40 votes
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Writing Mathematical Symbols in 20th century

Documents like the one you linked to were not typed on a typewriter. When writing on typewriters, it was common to leave some space in the document in which the formulas could be inserted by hand. ...
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  • 516
33 votes

Writing Mathematical Symbols in 20th century

It is really funny to read that in the beginning of 21-st century, some young people may think that journals and books printing had something to do with typewriters:-) If you look attentively at the ...
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27 votes
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Why did angular momentum get the letter L

I just want to comment that the agreement on letters, by which we write $\frac d{dt}\mathbf L=\mathbf M$ for the law of angular momentum, must have come very late -- after 1964. As evidence, note that ...
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25 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, ...
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23 votes
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Why is American and French notation different for open intervals (x, y) vs. ]x, y[?

Notation $()$ is traditional, and $].[$ was introduced by Bourbaki. Much of the Bourbaki notations and terminology became standard, but English speaking people are the most conservative ones in this ...
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23 votes
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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):
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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 ...
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22 votes
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What was Euler's motivation for introducing $i$ for $\sqrt{-1}$?

According to Florian Cajori, A History of Mathematical Notations (1928 - Dover reprint), Vol II, page 128 : 498. It was Euler who first used the letter $i$ for $\sqrt{-1}$. He gave it in a memoir ...
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20 votes
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How did mathematicians notate the empty set before $\varnothing$?

George Boole introduced the concept of empty set, or "nothing" as he called it, as the complement to the "universe" in his Mathematical Analysis of Logic (1847). His notations for ...
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19 votes
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Why is the radical symbol $\sqrt{}$ called "radical"?

"Radical" comes from Latin "radicalis", having roots, an equivalent "radix" was also commonly used earlier. While Rudolff did use the radix in 1525 his did not have the overbar on top, now called ...
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19 votes
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When did it become understood that irrational numbers have non-repeating decimal representations?

Before approximating roots Al-Samawal performs long division of 210 by 13 to five decimal places, not enough to notice that digits cycle after the sixth. And this is the problem with discovering it ...
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17 votes
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Why was delta ($\Delta$) chosen to represent change of a quantity?

There was a related question on Math.SE, which Mauro Allegranza answered with reference to Cajori's classic History of Mathematical Notations (v.II, p.205). It is a great source and is freely ...
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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.]...
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16 votes
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Who invented the way we write exponentiation?

Browsing the "original" historiographical" source for the "power" symbolisms , i.e. : Florian Cajori, A History of Mathematical Notations (1928, Dover reprint), page 335-on can be very istructive, ...
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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 $\mathbf R^3$ ...
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15 votes

Writing Mathematical Symbols in 20th century

I don't think that they had characters such as these in a typewriter. First off, that wasn't typewritten. Look at the "i"s in $\text{Variationsproblem}$ or the "fl" ligature in $\it\text{...
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15 votes
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What is the origin of polynomials and notation for them?

Although many problems that we now reduce to polynomial equations were solved since time immemorial early occurences are coached in verbal and/or geometric terms, and polynomials are not treated as ...
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14 votes
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Who invented short and long division?

The history of the idea underlying the short/long/synthetic division turned out to be far more complicated than I expected, somewhat reminiscent of the history of $0$, with no single inventor. ...
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14 votes

Has a digit ever been used to represent the number "10"?

Yes, it has been: , or more stylized , the depression made by the tip of a Babylonian wedge shaped stylus on a clay tablet. When a circular stylus was used (rarely) the symbol was just $\bigcirc$. The ...
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14 votes
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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 ...
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13 votes
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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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13 votes
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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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13 votes
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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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12 votes
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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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12 votes
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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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11 votes
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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 ...
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11 votes
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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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11 votes
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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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