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Questions tagged [notation]

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

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1answer
213 views

Notation for Christoffel symbols

In Christoffel's 1869 paper in which he introduced the Christoffel symbols on the 3rd and 4th pages, they are written as $\left[\substack{ij \\ k}\right]$ and $\{\substack{ij \\ k}\}$. The notation $...
2
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0answers
75 views

Earliest drawings of the plots of trigonometric functions

[Even though this question may seem as a duplicate of this question about the History of sine function, I'd like to ask it again - with a more specific title and a more specific focus (on specific ...
9
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1answer
167 views

When and why did $\frac{dy}{dx}$ become $\frac{d}{dx}y$?

It's obvious for us, that $\frac{dy}{dx}$ can also be written as $\frac{d}{dx}y$, but skimming through Leibniz or Eulers writings I couldn't see them write the latter. I speculate that this change ...
8
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3answers
304 views

Was English mathematics behind Europe by many years because of Newton's notation?

Below are several quotes suggesting that Newton's notation had the effect of retarding English mathematics by 50 years, 100 years, or even centuries. Here is my simplistic two-sentence historical ...
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0answers
59 views

What does the “G” for the similitude groups stand for?

When we have a bilinear symmetric/ bilinear anti-symmetric/hermitian form $b$ on a real/complex vector space $V$, one can consider the group of invertible matrices $A \in GL(V)$ which respect $b$, ...
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63 views

Notation $n=efr$ in algebraic number theory

When $\Bbb Q \subset K$ is a field extension of finite degree and when $p \in \Bbb Z$ is a prime number, the ideal $p O_K$ decomposes uniquely as a product $\prod_{i=1}^r P_i^{e_i}$ of prime ideals of ...
7
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1answer
117 views

Where does the letter S in “$S$-units” and in localization $S^{-1} R$ come from?

In number theory, we may encounter the notion of $S$-unit, $S$-integer, etc. where $S$ is a finite set of prime numbers (for simplicity). For instance, if $S = \{2,3\}$ then the $S$-integers are the ...
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0answers
43 views

What is the history and motivation for the (d-1,1) notation used to describe a field theory?

Very often in the literature of research papers and other articles, and maybe text books, on topics of quantum field theory, a theory may be described as a 3+1 or 0+1, or maybe even 1+1 theory. I ...
2
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1answer
145 views

D'Alembertian symbol $\Box$

The D'Alembertian is a generalization of the Laplacian operator to a space of arbitrary dimension and metric. Where does the D'Alembertian symbol $\Box$ come from? According to Wikipedia it has to ...
6
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1answer
88 views

Notation for fiber bundles - why E for total space?

I'm looking for info on why E is commonly used for the total space of a fiber bundle. I understand F (fiber) and B (base), but there doesn't seem to be any particularly obvious reason for choosing E.
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0answers
132 views

Who was the first to use the “does not exist” sign ∄?

Who was the first to use the "does not exist" sign ∄? I'm aware that Giuseppe Peano originated serifed ∃ and, moreover that Whitehead and Russell repurposed Peano's serifed ∃; I'm also aware that ...
4
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1answer
81 views

What is the origin of q-calculus notation?

It is kind of cute that q-analogues are used in physics (see this link for example), but it is also kind of confusing because the 'q' does not stand for 'quantum'. It predates that use! So, where ...
3
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1answer
170 views

Why is distance sometimes abbreviated S?

While distance in physical formulas is often abbreviated as d (which is pretty intuitive), another common abbreviation is s, as seen e.g. here, here or here. It also seems to be used in optics to ...
5
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2answers
111 views

First appearance of the product symbol ($\Pi$)

As far as I can tell, the first occurrence of the sum notation ($\Sigma$) was in Euler's book Institutiones calculi differentialis: Quemadmodum ad differentiam denotandam usi sumus signo $\Delta$, ...
2
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2answers
320 views

Why is kinetic energy denoted by the letter $T$ in quantum mechanics?

I think the question is self-explanatory but stackexchange requires me to write something here.
7
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1answer
252 views

How were variables used and understood in (particularly) 19th century maths?

