61
votes

### Naming in math: from red herrings to very long names

Let me mention as a counterpoint that there is less need for
new terminology than one might expect. Mathematical exposition
is often more successful and clearer without new terminology, and
one should ...

Community wiki

56
votes

### Does this geometry theorem have a name?

Even more is true for this theorem. Check out this drawing from Arseniy Akopyan wonderful book of Geometry in Figures (Second, extended edition, 2017). On page 65 we find Figure 4.7.29)
In the ...

55
votes

### Who started the "-oid" suffix fashion in math?

The suffix "-oid" means the same as "quasi", so "resembling", "like". A groupoid is a quasi-group, like a group. There are hundreds of words in that category, ...

53
votes

Accepted

### What is quantum algebra?

Quantum algebra is an umbrella term used to describe a number of different mathematical ideas, all of which are linked back to the original realisation that in quantum physics, one finds ...

49
votes

Accepted

### Whence “homomorphism” and “homomorphic”?

I found this footnote on page 195 of Fricke and Klein's Vorlesungen über die Theorie der automorphen Functionen (1897):
Translation:
The term "homomorphic" seems more appropriate than the ...

45
votes

### The origin(s) of the word "elliptic"

Your saying "elliptic functions are the functions on elliptic curves over $\mathbb C$" is somewhat misleading, I think. First came elliptic integrals measuring arc-length on an ellipse. These are ...

41
votes

### Name for abelian category in which every short exact sequence splits

The abelian categories in which all short exact sequences split I would call "split abelian categories", reserving the term "semisimple abelian category" for a more restrictive condition. Roughly, ...

39
votes

### What is the name of the 65537-gon?

"$65537$-gon" is the name. Likewise "$257$-gon":
writing (let alone saying) something like "diacosipentacontaheptagon"
serves less to communicate $-$ if indeed it succeeds in communicating at all $-$...

38
votes

### What do named "tricks" share?

To my way of thinking, the other answers are missing an important
element, a necessary feature for a mathematical tool or method to
be called "trick."
Namely, in order to be called a "trick," a ...

Community wiki

36
votes

### Why are they called Spherical Varieties?

Since I am being asked the same question repeatedly and since the given answers are not quite correct, I post another answer despite the thread being so old.
According to a talk by Domingo Luna ...

36
votes

Accepted

### Cardioid-looking curve, does it have a name?

The name of the curve is cochleoid (= shell-shaped rather than cardioid = heart-shaped).
I compare the two below (gold = cochleoid, blue = cardioid). The distinction shell/heart refers to the ...

34
votes

### Why are free objects "free"?

Jakob Nielsen's 1921 paper in Danish, with the title "Om Regning med ikke-kommutative Factorer og den Anvendelse i Gruppetoerien", is where he proved that subgroups of free groups are free. I don't ...

33
votes

### Cardioid-looking curve, does it have a name?

Not an answer - just want to note that the curve has more hidden branches. They can be seen looking at the parametric equation
$$
x=\frac{\sin(\varphi)}\varphi,\quad y=\frac{1-\cos(\varphi)}\varphi
$$
...

Community wiki

32
votes

Accepted

### The letter $\wp$; Name & origin?

Apparently first introduced by Weierstrass in Winter 1862/63 lectures published by H. A. Schwarz (1881, 1885, 1892, 1893), §9:
Mit der Sigma-Function $\mathfrak Su$ ist die Pe-Function $\wp u=\wp(u\...

32
votes

Accepted

### Who is Mrs. Gerber?

Check out the original reference "A theorem on the entropy of certain binary sequences and applications - I" by Wyner and Ziv: https://doi.org/10.1109/TIT.1973.1055107. Footnote 2 on page ...

31
votes

### Main statement as theorem or corollary

Another approach is to present both as theorems, but to present only A as a `marquee result' in the introduction, mentioning that it follows from the stronger but more technical B.

29
votes

### The origin(s) of the word "elliptic"

The origin of all these uses is very different. Joe Silverman explained the genesis of the sequence ellipse $\rightarrow$ elliptic integral $\rightarrow$ elliptic function $\rightarrow$ elliptic curve....

28
votes

### Naming in math: from red herrings to very long names

Let me address the question "what happens if some name it has already been used but you don't agree with the choice?", by giving a recent example from (mathematical) physics. The 2012 experiment that ...

Community wiki

27
votes

Accepted

### Origin of the name ''momentum map''

According to §1.3 and §11.2 of Marsden and Ratiu [1994] (see detailed citation given below), the momentum map concept can be traced back to Sophus Lie's 1890 book, and is an English translation of the ...

27
votes

Accepted

### What is a "scholium"?

I am not a specialist in either etymology nor the english language (I am not a native speaker of english as well) but since the words scholium and porism have both greek origins, I thought it might be ...

27
votes

### What is an explicit bijection in combinatorics?

This is not at all intended as a complete answer to the question, but one criterion that feels important is that for a bijection $f$ to count as explicit, one shouldn't need to know in advance that ...

27
votes

### Are there any other examples where "weak" and "strong" are confused in mathematics?

Munkres's book Topology (p. 78) contains the following warning about coarser and finer topologies:
Many mathematicians use the words "weaker" and "stronger" in this context. ...

26
votes

### What is the "serious" name for the topograph (for a quadratic form)

There's no more serious name for the topograph, as far as I know. And Conway puts a lot of thought into his names, so I think it's best to keep it. I think it's meant to fit into a larger ...

25
votes

Accepted

### What is Barr-Beck?

It is well-attested in the category theory literature (e.g. in Mac Lane's Categories for the Working Mathematician, Chapter VI) that the well-known theorem giving necessary and sufficient conditions ...

24
votes

Accepted

### Groups that satisfy ${ [x,y]^2 \approx 1 }$

This variety of groups has indeed been considered in the literature. It is known that the following conditions hold for every group $G$ satisfying the identity $[x,y]^2=1$:
$[[x,y_1,\ldots,y_m],[x,...

24
votes

Accepted

### The verbs in combinatorics: Enumerating, counting, listing and all that

I'm not sure if this is exactly what you're looking for, but the main topic of Herb Wilf's article What is an Answer? is how to answer the question "How many ______ are there?" His basic ...

20
votes

Accepted

### Why are free objects "free"?

Free objects were first defined* by MacLane in Duality for Groups. That paper gives "free" a curious political context, I quote from page 486:
Call the dual (in this sense) of a free (nonabelian) ...

20
votes

### What is an explicit bijection in combinatorics?

One criterion not mentioned yet is naturality in the categorical sense, which can also be phrased as equivariance with respect to permutation actions. This approach has been extensively developed by ...

20
votes

Accepted

### Emergence of the orthogonal group

Your quote about Cartan thinking of $B_n$ and $D_n$ as 'projective groups..." is actually Cartan describing the lowest dimensional homogeneous space of these groups (except, of course, for a few ...

20
votes

Accepted

### Is it a new discovery on conic section?

It suffices to consider the case when $\Omega$ is a circumcircle, so let it be.
At first, the points $A_b, A_c, B_c, B_a, C_a, C_b$ lie on a conic if and only if
$$
\frac{AB_a\cdot AB_c}{AC_a\cdot ...

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