# 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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### 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 ...
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 ...
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### 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 ...
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### 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
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)...
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 ...
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### 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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### 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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### 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 ...
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
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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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### 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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### 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 ... 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?
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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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### 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&...
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### 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 ...
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### 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 ...
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