Context: I have been thinking about Frege's Begriffsschrift, where he introduces a version of what we now think of as the standard quantifier/variable notation. Philosophers who write on Frege tend to ...
4
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1answer
167 views

First appearance of tensor product symbol $\otimes$

I was asked recently if the tensor product symbol $\otimes$ had been used before Bourbaki's publication on multilinear algebra in 1948 (a draft of this document can be seen at http://sites.mathdoc.fr/...
1
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1answer
49 views

Notation for conditional probability

In mathematics terminology, a function is defined over two sets. One is is input set and other one is output set and for a particular input element, we the following notation $$f(x) = y$$ where $x$ ...
3
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0answers
107 views

Who was the first known mathematician to graph an equation?

A friend of mine pointed out that there were no graphs in Adam Smith's The Wealth of Nations, which was published in 1776. This surprised me because René Descartes (1596-1650) is well known as being ...
4
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2answers
268 views

Did Euler ever write $f(x)$, with parentheses?

Euler is often credited with introducing the notation $f(x)$, and people cite the example $f(\frac{x}{a}+c)$, where he had to use parentheses around the function argument. On the other hand, when the ...
0
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1answer
161 views

Instances of alternative notation being used for the trigonometric functions?

Consider the three "main" trigonometric functions, sine cosine and tangent; whose notations are sin(x); cos(x); tan(x). Are there instances of alternative notations being used for these particular ...
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2answers
374 views

Why is the Digamma function always denoted with the letter “psi”?

My question is on the notation of the Digamma function. The Factorial function $n!$ (which is met in secondary school), is conceptually seminal to the Digamma function. The Factorial function is ...
8
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3answers
449 views

$\frac{dy}{dx}$ versus $\frac{{\mathrm d}y}{{\mathrm d}x}$

When I first learned calculus a few decades ago, the books I read used italicized letter "d"s in derivatives (like this: $\frac{dy}{dx}$). But a few years ago, I started seeing upright "d"s (like ...
7
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0answers
397 views

\mathbb versus \mathbf

When was the use of \mathbb popularized as an alternative to \mathbf? Of course there are the subjective preferences of certain authors, but when I read older articles, there appears to be an almost ...
3
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1answer
103 views

Origins of the Equals Signs

I asked this over on Math Stackexchange, and someone said it might be good to ask it over here too. Some authors use different equals signs for different purposes. For the most part, they are "$=$", "...
0
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1answer
209 views

How did Newton write his equations?

Once, after a lecture, my professor of differential equations said, that Newton did not use derivatives in his work as we do today. He told us that Newton rather used some series expansions for his ...
7
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1answer
221 views

Historical occurrences of mathematicians substituting terms for $x$ in the denominator of $\mathrm{d}y/\mathrm{d}x$?

This answer, to a question on teaching the chain rule, suggests writing something like this $$ \frac{\mathrm{d}\, \mathrm{e}^\sqrt{s}}{\mathrm{d}\,s}=\frac{\mathrm{d} \,\mathrm{e}^\sqrt{s}}{\mathrm{d}\...
5
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4answers
220 views

Examples of when the development of math notation accelerated progress in math research?

Sometimes, coming up with good mathematical notation is key to understanding parts of mathematics. For example, consider the quadratic formula. Brahmagupta formulated a version of the quadratic ...
2
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2answers
1k 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} \\ \...
7
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1answer
178 views

What is the name of this numeral system?

In a XVth century french manuscript on arithmetic and astrology, there is a description of a numeral system as follows (it starts here in the manuscript). Numbers between 1 and 9 are depicted by a ...
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1answer
162 views

What are early examples of the rare notational convention to make the sign of the real number represented by a letter depend on the typography?

Question. What early published or citably attested examples (preferably in the mathematical literature) can you give of the following convention? Let $\mathbb{S}$ denote some nonempty subset of some ...
7
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4answers
375 views

Why is the letter $\vec{r}$ used for position?

