7
votes
2answers
345 views

What is the history behind the development of the term “coefficient”? [closed]

Why are coefficients called "coefficients"? For example I learned that squaring a number is called "squaring" because it actually refers to "making a square". That's how it was developed. ...
3
votes
1answer
55 views

Why are normal subgroups called “Normal”?

Why are normal subgroups called "Normal"? Who is credited with naming them, and why are they named such?
21
votes
3answers
676 views

Who named “Quotient groups”?

Who decided to call quotient groups quotient groups, and why did they choose that name? A lot of identities such as $$\frac{G/A}{B/A}\cong \frac{G}{B}$$ suggest that whoever invented the notation ...
0
votes
2answers
91 views

Why do some sources call calculus, “the calculus”?

No need to cite specific sources since I think it's a fairly common thing to see. What's up with that? Thank you Edit: I've seen it in several places. Here's where I'm currently looking at it at: ...
6
votes
1answer
55 views

Closed and Open Set - History of Terms

I know very little in the way of math history, but I question that was bothering me recently is where the terms open and closed came from in topology. I know that it's easy to ascribe a sense of ...
1
vote
0answers
48 views

Why are frames called “frames”?

Definition: A frame $F$ is a suplattice such that for any $x_{i}, y\in F$ (for $i\in I$, $I$ a set), we have $$y\wedge\left(\bigvee_{i\in I}x_i\right)=\bigvee_{i\in I}(y\wedge x_i).$$ Why are ...
5
votes
2answers
622 views

Why the name “square root”?

Why do we say that $\sqrt{a}$ is a square root of $a$? Is this because $\sqrt{a}$ is a root of the function $f(x)=x^2-a$? Cubic root similarly? Thanks in advance
30
votes
6answers
1k views

Why are integrals called integrals?

What is the historical background for this term? I cannot quite see what is integral about an integral, even if we go back to the viewing it as the area under a curve. It seems a strange choice of ...
6
votes
1answer
125 views

History of the terms “prime” and “irreducible” in Ring Theory.

In ring theory, a nonzero, nonunit element $p$ of a integral domain is called irreducible if $p=ab$ implies that exactly one of $a$ and $b$ is a unit, and it's called prime if $p\mid ab$ implies that ...
3
votes
3answers
99 views

Colloquialisms in Math Terminology

What are some of your favorite colloquial sounding names for mathematical objects, proofs, and so on? For example, manifolds are often described using an atlas and a neighborhood describes a small ...
14
votes
2answers
650 views

Why is analysis called “analysis”?

Just as the topic says, how did the name "analysis" come to denote the specific mathematical branch dealing with limits and stuff? The term "analysis" seems very generic compared to the words for the ...
2
votes
1answer
98 views

Definition of the $\sec$ function

I am a postgraduate student of mathematics from Slovenia (central Europe) with quite some experience in mathematics. While answering questions on this site, I often encounter the function $\sec(x)$ ...
2
votes
1answer
63 views

How did the Symmetric group and Alternating group come to be named as such?

The Dihedral group makes sense, "Di" means two, and "hedral" means.. shape I think (I've just realised how much of what I think words mean are guesses based on experience) like a "polygon" is a 2d ...
2
votes
1answer
49 views

The Jacobi nome $q$

Does anyone know why $q = e^{-\pi K'/K} = e^{\pi i \tau}$ is called the nome? Is there a historical reason? Does the word nome mean something in Latin or German?
3
votes
0answers
30 views

Terminology Regarding Basic Properties of Functions

Is there a cultural difference between saying that a function is 1-to-1 or injective, onto or surjective and a 1-to-1 correspondence or bijective?
1
vote
1answer
128 views

Why is it called 'discrete' mathematics?

