30
votes
Why are $X$ and $Y$ commonly used as mathematical placeholders?
See Earliest uses of mathematical symbols, which quotes
F. Cajori, A History of Mathematical Notations, 2 volumes (1928-29)
The use of z, y, x ... to represent unknowns is due to René Descartes, ...
- 10.6k
28
votes
Accepted
How did Isaac Newton write the integral symbol?
Newton used both vertical bars ($\overset{|}{x}$) and rectangles ($\boxed{x}$) to denote integrals in his Quadratura curvarum published in 1704.
Here, the bar notation is used on the bottom of page 9 ...
- 396
23
votes
When was the first recorded use of subscript in mathematics to represent index?
Looking in Mathsym, I find:
$\bullet \;$Use of $\;{}^1a,\;{}^2a,\;{}^3a$ in Laplace, 1772.
Histoire de l'Académie royale des sciences, p. 294
It didn't catch on.
$\bullet \;$Then Cauchy, 1815, with ...
- 10.6k
18
votes
Accepted
What is the origin of the $\hbar$ symbol?
$
{\def\Target#1{\rlap{\smash{\label{#1}\phantom{\tag{#1}}}}}}
{\def\BackUp{\raise{0.25em}{\Tiny{\boxed{\boldsymbol{\Uparrow} \hspace{-2px}}}}}}
$tl;dr– It's unclear. The symbol $`` \hbar "$ itself ...
- 459
17
votes
Is the symbol for set membership $\in$ derived from greek letter $\epsilon$?
Yes, it is.
In Giuseppe Peano's Arithmetices Principia (1889), the $\epsilon$ symbol is explained as follows (page x):
Signum $\epsilon$ significat est.
[The sign $\epsilon$ means is.]...
- 15.2k
16
votes
Accepted
How long has the order of priority of arithmetical operations been widely taught in high schools?
This question comes up often, but there is no up to date scholarly study of it that I know of. The most comprehensive recent accounts (and they are rather brief) seem to be Jeff Miller's Earliest Uses ...
- 80k
16
votes
Why do I , J and K in mechanics represent X , Y and Z in maths?
This usage of $\mathbf i$, $\mathbf j$, and $\mathbf k$ is not specific to physics. It is also used in mathematics, specifically when teaching linear algebra or multivariable calculus in $\mathbf R^3$ ...
- 5,869
16
votes
Accepted
Why isn't the symbol for Beryllium 'B' rather than 'Be'?
Chronology is an important aspect in this case. Let's first understand how beryllium was discovered.
Emeralds and beryl were known to ancient civilizations, they were first recognized as the same ...
- 341
15
votes
Accepted
When was the function arrow notation $x \mapsto y$ first used?
I believe the when can be narrowed down to 1963-64, and by whom to, likely, a Bourbaki member. In the treatise, a lower and upper bound are
Intégration, Chap. 7-8 (1963): still uses $\to$ (e.g. pp. ...
- 7,809
15
votes
History of italicising variables and mathematical formatting in general
In another answer of mine, we see an image of
"Disquisitiones generales circa superficies curvas" from 1828 by C.F. Gauss.
Note that already here the mathematical letters are set in italic. ...
- 10.6k
15
votes
History of italicising variables and mathematical formatting in general
Rene Descartes's La Géométrie of 1637 uses the same typographic convention used today in France: in equations, lower case letters are set in italics but capital letters are set in upright text. This ...
- 2,697
14
votes
Accepted
Who invented the divisibility symbol and why is it backwards?
In mathematics, we often write relations between $a$ and $b$ in the form $aRb$. I mean this both in the sense that we write that string to represent an abstract relation, as well as using that form to ...
- 308
14
votes
Accepted
Why is the letter $\vec{r}$ used for position?
The $r$ is for "radius", and in particular, describes the radial vector from the origin to the location described by the vector. This is sensible because some sort of polar or spherical coordinates ...
14
votes
Accepted
What was the motivation for the choice of the subset symbol?
That Schröder was influenced by Peano is very unlikely. When introducing his inclusion symbol in Vorlesungen, Schröder explicitly cites $<$ for numbers in arithmetic as motivation, and his version ...
