Questions tagged [notation]

For questions about the history and development of how symbols and related objects are written.

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First use of corner quotes for Gödel numbers

Who first used the corner quotes, ⌜ and ⌝, or $\texttt{\Godelnum}$ with Sam Buss's macro, for the notion of Gödel number? Quine introduced corner quotes, but did not use them for the notion of Gödel ...
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4 votes
1 answer
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What is the S notation in Student's The Probable Error of a Mean?

In William S. Gosset's The Probable Error of a Mean (JSTOR), he begins to derive the $t$ sampling distribution as follows. Samples of $n$ individuals are drawn out of a population distributed ...
7 votes
1 answer
81 views

Greater-than symbol in Byrne's *The Elements of Euclid*

I was surprised to find that Oliver Byrne's 1847 marvelous The Elements of Euclid (color version)1 uses $\sqsubset$ to mean "greater than" and $\sqsupset$ to mean "less than," in ...
14 votes
2 answers
1k views

History of italicising variables and mathematical formatting in general

In the modern day, especially with the advent of $\mathrm\TeX$, it is common practice to italicise variables. This can be seen as far back as Hann, J. (1850). Examples on the Integral Calculus. What's ...
3 votes
1 answer
183 views

Why isn't the symbol for Beryllium 'B' rather than 'Be'?

What I have understood is, generally the symbol of an element is kept as the first letter of the element's name itself (H, N, O...) unless there's already a symbol with that letter, in that case, we ...
1 vote
1 answer
93 views

Why is $T_{\mu\nu}$ the Standard Notation for the Stress-Energy-Momentum Tensor

My question is simple: why do we use $T_{\mu\nu}$ to denote the stress energy momentum tensor, and when was the concept of the stress energy tensor first (or roughly the first) introduced (and by whom)...
13 votes
1 answer
223 views

First use of "Spur" (trace) for linear maps / matrices

Every student of linear algebra learns about the trace of a linear map. Its easiest (albeit not most conceptual) definition is: write the map as matrix, then the trace is the sum of the diagonal ...
5 votes
1 answer
131 views

Why are the symbols E, F, G, L, M, and N used for the coefficients of the fundamental forms?

In differential geometry, if $e_1$ and $e_2$ are bases for a tangent space $T_pM$, then the coefficients of the first fundamental form is: $$\begin{align}E&:=\left<e_1,e_1\right>\\F&:=\...
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1 vote
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What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?

The symbol $\perp\!\!\!\!\perp$ in statistics is a way to denote statistical independence of a collection of random variables. I have seen two forms of it. The first is highly suitable in writing ...
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2 votes
0 answers
124 views

Where does the abomination that is probability notation come from? [closed]

Those with experience may deny it, having suffered too long ago. But it stares you in the face with the somnolent, expressionless eyes of every student being exposed the first time. Probability ...
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3 votes
1 answer
257 views

Why is electric potential denoted by $\phi$?

I haven't found any explanation for it, and I'm curious.
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Why is the ring of algebraic integers denoted by $\mathcal O_K$?

Why/when was the curly-O notation chosen for the ring of integers of an algebraic number field $K$?
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1 vote
1 answer
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Question from Whiteside V. 1 - what did Newton mean by a:b :: c:d notation?

I'm reading volume 1 of Whiteside's 'Mathematical Papers of Isaac Newton,' and on pp. 383-384, Newton reaches a conclusion on his "Example 1st" in the statement "55:-54 :: p:q..." -...
9 votes
0 answers
162 views

Origin of the special Finnish notation for difference of antiderivative

Apologies for a question that is specific to one country (but perhaps others find it a curious example of how mathematical notation can vary between countries). In Finnish calculus texts, if $F$ is an ...
3 votes
0 answers
180 views

Why is this notation used to define points in (elementary) analytic geometry?

I have always found strange that in elementary analytic geometry points are defined by their names followed by their coordinates, for example: "Find the distance between $A(5, -3)$ and $B(2, 1)$....
1 vote
0 answers
317 views

How has $\tan(x)$ become more popular than $\operatorname{tg}(x)$?

