# $\sin$ vs. $sin$ - history and usage

One thing newcomers to TeX or MathJax often get wrong is that they write something like $sin(x)$ instead of $\sin(x)$ - the point being that common mathematical functions with names consisting of several letters are usually typeset in non-italic letters as opposed to the names of variables. So, if you write sin you'll get $sin$ typeset as if you meant to multiply the variables $s$, $i$, and $n$ while with \sin it looks much better.

[In case this is new to you: Should you need something like $\operatorname{diag}$ where \diag is not defined, you can for example use \operatorname{diag}.]

This is for example explained in Knuth's TeX book in the chapter about the "fine points of mathematics typing". However, there are at least two other situations where I think non-italics are also to be used:

• The Leibniz notation should not be used like this: $\frac{{\color{red}d}^2y}{{\color{red}d}x^2}$, but rather like so: $\frac{\mathrm{{\color{red}d}}^2y}{\mathrm{{\color{red}d}}x^2}$, because we're not talking about a variable $d$ but an operator $\mathrm d$.

• Well-known constants should not be typeset in italics because, well, they're not variables. So, Euler's identity is not ${\color{red}e}^{{\color{red}i}\pi}-1=0$ but $\mathrm{\color{red}e}^{\mathrm{\color{red}i}\pi}-1=0$.

[For the record, Knuth's TeX book doesn't agree with this.]

I've already learned from this question that in case of the Leibniz notation there's actually an international standard saying it should be done like this, but that still leaves a couple of questions open for me:

• What is the history of these typographical conventions? (Or maybe one should better ask when and why typesetters started to use italics for variables.)

• Does the ISO-80000-2:2009 standard (which sadly is not accessible to mere mortals) say something about $\mathrm e$ vs. $e$ and $\mathrm i$ vs. $i$?

• How do publishers of mathematical books or papers deal with this? Have you ever encountered one who insisted on getting things like the above "right" one way or the other?

[My apologies for cramming several questions into one, but I think they are all intimately related.]

• I've always found bizarre the imposition that mathematical constants should be upright and physical constants italics. Very few pure mathematicians use upright “e” and “i”, as far as I know. Some publishers insist that “d” for the differential is upright. Whether “d” is an operator is debatable. Sep 17, 2014 at 9:49
• Regarding $sin$, note that also the spacing is different fro sin, to mimic the product of three separate variables $s\cdot i \cdot n$. Sep 17, 2014 at 9:59
• @Frunobulax As far as I know, the speed of light is $c$ (italic). The rationale for this was that physical constants can change their value when more precise measurements are available. So I was told: being a mere mortal, I can't access the ISO secret books without paying a huge amount of money, so I can only speak “second hand”. If the real rationale is that, I'm happy not to follow that convention. Sep 17, 2014 at 10:11
• Yeah, what's the point of a standard when you don't have access to it? Sep 17, 2014 at 10:15
• Perhaps ask in tex.stackexchange.com ?
– lhf
Sep 17, 2014 at 13:05


Then you put something like ddif{q}{t} to get the desired result.

Because the thing has a date in it, and invoked by \usepackage{} then it is more robust to formatting changes &c.

But \operatorname{} is a bit long, and i reassign this to \fn{}, eg \fn{isi}(values).

• I support this idea. I always start writing any paper with redefining these things. Mar 13, 2019 at 10:25

I've just read an article which at least partly answers my questions: https://nickhigham.wordpress.com/2016/01/28/typesetting-mathematics-according-to-the-iso-standard/.

This not about $\TeX$. It is a typographical convention designed to aid in understanding. Remember books have been printed on paper centuries before the computer era.

In any mathematical expression or formula, we use the signs, $+, -, /$ denoting arithmetical operations. But for some reasons (economy?) the symbol for multiplication, $\times$, is omitted. So the high school formula is never written as $(a+b)^2 = a^2 + b^2 + 2\times a\times b$. So when we see $max$ in an expression typographers want to help the readers not to confuse with the product of $m$, $a$, and $x$.

For this purpose all variable names (usually single letters) are written in italics and word-abbreviations such as max, min, deg, tan, log, exp are written in upright fonts. (I am told physicists following Einstein summation convention have to be pre-empt such an assumption in rare situations where no summation is intended).

Now $\TeX$ is smart enough to know that between two variables if there is no arithmetical operator it should be multiplication: that is why when we type spaces between two variables inside dollars that space is ignored by the $\TeX$ engine.