I understand why you would refer to mathematics which concerns itself with all of the numbers on the number line as 'continuous' but why would you refer to countable or finite mathematics as ...
2
votes
2answers
318 views

Fundamental theorem of linear algebra

When I studied linear algebra we (our books, our professors) used to call Fundamental theorem of linear algebra the theorem that says: Fundamental theorem of linear algebra: A linear ...
5
votes
1answer
97 views

the word “derivative”

When did the word "derivative" come into use in calculus, and why? As in Can the word "derive" be used to mean "take the derivative of"? the word "derivative" in normal English ...
5
votes
1answer
110 views

Does Whitehead and Russells' PM distinguish Proof from Demonstration?

I'm currently at Chapter 4, vol. 1 and 1st ed. I have to ask this question because the most important thing about this book is in its minute details. Thanks. Take *3.3 for example. Acording to this ...
7
votes
3answers
575 views

Why are compact sets called “compact” in topology?

Given a topological space $X$ and a subset of it $S$, $S$ is compact iff for every open cover of $S$, there is a finite subcover of $S$. Just curiosity: I've done some search in Internet why compact ...
1
vote
1answer
82 views

From $\mathsf{O}$ to $\mathsf{I}$ via $\infty$

The following is not true mathematics, but a little imaginary story about mathematical symbols. I wonder if there is - in parts - a true (etymological) story behind it. Once there was a symbol ...
3
votes
0answers
87 views

Why tensors are called tensors and how this relates to the rigorous definition?

The algebraic motivation for tensors is fairly good: we know how to deal with linear maps, we must deal with multilinear maps, so we want to reduce them to linear maps. The name tensor however seems ...
0
votes
1answer
320 views

Definition: finite type vs finitely generated

The mathematical term "finite type" appears more and more in the modern articles nowadays. But it is still hard to be found in the standard textbooks. I learned the definition of it from Stacks ...
4
votes
1answer
89 views

Why do we traditionally use letter U for open sets?

Most of traditional usages of symbols in mathematics have origin in English, German or French words that start with that letter, for an example: $p$ for a prime number, $\mathbb{Z}$ for integers (ger. ...
1
vote
1answer
53 views

Whats the name of this function?

I read this function in an exercise. It looks quit familiar to me, however I do not know its name. Whats the name of the $\rho_n$ function and who brought it up first?
25
votes
2answers
1k views

Word origin / meaning of 'kernel' in linear algebra

It may be the dumbest question ever asked on math.SE, but... Given a real matrix $\mathbf A\in\mathbb R^{m\times n}$, the column space is defined as $$C(\mathbf A) = \{\mathbf A \mathbf x : ...
3
votes
1answer
49 views

Why are “restricted Lie algebras” called restricted?

Restricted Lie algebras are Lie algebras of characteristic $p$ with an additional unary operation which is like raising to $p$th power. I didn't find any motivation for this strange choice of the name ...
11
votes
1answer
243 views

What is “inner” about the inner product?

The inner product I am asking about is the one that generalizes the dot product for an arbitrary inner product space. Why is it called an "inner" product? Is there an outer product? Who named it ...
6
votes
1answer
116 views

Who introduced the term “norm” into mathematics?

I've always been curious about the motivation behind the use of the word norm, as used in linear algebra and functional analysis, for a function that assigns a positive number to a vector. Who ...
1
vote
1answer
83 views

Why are regular $p$-groups called “regular?”

In the concept of regular $p$-Groups, what does "regularity" stand for? What is "regular" in such groups? I would like to know idea behind defining these groups, and naming these groups "regular." ...
12
votes
2answers
622 views

What is the mathematical intuition behind àl-jàbrà?

The term algebra comes from the arabic term àl-jàbrà that means "to force", "to restore". Over centuries mathematicians, in east and west, celebrate by this term mathematical disciplines. What is ...
12
votes
3answers
237 views

Why “integralis” over “summatorius”?

It is written that Johann Bernoulli suggested to Leibniz that he (Leibniz) change the name of his calculus from "calculus summatorius" to "calculus integralis", but I cannot find their correspondence ...
5
votes
2answers
439 views

The origin/use of “derivative” and “differentiate”

Apologies if there is a duplicate somewhere; I couldn't find one. The use of the root "deriv" in the context of differentiation seems odd: we have differentiation, differentials, differentiable, ...
3
votes
2answers
112 views

Who did first use the term “simple” in group sense and why?