- 80k
13
votes
Accepted
Is the symbol for set membership $\in$ derived from greek letter $\epsilon$?
Yes and no. Peano originally used $\epsilon$ in Arithmetices Prinicipia Nova Methodo Exposita (1889), and stated that the symbol was an abbreviation for Latin est (is), apparently using a Greek letter ...
- 80k
13
votes
Accepted
Origin of Q for the set of rational numbers?
TL;DR:
Dedekind was the first to use a letter (R) for sets of rational numbers in 1872, then, starting from 1895, Peano began to use the letter r (lowercase) to denote the same set (and, from 1889, R ...
- 4,400
12
votes
Accepted
Why did I learn to write the base of the logarithm differently from the rest of the world?
It helps to remember that there was no consensus notation for logarithms well into 20th century, with $\mathrm{l}\,x$, $\log x$, and $\mathrm{Log}\,x$ often used by different authors and in different ...
- 80k
12
votes
Accepted
Notation from Weyl's algebraic number theory book
On page 10 of that book the author wrote
The most important example of a ground field is the field of common rational numbers for which I use the freely invented symbol 9...
where he uses the ...
- 2,697
12
votes
Accepted
Why are the symbols E, F, G, L, M, and N used for the coefficients of the fundamental forms?
See the paper by Gauss, Disquisitiones generales circa superficies curvas, from 1828. On page 24, we find:
$$
E\,dp^2 + 2F\,dp\,dq + G\,dq^2 .
$$
Since then everyone continued to use the letters $E,F,...
- 10.6k
12
votes
Accepted
First use of "Spur" (trace) for linear maps / matrices
Comments by user njuffa (Thank You!) lead me to what I believe is what I was looking for:
R. Dedekind: Über die Discriminanten endlicher Körper. In: Abhandlungen der Königlichen Gesellschaft der ...
- 1,012
11
votes
Why is the action from the principle of least action traditionally denoted $S$?
The notation was introduced by Hamilton in 1834, who shifted the focus from the original Maupertuis-Euler version of the least action principle. The tradition followed him probably because his ...
- 80k
11
votes
Accepted
Why is the Digamma function always denoted with the letter "psi"?
I believe it’s because this function was used, and denoted “psi”, much before it got a name.
Indeed, it looks like $(\log\circ\,\Pi)'$ and $(\log\circ\,\Gamma)'$ first occur in Euler (1755, pp. 797-...
- 7,809
11
votes
Accepted
Origin of $\ll$ notation
Vinogradov likely adapted $\ll$ from Poincaré and Borel, who used it for asymptotic series in 1890s (Cajori cites Borel, *Leçons sur les séries divergentes", 1901). Physicists used it for vague &...
- 80k
10
votes
Writing Mathematical Symbols in 20th century
I was one of those secretaries that knew how to use those beasts. In fact, I used a manual typewriter (not a Selectric) to type these formulas for the 30 chemists I worked for at General Tire in the ...
- 101
10
votes
Who introduced the notation $y|_{x=a}$?
You can see :
Giuseppe Peano , Lezioni di Analisi Infinitesimale, 2 vols., 1893, page 17 :
$$[f(x)]_{x=a}=f(a).$$
Not sure it is the earliest... but Peano was a prolific "inventor of notations".
...
- 15.2k
10
votes
Accepted
Is the prime notation for derivatives $f'$ due to Euler?
I agree, as there is further evidence that Lagrange got his primes from Euler:
1. Everyone since Cajori (1923, p. 6; 1929, p. 207) quotes Théorie des fonctions analytiques (1797) for the (sic) “new” ...
- 7,809
10
votes
$\frac{dy}{dx}$ versus $\frac{{\mathrm d}y}{{\mathrm d}x}$
One already finds upright d's in Lacroix's Traité élémentaire de calcul différentiel et de calcul intégral (1802). I don't now if this is the earliest, but it is interesting to note that the ...
- 1,824
10
votes
Was English mathematics behind Europe by many years because of Newton's notation?
Several factors come together to suggest that the idea that "English mathematics [was] ever significantly behind -- by say 50 years, 100 years, or even centuries" (i.e. in the post-Newtonian 18th or ...
- 5,125
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