# Questions tagged [notation]

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

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### 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 ...
152 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 $\Delta$, ...
1k views

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

Kinetic energy is often written as $K$, $KE$ or $E_k$. Where does $T$ come from in quantum mechanics? Why and how did it come to be different?
286 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 ...
264 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/...
67 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 $x$ ...
130 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 ...
472 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 ...
581 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 ...
893 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 ...
647 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 ...
984 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 ...
258 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 "$=$", "...
373 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 ...
343 views

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### Abbreviated Notation for Groups, Rings and Fields

Groups, Rings and Fields are often referred to by the set involved without mention of the operation(s). For example, the "group (G,+)" may be called the "group G". When did this practice originate ...
2k views

### Who gets credit for the real numbers?

If Simon Stevin already pioneered the unending decimal representation for every number (rational, surd, etc.) at the end of the 16th century, why do Cantor and Dedekind (who certainly gave a more ...
82 views

### Whence originates the use of the nabla (∇) for a connection or covariant derivative?

Who introduced it, when, where, and with what if any rationale? (Note that I am not asking about the origin of the nabla symbol, which is covered here.)
934 views

### How did the bra-ket notation become mainstream in quantum mechanics?

I noticed that Dirac bra-kets and their algebra are very much like the linear algebra. A ket is like a vector, a bra is like the conjugate transpose of a vector, a bra-ket is like a complex inner ...
As per the title: where did the notation $a\wedge b$ for the exterior product of $a$ and $b$ originate, and/or who popularised it? I'm especially interested in motivation for the choice of this symbol ...