Who did first use the term "simple" in group sense? More appreciated if I learn the original word(might be in French, Galois???)... and also... Why do you think that this term is chosen ...
2
votes
1answer
117 views

Where does the symbol $\mathcal O$ for sheaves come from?

Sheafs are often denoted by the letter $\mathcal O$. What does this O stand for? To me it seems that more natural choices of symbols for sheaves would be $\mathcal S$ or $\mathcal F$ (for the french ...
3
votes
1answer
83 views

Why do we refer to certain self-adjoint operators as positive/positive definite as opposed to nonnegative/positive?

A self-adjoint linear operator $\tau$ is referred to as positive if is associated quadratic form $\langle\tau v,v\rangle\geq 0$ for all $v$, and is referred to as positive definite if $\langle\tau ...
4
votes
1answer
74 views

Who introduced the term Homeomorphism?

Who introduced the term Homeomorphism? I was wondering about asking this question on english.stackexchange but I think this term is strongly (and maybe solely) related to mathematics.
1
vote
2answers
293 views

What is the Greek version of $\;\cal{quod~erat~demonstrandum}\;$?

What is the Greek version of "quod erat demonstrandum"? Edit: $\quad$The symbol $\square$ will denote the end of a proof; it may be read as "Q.E.D." abbreviating the Latin quod erat ...
2
votes
2answers
98 views

Why the terms “unit” and “irreducible”?

I'm trying to understand why in a ring we choose the names unit to an invertible element and irreducible element in this definition Maybe historical reasons? For example, I suppose the second ...
5
votes
2answers
154 views

Why the SVD is named so…

The SVD stands for Singular Value Decomposition. After decomposing a data matrix X using SVD, it results three matrices, two singular vactors U and V, and one singular value matrix whose diagonal ...
8
votes
1answer
537 views

Why is logistic equation called “logistic”?

The logistic function solves the logistic ODE which is the continuous version of the logistic map. However, I was not able to find why any of these things are called "logistic".
2
votes
1answer
181 views

What is the purpose of defining the notion of inflection point?

What is the purpose of defining inflection point? I know that it is defined to be the point where the second derivative is zero and the second derivative sign changes. It has to have some purpose ...
3
votes
0answers
85 views

Who established the word “ Degree of freedom ” in statistics?

I wonder who is the first one that established and applied the word : "degree of freedom" in statistics? Why he/she need degree of freedom in the calculation of many statistical values?
27
votes
3answers
834 views

Where does the word “torsion” in algebra come from?

Torsion is used to refer to elements of finite order under some binary operation. It doesn't seem to bear any relation to the ordinary everyday use of the word or with its use in differential geometry ...
4
votes
1answer
330 views

Where does the word “hypergeometric” come from?

A friend of mine asked me how the "hypergeometric distribution" got its name. My guess is that an answer to this question will explain what is "geometric" about the distribution, and also why ...
4
votes
2answers
459 views

How many classification of mathematical topics exists?

I found only one Mathematics Subject Classification, are there more?
4
votes
1answer
2k views

Why are vector spaces sometimes called linear spaces?

I have never come across the term 'linear space' as a synonym for 'vector space' and it seems from the book I am using (Linear Algebra by Kostrikin and Manin) that the term linear space is more ...
8
votes
1answer
363 views

When was the term “mathematics” first used?

By the second century, in the Almagest, Ptolemy provides a modern conception of "mathematics" as a "science": 'Mathematics' ... is an attribute of all existing things, without exception, both ...
1
vote
0answers
119 views

Etymology of algebra (as k-algebra)?

Why algebra (over a field) is called "algebra?" (My random guess is that it's a back-formation of some algebras, chopping adjectives from say Lie algebra or Clifford algebra, etc.) And when was that ...
9
votes
2answers
879 views

Why are even/odd functions called even/odd?

Bit of a silly question, someone told me that the reason even functions are called 'even' and odd functions are called 'odd' is that all (single-variable) monomials with even powers are even functions ...