I'm sorry if this is a dumb question but I've never heard a convincing explanation for why seemingly all of physics names the position vector "$\vec{r}$". I've tried translating it into just about ...
0
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1answer
63 views

Has the modern logic negation $\lnot$ been adapted from Frege's Begriffsschrift?

Has the modern logic negation $\lnot$ been adapted from Frege's Begriffsschrift?
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2answers
357 views

Is the prime notation for derivatives $f'$ due to Euler?

Cajori, the website on Earliest Uses of Symbols of Calculus and many other sources claim that Lagrange introduced the notation $f'(x)$ for the derivative of $f(x)$ with respect to $x$. But I see Euler ...
5
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2answers
207 views

Notational change with Integrals

A little over 50 years ago I took my first Calculus class and learned the conventional form of an integral as: $$ \int f(x)\,\, \textrm{d}x $$ That is, the integral sign (definite or indefinite) ...
3
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1answer
300 views

Why do we write $E=mc^2$ and not $E=c^2 m$?

My question goes from Phys.SE where people advised me to ask my question here. I always learn in maths and physics when something is a constant in an equation we have to put it before which varies. ...
4
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1answer
1k 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 ...
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2answers
129 views

Why $x_a$ (or $x_o$) and not $a_x$? (conventions for algebraic quantities)

It's my understanding that the convention of using letters from the end of the alphabet ($x$, $y$, $z$) to represent $variables$, and letters from the start of the alphabet ($a$, $b$, $c$) to ...
4
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1answer
170 views

Why is the action from the principle of least action traditionally denoted $S$?

In theoretical physics, a Hamiltonian is traditionally denoted by some variant of $H$, a Lagrangian is some variant of $L$, but why is an action always some variant of S (as opposed to, say, $A$)? ...
5
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2answers
247 views

Is the symbol for set membership $\in$ derived from greek letter $\epsilon$?

Title self explains: Is the symbol for set membership $\in$ derived from greek letter $\epsilon$? What is their historical relationship? Obviously the letter must be older, since greek alphabet is ...
7
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3answers
746 views

When was the function arrow notation $x \mapsto y$ first used?

The notation $x\mapsto \sin x $ and its meaning are well-known to most mathematicians. Less well-known seems to be the fact that $x \mapsto y$ means the same as Church's $\lambda x.y$ and Frege's $\...
3
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1answer
139 views

First use of litte $o_p$ (little $o$ in probability) notation?

I have a follow up question from my previous question on math.SE, where I asked about the First use of little $o$ notation - for those who want to check - the answer goes back to Landau ($1909$), this ...
5
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1answer
355 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 ...
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1answer
426 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 ...
2
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1answer
85 views

reference need about History of prime number development

Im trying to connect my study to a breif history of prime numbers . Also im interesting in reading history of numbers how they come and how they developed . So can any one suggest for this question a ...
4
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1answer
299 views

What is the history of using $i$/$\iota$ as the imaginary unit?

I'm interested in particular in knowing about when $\iota$ began to be used as the imaginary unit/who began to use it. A majority of all text books that I have seen tend to just use $i$ as the ...
7
votes
2answers
313 views

Who introduced the notation $y|_{x=a}$?

When a variable $y$ depends on other variables, say $y=c x^3$, one often writes $$y|_{x=2}$$ to say "$y$ when $x$ has value $2$". This might be more familiar in the context of derivatives where we ...
3
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2answers
525 views

Why the thermoelectric figure of merit is denoted “ZT”?

Why the thermoelectric figure of merit is denoted ZT? Does ZT come from the abbreviation of words in some language? Update: So far T has been figured out --- it is the temperature to make the whole ...
4
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1answer
182 views

Why do we use brackets for function parameters?

I know that a function is called "function" because it's an "execution" of operations. Abbreviated notation is f. But why do we write f(x) and not ...
7
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0answers
8k views

Who first defined the “equal-delta” or “delta over equal” ($\triangleq$) symbol?

The symbol $\triangleq$ is used in mathematics (and physics) for a definition. It is instantiated for instance in the Unicode Character 'DELTA EQUAL TO' (U+225C). The notation $t \triangleq m$ (...