# Questions tagged [notation]

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

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### How did mathematicians notate the empty set before $\varnothing$?

I recently learned that $\emptyset$ or $\varnothing$ is a relatively new notation for the empty set created in 1939. I know $\{\}$ is also used along with $\{\cdot\}$ to denote empty sets. What was ...
8k views

### What is the origin of polynomials and notation for them?

This may be quite a broad question, but lately I've been wondering about the history behind polynomials. Nowadays these are pretty much the simplest kind of functions to work with, but I'd like to ...
397 views

### Where did Cartan introduce his notation for basis vectors and covectors?

There is a notation used in differential geometry and general relativity in which the partial derivative operators $\partial_\mu$ are used as the basis for the space of contravariant vectors, and ...
2k 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 ...
66 views

### Origin of alternate base annotation

In modern arithmetic textbooks, students are taught about alternate numeric bases. The notation for indicating the base of a number is to attach the base as a subscript. The subscript is itself a ...
349 views

### Why did Cantor (and others) use $\mathfrak{c}$ for the continuum?

Kontinuum is German for continuum, but Cantor used $\mathfrak{c}$. Revision. J.W.Perry questions whether or not Cantor ever in fact used the symbol $\mathfrak{c}$. I must admit I just assumed that he ...
2k 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 ...
223 views

### When did the use of the comma as a decimal mark become extinct in the US?

The US and the UK uses a baseline dot as the decimal mark. Most other European countries use the comma. Here is a short piece on the history of this matter. My question is: When did the use of the ...
514 views

### Were there alternative names for electron orbitals?

Electrons orbits are referred to as s, p, d, and f, then alphabetically. These stand for sharp, principal, diffuse and fundamental respectively (or maybe the German translations). Was any other ...
359 views

### Why was the reduced Planck constant introduced and when?

When was the reduced planck constant $\hbar= h/2\pi$ first introduced and what was the reason behind introducing such a constant? I know that $E=\hbar \omega$ and $p=\hbar k$ and writing again and ...
4k 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 ...
2k views

### Why is the radical symbol $\sqrt{}$ called “radical”?

This question arose in a conversation with a teacher who was introducing square roots to her students. I know from the website Earliest Uses of Symbols of Operation that the symbol $\sqrt{}$ has its ...
5k views

### Why was delta ($\Delta$) chosen to represent change of a quantity?

In many fields, it's common for $\Delta$ (the Greek letter delta) to represent a change or difference. Math uses it, physics uses it, engineering uses it, etc. Why was $\Delta$ chosen for this? I ...
1k 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 ...
347 views

### Modern usage of alchemical symbols

As far as I know, not many (if any) alchemical symbols have survived in modern nomenclature of science, either in chemistry or any other. I think $\LaTeX$ doesn't even support most of them! I know ...
775 views

### Why is the notation $\sin^{-1} x$ so common?

$\sin^{-1} x$ means the inverse of $\sin x$ (it is also often called $\arcsin x$), but it can fairly easily be confused with $\sin(x)^{-1}$. Why is it used, when $\arcsin x$ is easier to type and is ...
10k views

### Who invented short and long division?

I am curious who came up with algorithms that we use today to manually solve mathematical division problems, such as short or long division; how were they established or standardized that way and why?...
319 views

### How was the use of upper and lower indices in tensor notation developed?

It is just a notation, but it is so economical and so systematic. So who invented them? A handy notation should be helpful for the development of the whole field.
50 views

### Use of $h$ in the Newton Quotient [duplicate]

Why do we typically use $h$ for $$\frac{\mathrm{d}f}{\mathrm{d}x}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ A student asked me this the other day. My guess was that it was originally height, because ...
184 views

### Use of $h$ in the Newton Quotient

Why do we typically use $h$ for $$\frac{\mathrm{d}f}{\mathrm{d}x}=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$$ A student asked me this the other day. My guess was that it was originally height, because ...
2k views

### Who really invented the integration symbol?

Most of the sources online say that Leibniz invented the sign. There's also this answer on this site which says so. That is fine. But recently when I was watching Cosmos, I noticed this: See the ...
831 views

### When was the vector notation in physics and other sciences first introduced?

The vector notation in physics is a very compact and easy way to write things down, and according to Feynman it also saves print. When exactly did scientists realize that they were summarizing things ...
5k views

### Why did angular momentum get the letter L

Note - this question was inspired by this questions on physics.SE. Many (most) physical quantities are denoted with a single letter - latin or greek. For many, the letter chosen makes sense: $t$ for ...
1k views

### Who invented the way we write exponentiation?

Why do we write $a^n$ instead of $^n\!a$ for exponentiation? What benefit is there to writing the base before the exponent? With addition and multiplication order doesn't matter since $a + b = b + a$, ...
1k 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 ...
153 views

### When was the short notation for large numbers first introduced and why?

While the long notation or long scale uses multiples of millions to denominate larger numbers (e.g., 10^12 being a billion, a million of millions, thus bi-llion), the short notation (the standard in ...