# Tag Info

### 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, ...
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### 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 ...
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### Who invented the Leibnitz notation $\frac{d^2y}{dx^2}$ for the *second* derivative?

Leibniz did use this notation for instance in his paper Supplementum geometriae practicae, Acta Eruditorum, April 1693, p. 179 (Google Books link):

### 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 ...
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### 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 ...

### 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.]...
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### Who first introduced the notation $\mathcal{O}$ in algebraic geometry or algebraic number theory

Your guess is right: the notation $\mathfrak o$ goes back to Dedekind. If you get a copy of Dirichlet-Dedekind's Vorlesungen über Zahlentheorie and look in Dedekind's famous XI-th Supplement, which ...
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### 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 ...

### 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 $\mathbf R^3$ ...

### 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. ...

### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 $E,F,... 12 votes Accepted ### First use of "Spur" (trace) for linear maps / matrices Comments by user njuffa (Thank You!) lead me to what I believe is what I was looking for: R. Dedekind: Über die Discriminanten endlicher Körper. In: Abhandlungen der Königlichen Gesellschaft der ... 11 votes Accepted ### Where did John Wallis get the idea for$\infty$? from "Earliest Uses of Various Mathematical Symbols" Infinity. The$\infty$symbol was introduced by John Wallis (1616-1703) in 1655 in his De sectionibus conicis (On Conic Sections) as ... 11 votes Accepted ### Why is the Digamma function always denoted with the letter "psi"? I believe it’s because this function was used, and denoted “psi”, much before it got a name. Indeed, it looks like$(\log\circ\,\Pi)'$and$(\log\circ\,\Gamma)'$first occur in Euler (1755, pp. 797-... 11 votes Accepted ### Origin of Q for the set of rational numbers? tl;dr Dedekind was the first to use a letter (R) for sets of rational numbers in 1872, then, starting from 1895, Peano began to use the letter r (lowercase) to denote the same set (and, from 1889, R ... 11 votes Accepted ### Why isn't the symbol for Beryllium 'B' rather than 'Be'? Chronology is an important aspect in this case. Let's first understand how Beryllium was discovered. Emeralds and Beryl were known to ancient civilizations, they were first recognized as the same ... 10 votes ### Who introduced the notation$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". ... 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” ... 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 ...