I know that some Eastern European and Middle Asian countries denote the tangent by $\operatorname{tg}$. For many years, I have used $\tan$ instead, but am currently thinking of changing that notation ...
1 vote
0 answers
153 views

Why is “h” used for height? [closed]

In Mathematics, it is common to use $h$ for height in various languages, including those whose word for height does not start with h. Why is that?
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1 vote
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141 views

The exclamation mark over a relation symbol

My old linear-algebra teacher, whom I can no longer ask, wrote on a black board an exclamation mark over the binary symbol of a logical formula, the main symbol of which is that binary symbol, to say ...
4 votes
3 answers
400 views

Notations for Laplacian: $\nabla^2$ vs. $\Delta$

For a (sufficiently smooth) function $f\colon \Bbb R^n\to\Bbb R$, the Laplacian of $f$ is defined to be $\sum_{j=1}^n \frac{\partial^2 f}{\partial x_j^2}$. There are two notations for the Laplacian ...
1 vote
1 answer
103 views

When did contemporary practices for indicating ecliptic longitude supplant those containing zodiacal signs?

Ecliptic longitude may be expressed in degrees; my understanding is that prior to the 19th century, expressions of ecliptic longitude contained zodiacal signs. What contemporaneous accounts describe ...
1 vote
0 answers
83 views

Usage of postfix notation for quantifiers

All the logical notations I've seen, from the Begriffschrift notation on, place quantifiers before the proposition containing the variables the quantifier binds. For example, in modern notation we ...
7 votes
2 answers
240 views

Reverse subtraction: has any culture had a symbol (call it $\oplus$) where $A \oplus B$ (read in the same direction as in the language) $:= B - A$?

The standard use of the minus sign is such that $A-B$ means you subtract B from A. Thus $$5-2 = 3.$$ Has any culture used a symbol (let's call it $\oplus$) where $A \oplus B$ means you subtract A from ...
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25 votes
6 answers
2k views

When was the first recorded use of subscript in mathematics to represent index?

(Disclaimer: apologies for any incorrect usage of mathematical terminology throughout this question.) In modern mathematical notation, a variable with a subscript can represent a couple of different ...
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9 votes
1 answer
803 views

Origin of Q for the set of rational numbers?

It seems many sources$^1$ attribute the use of the letter "Q" to represent the rationals to the N. Bourbaki group (in the 1930's); however, the Wikipedia entry on rational numbers claims ...
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8 votes
1 answer
240 views

Origin / first use of $\mathbb{Z}$ (blackboard bold Z)?

I'm aware that the choice of "Z" comes from German zahlen (for "numbers"); however, I was curious to know when the dedicated font, which I believe is called "blackboard bold&...
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1 vote
2 answers
207 views

Why is there no notation for tetration similar to summation?

I noticed that we use $\sum$ and $\prod$ for summation and infinite product (I don't know why it does not have a name like the other two), but we use different looking notation for tetration. Is there ...
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2 votes
0 answers
53 views

Notation for the "binomial form" of a polynomial

In Hardy's A Course of Pure Mathematics (§117 in the 10th edition), in a discussion of differentiation of polynomials, he introduces what he calls the "binomial form" of a polynomial: $$ ...
2 votes
1 answer
184 views

Origin of the notation $s = \sigma + j\omega$ in electrical engineering/control theory

In analytic number theory it is traditional to write a complex variable as $s = \sigma + it$, with the letter $t$ going back to Riemann's paper on the zeta-function (1859) and the letter $\sigma$ ...
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10 votes
1 answer
717 views

What is the origin of the "Japanese bracket"?

In discussions of Sobolev spaces one often sees the Japanese bracket, $$\langle x \rangle = (1+|x|^2)^{1/2},$$ as useful shorthand. I was not easily able to find information about this term. (1) What ...
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7 votes
3 answers
326 views

When did physicists begin using the symbol $G$ for Newton's gravitational constant?

The Cavendish experiment was equivalent to measuring $G,$ Newton's gravitational constant. However, because physicists at the time did not write equations in the same way we do now, Cavendish didn't ...
3 votes
0 answers
176 views

How long have parenthesis (brackets) been used?

If you look at a work such as Bertrand Russel's Principia Mathematica there are no brackets at all. So are brackets a recent invention? Newton used to draw a line above long expressions to group terms....
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1 vote
1 answer
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How old are the shape of the numbers based on the number of angles?

There is a famous image that pretends to explain the origin of the shapes of the digits by the number of angles in them. I do know that it is erroneous but I would like to know if this is an old ...
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4 votes
1 answer
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Why are there so many different, and widely accepted, notational systems for boolean logic?

I can write out the following CNF in various different ways: In mathematical textbook notation: $(A \land B \land C) \lor (\lnot A \land B \land \lnot C) $ In C-like programming notation: ...
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2 votes
0 answers
155 views

What symbols have been used for "many" (or "a large amount of") or "a few" (or "a small amount of") in the history of mathematics or other fields?

