

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

I also love working with annihilators....

• All of our rooms are occupied... How long will you be staying? Jan 13 '15 at 20:07
• That's a shame because I have an infinite amount of millionaire friends who wanted to dine at the restaurant.... Jan 13 '15 at 20:12
• @Eleven-Eleven Countable or uncountable? Are they drinking beer? Do they know their limits? Jan 13 '15 at 21:32
• @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,.... Jan 14 '15 at 13:49

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

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.

• The popcorn / Christmas-tree function! Jan 18 '15 at 16:20

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).

• And premice! (Or is there another phrase for those now?) Jan 13 '15 at 21:28
• Hilarious name indeed! Could not resist myself from sharing it in my Facebook. Jan 14 '15 at 21:50
• Numberphile did a video on this, IIRC. Jan 14 '15 at 23:33

Here's my favorite: cleavage (SFW).

• The URL contains "show/cleavage". That in and of it self felt like a risky click. Alas, disappointed at the safety of it. Jan 14 '15 at 11:44
• @Axoren How is “cleavage” ever a risky click? Jan 14 '15 at 21:09
• When you're at work. Jan 14 '15 at 22:25
• @Axoren Added a SFW tag. Jan 14 '15 at 22:52

The monster group
A group with $808017424794512875886459904961710757005754368000000000$ elements.

• An article about them in Scientific American was titled "The capture of the monster". Jan 13 '15 at 18:12
• Do not forget the Baby Monster Group. Jan 14 '15 at 8:58

The Hairy Ball theorem and forgetful functors make me giggle!

• What did the forgetful functor do for her stoner friend? She left a joint as a free object! Jan 14 '15 at 3:00

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.

Diagram chasing is rather fun.

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

• That stuff looks Alien to me. Jan 14 '15 at 0:13

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).

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.

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

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

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.

• Couldn't you also translate that as "bridge of asses"? Or "ass-bridge"? That's much more fun. Jan 13 '15 at 20:10
• Sure, an ass is a donkey after all. :-) Jan 13 '15 at 20:20
• Sylvester invented all kinds of strange mathematical words: syzygy (mentioned above), catalecticant, cumulant, cyclotomic, etc.
– user64687
Jan 14 '15 at 16:25

Some examples could be:

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.

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.

Graph Theory has its "snarks".

• What about grumpkins? Jan 13 '15 at 22:38

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.

• 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
• It's not exactly non-mathematical, either, as units are quite relevant to mathematics. Jan 15 '15 at 22:58

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.

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.

• Sorry to be a party-pooper (ahem), but "Kac" is pronounced like "Katz".
– user64687
Jan 16 '15 at 10:33
• Supposed to be pronounced like Katz. Doesn't mean people pronounce it that way in reality. =) Jan 16 '15 at 16:39

Here is one from sorting.

I've always been fond of the spectral theorem.