Questions tagged [notation]

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

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Notation for Propositional values in Church's "Simple Theory of Types"

In Alanzo Church's "A Formulation of the Simple Theory of Types" (The Journal of Symbolic Logic 5 no.2 (1940) 56--68, DOI:10.2307/2266170), he adopts the ...
1 vote
1 answer
103 views

David Hilbert's paper: Substitution of the group of cyclotomic field

A question about a notation in David Hilberts's "Ein neuer Beweis des Kroneckerschen Fundamentalsatzes über Abelsche Zahlkörper" (here a german online available source, not sure if there ...
8 votes
4 answers
4k views

Why is calculus missing from Newton's Principia?

I'm not suggesting that Newton did not discover calculus - the question is written this way to express my surprise that the Principia does not use the methods of calculus (or 'fluxions'). He instead ...
4 votes
1 answer
498 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 ...
0 votes
0 answers
49 views

Why is the standard deviation bias correction factor called c₄?

The term to remove bias from an estimate of standard deviation for a normal distribution is referred to as $c_4$. What is the origin or reason for using that notation for the correction factor?
44 votes
5 answers
8k views

Writing Mathematical Symbols in 20th century

As I was reading some papers written by Schrödinger and Heisenberg back in 1920s, I noticed that the symbols they use such as the integral or summation sign or calligraphic letters are as if printed ...
3 votes
2 answers
185 views

Seeking Comprehensive References on the History of Scientific Notation

I am on a quest to uncover the rich tapestry of history surrounding scientific notation as a way of expressing numbers. Specifically, I'm interested in scholarly books, peer-reviewed articles, and ...
12 votes
1 answer
1k views

What was the motivation for the choice of the subset symbol?

I gather that the symbols $\subset$ and $\supset$ were introduced by Ernst Schröder in his 1890 Vorlesungen über die Algebra der Logik. This account also appears—attributed to good old Cajori—in an ...
9 votes
1 answer
189 views

History of greater-than symbol used in reverse?

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 ...
3 votes
0 answers
145 views

How did Hindu-Arabic Numerals get their shapes?

I’ve noticed a recurring post on social media that presents an image suggesting the shapes of Hindu-Arabic numerals are connected to the angles within their design: This claim seems dubious to me. I ...
10 votes
4 answers
16k views

Old square bracket notation for units

As discussed in this answer https://physics.stackexchange.com/a/77691/667 there are several common conventions for the notation $[q]$ of a physical quantity $q$. However, I often see people to put ...
1 vote
0 answers
107 views

Historical Accounts of Confusion in Alphabetic Number Systems?

I’m delving into the intriguing world of alphabetic number systems (greek, for instance), where letters serve a dual purpose—forming words and representing numerical values. I’m curious about the ...
10 votes
1 answer
4k views

How did the obelus ÷ come to stand for division?

The obelus ÷ represents division on calculator keyboards, and sometimes in elementary education. It has a long non-mathematical history starting before 200 BC. Its ...
41 votes
1 answer
4k views

What was Euler's motivation for introducing $i$ for $\sqrt{-1}$?

[Mauro Allegranza has answered the question of who introduced the notation $i$ (Euler, followed later by Gauss), so I have changed the title. I have also edited the question in other ways to make it ...
1 vote
1 answer
72 views

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 ...
12 votes
5 answers
4k views

What is the origin of the $\hbar$ symbol?

Equations involving Planck's constant, $h ,$ are often simplified by instead writing them in terms of the reduced Planck's constant, $\hbar \equiv \frac{h}{2 \pi}.$ But where did the symbol for the ...
4 votes
1 answer
125 views

Who first referred to the number of nonzero entries of a vector as its $\ell_0$ norm?

It is common in the compressed sensing literature to refer to the number of nonzero entries of a vector as its $\ell_0$ "norm." The scare quotes are there because strictly speaking, the $\...
-3 votes
1 answer
141 views

is the shape of the Greek letter pi inspired in the Lion's Gate at Mycenae? [closed]

some references put that the shape of the Greek letter pi is inspired in the lion's gate at Mycenae: The Symbolism of the Greek Alphabet" by Thomas Taylor(1833) "The Secret Life of Symbols&...
2 votes
1 answer
458 views

Use of blackboard bold "ℝ" to refer to real numbers?

I was looking at Wikipedia's wonderful table of the history of certain mathematical symbols, and there was a certain glaring omission: the use of ℝ to apply to the set of all real numbers. They have ...
5 votes
1 answer
4k views

How did the theory of the Horus-eye fractions originate?

In a book, I saw a short anecdote about something called the "Horus-eye" hieroglyph, supposedly used in parts to represent fractions (the book dates to 1997). Wikipedia has an article on the symbol ...
2 votes
0 answers
72 views

History behind Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$ for a commutative Noetherian ring

In 033Q we find defined what some sources call “Serre's conditions $\mathrm{S}_k$ and $\mathrm{R}_k$” (if you don't know what a scheme is, you can read the definition for a commutative Noetherian ring ...
1 vote
0 answers
40 views

Origin of $V_a$ (median) notation

My question about median of a triangle. The English equivalent of the Turkish word "kenarortay" is "median". In English-language geometry sources (like books or web pages), the ...
3 votes
1 answer
109 views

First use of ~ and ≍ (\sym and \asymp)

The relations ~ and ≍ are frequently used in math and computer science, at least within number theory and analysis of algorithms. What is their origin? Definitions Suppose $g(x)$ is an eventually-...
3 votes
0 answers
94 views

Where does the "operator to the right" notation originate?