When making notes recently I felt like using a symbol for "a large amount of", and it occurred to me that surely others before me must have experienced the need for such a symbol. What ...
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10 votes
2 answers
2k views

Why do I , J and K in mechanics represent X , Y and Z in maths?

Why are letters $i$, $j$, and $k$ used for axes names in mechanics while letters $x$ , $y$ and $z$ are used in mathematics? Why these dimensions weren't called A, B and C or F, G and H?
6 votes
0 answers
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What is the origin in the discrepancy between engineers' and physicists' notation of waves?

my question is very simple. Physicists use this notation in order to write a (for example) plane wave: $$ \xi(z) = \xi^+ \mathrm{e}^{+\mathrm{i}kz} + \xi^- \mathrm{e}^{-\mathrm{i}kz}, $$ where $\xi^+$ ...
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3 votes
0 answers
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Origin of notation "R with a stroke on the leg" for the square-root (℞)

The following text from Ars magna (1545) by Girolamo Cardano is known as the inception of complex numbers: "imaginaberis ℞ m 15" (You will imagine the square root of minus 15): The "R&...
10 votes
2 answers
260 views

Who introduced the divisibility symbol $a\vert b$ ("$a$ divides $b$") and when?

I have just stumbled across this post and became curious about the same question, namely the part regarding the origin/history of the vertical bar symbol $a\vert b$ that we use to denote "a ...
2 votes
1 answer
284 views

Differences between modern and old mathematical notations

Note: I didn't write the word "ancient" in the title because I want to see the notation from 1400 A.D. to 1700 A.D. Mathematical notation has changed very much from the past millennium, and ...
1 vote
0 answers
80 views

First use of $K$ in notation for continued fractions

I will be giving a lecture soon (on Friday) about continued fractions. One of the historical compressed notations for continued fractions uses $K$ (from the German word for continued fraction): $$ ...
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5 votes
0 answers
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How did Hertzsprung-Russell diagrams end up so confusing?

HR diagrams show in which of several sequences individual stars fall, each respecting the rough principle that hotter stars are of higher luminosity. (Sequences other than the main sequence may bend ...
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1 vote
1 answer
132 views

Why did Sylvester Gates choose the name Adinkra?

Sylvester James Gates was one of the co-discoverers of Adinkras. These are graphical representations of susy (supersymmetry) algebras. They are named after a West African people — the Akan of Ghana ...
1 vote
1 answer
2k views

Where did the contour integral sign appear for the first time?

A simple question: Where did the contour integral sign appear for the first time? Wikipedia says that it was introduced by physicist Arnold Sommefield in 1917 ( Table of mathematical symbols by ...
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3 votes
1 answer
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Why are the first three multiplicative SI prefixes lowercase?

The BIPM specifies twenty prefixes for the International System of Units (SI). All ten of the fractional prefixes are lowercase. However, only seven of the multiplicative prefixes are uppercase, the ...
1 vote
0 answers
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Origin of (f×g)(x) and (f∘g)(x) notations

Who and when began the writing of function multiplication, $f(x)×g(x)$, as $(f×g)(x)$ and of function composition, $f\big(g(x)\big)$, as $(f∘g)(x)$?
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1 answer
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Why do we use $U$ for potential energy in classical mechanics?

I am unaware if someone has asked this before, but I am studying classical mechanics and I don’t know why do we use $U$ for potential energy. I have read that Rankine used it first, but I can’t find ...
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4 votes
1 answer
181 views

Has any large group of people used a base other than 10, 20 and 60 for ordinary purposes?

Wikipedia's list of numeral systems lists only $10,20,60$ as having been used in history. There are about twenty-five sets of symbols there used by different groups of people, but only three different ...
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5 votes
0 answers
183 views

Who introduced the comma notation for partial derivatives?

In general relativity, it is common to use the comma notation for partial derivatives $$\frac{\partial g_{\mu\nu}}{\partial x_\rho} = g_{\mu\nu_,\rho}$$ Where did this notation first appear? Was it ...
0 votes
1 answer
160 views

History of points with coordinates notation

In this MathEducator StackExchange article, "Notation of points with coordinates", it's posed the question about what is the best notation for geometrical points and their coordinates: $P(3, ...
2 votes
0 answers
45 views

First historical register of an improper fraction [duplicate]

I'm looking for the earliest known written register of an improper fraction, that is, a numerical fraction in which the numerator is greater than the denominator (like 3/2). By the way, who invented ...