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:
- Cantor dust
- Gabriel's Horn (also known as Torricelli's trumpet)
- Koch snowflake
- Knaster–Kuratowski fan (also known as Cantor's leaky tent or Cantor's teepee depending on the presence or absence of the apex; there is also Cantor's leakier tent)
Are there more such unusual terms in mathematics?
Jan 17 update: for fun, word cloud of all terms mentioned here so far:
and another, more readable:
39 Answers
12 Next $\begingroup$I've always liked 'abstract nonsense'.
To quote wikipedia:
$\endgroup$ 4 $\begingroup$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.
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
Arnold's Cat Map (this kills the cat)
The condom/glove problem (do NOT do this)
$\endgroup$ 5 $\begingroup$I've always been fond the term pointless topology.
$\endgroup$ $\begingroup$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.
$\endgroup$ 1 $\begingroup$I always wanted to get a room at the Hilbert Hotel.
I also love working with annihilators....
$\endgroup$ 4 $\begingroup$A Killing field is not as bloody as it sounds; it's actually a certain type of vector field named after Wilhelm Killing.
$\endgroup$ 1 $\begingroup$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.
$\endgroup$ 1 $\begingroup$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).
$\endgroup$ 1 $\begingroup$ $\endgroup$ 2 $\begingroup$Here's my favorite: cleavage (SFW).
$\endgroup$ 4 $\begingroup$The monster group
A group with $808017424794512875886459904961710757005754368000000000$ elements.
The Hairy Ball theorem and forgetful functors make me giggle!
$\endgroup$ 1 $\begingroup$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.
$\endgroup$ $\begingroup$Diagram chasing is rather fun.
$\endgroup$ 1 $\begingroup$Alien Ring Structure - from Mochizuki's papers on inter-universal Teichmuller theory.
$\endgroup$ 1 $\begingroup$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).
$\endgroup$ $\begingroup$ $\endgroup$ $\begingroup$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.
$\endgroup$ $\begingroup$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.)
$\endgroup$ $\begingroup$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.
$\endgroup$ 3 $\begingroup$Some examples could be:
- Dessin d'enfant (child's drawing).
- Germ
- Skyscraper sheaf
- Salt and pepper function
- Nuclear topology
- Radon measures
- Polish spaces
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.
$\endgroup$ 1 $\begingroup$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.
$\endgroup$ $\begingroup$Graph Theory has its "snarks".
$\endgroup$ 1 $\begingroup$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.
$\endgroup$ 2 $\begingroup$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.
$\endgroup$ 0 $\begingroup$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.
$\endgroup$ 2 $\begingroup$Here is one from sorting.
$\endgroup$ $\begingroup$I've always been fond of the spectral theorem.
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