If any of you have ever written code in DirectX, you're sure to have noticed that applying a linear operator $A$ to a vector $x$ is done as $xA$, instead of the (nowadays usual) $Ax$. I wanted to know ...
6 votes
3 answers
1k views

Was the concept of zero ever developed without relation to positional number systems?

Are there any ancient civilizations which had concept of zero but didn't not use positional numerals for any somewhat non-negligible (from historical point of view) amount of time? If there are such ...
1 vote
0 answers
84 views

First time equilibrium notation was used

I was wondering when was the first time that a chemist wrote a chemical equilibrium with the $\rightleftharpoons$ symbol. And if it was before or after Arrhenius's dissociation theory.
29 votes
2 answers
832 views

How did Isaac Newton write the integral symbol?

Isaac Newton is known as the discoverer of the FTC (Fundamental Theorem of Calculus), so maybe he wrote the integral symbol and derivative symbol. I know he wrote the derivative symbol as $\dot y$ but ...
2 votes
3 answers
29k views

"Calories" vs "calories"

Why was it decided to differentiate kcals from calories with a capital 'C'? It seems kind of odd to me. 1 Cal = 1 kcal = 1000 cal What were the reasons ...
3 votes
0 answers
229 views

Origin of the usage of $\lambda$ to represent eigenvalues

I'm curious whether anyone knows how $\lambda$ came to be used to represent eigenvalues and or who (if anyone) was responsible for the convention. I've looked through a couple of books on the history ...
1 vote
0 answers
55 views

Where did the index of a subgroup notation $[G:H]$ begin to be used?

In texts of algebra, the cardinality of cosets is written in $[G:H]$ or $|G:H|$. Where did this notation originate? The history about $G/H$ can be found here. $[G:H]$ is called index of a subgroup. ...
2 votes
2 answers
476 views

Gate 44 at the Colosseum in Rome: XLIIII or XLIV? When and why the change?

We teach our children in school that 4 is written in Roman numerals as IV and not as IIII but at the Colosseum in Rome, gate 44 is identified as XLIIII and not as XLIV. When did the change from IIII ...
4 votes
2 answers
11k views

Why were the SI-unit prefixes chosen to be a multiple power of 3?

Why were the SI unit prefixes, i.e. \begin{align} \mathrm{giga} && 10^9 \\ \mathrm{mega} && 10^6 \\ \mathrm{kilo} && 10^3 \\ \mathrm{milli} && 10^{-3} \\ \...
57 votes
3 answers
14k views

Why are $X$ and $Y$ commonly used as mathematical placeholders?

I realize that $X$ and $Y$ are relatively popular terms when wanting to use a placeholder for an unknown English or math term. What is the origin of this term, and why was it $X$ and $Y$; why not the ...
14 votes
2 answers
5k views

Who invented the divisibility symbol and why is it backwards?

When we want to perform division, we write e.g. $8/2$ (this is what we already learn at school). But when we want to express that $2$ is a divisor of $8$, we write: $2\mid 8$. What the heck?? I do ...
6 votes
4 answers
13k views

Why are US Bonds measured in '32nd' ticks?

I am a programmer that has been working for fixed income financial companies for the past couple of years. As such, I have learned about a weird notation on fixed income products. In the US, bonds ...
1 vote
0 answers
100 views

Why is 'total angular momentum' denoted by the letter $J$ in quantum mechanics?

In quantum mechanics, we say $J$ ('total angular momentum') = $L$ ('orbital angular momentum') + $S$ ('spin angular momentum'). Apparently $S$ is from 'Spin', but why $J$ for the total angular ...
1 vote
0 answers
101 views

Why have advocates for positional number systems based on divisibility favoured base 12?

In the early twentieth century, with Esperanto and the like going on, a small movement called "dozenalism" began, with the aim of replacing base 10 with the purportedly more natural base 12. ...
1 vote
1 answer
341 views

Who introduced the mixed fraction notation?

Who introduced mixed fraction notation? This notion is a source of confusion to me because it may be interpreted as multiplication.
13 votes
2 answers
22k views

How long has the order of priority of arithmetical operations been widely taught in high schools?

Browsing Facebook, I often come across posts like this, to test peoples' understanding of order of operations. This inevitably prompts a deluge of answers that either misunderstand the concept or ...
2 votes
0 answers
122 views

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 ...
1 vote
1 answer
197 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 ...
8 votes
3 answers
495 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 ...
4 votes
1 answer
107 views

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 ...
14 votes
2 answers
2k 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
0 answers
182 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 $B(2, 1)$....
15 votes
1 answer
396 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 ...
2 votes
1 answer
124 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)...
6 votes
1 answer
158 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&:=\...
28 votes
1 answer
2k views

Why did I learn to write the base of the logarithm differently from the rest of the world?

It only occurred to me recently, in connection with this MO posting, that the way I write the base of the logarithm is not shared by the rest of the world. I am Dutch, and I learned at school to write ...
6 votes
6 answers
2k views

Has a digit ever been used to represent the number "10"?

Ten is special to humans, as there are 10 fingers on two hands, and fingers are still the basic counting medium for people. So, was there any digit representing the number "10" in a positional system ...

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