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According to the international standard ISO 80000-2:2009, mathematical constants such as e, π and i are printed in roman. This is rarely followed by mathematicians and I wonder what the rationale for italicizing these symbols is. Is it simply a convention to italicize single Latin letter / Greek small letter mathematical symbols in general or are “e”, “π” and “i” seen as variable rather than constant symbols? After all, one may introduce something with a variable, e.g.: “Let ε be greater than 0.” Likewise, one might write: “Let e be Euler’s number.”

So is it the case that e, π and i are actually used as variables (!) and their introduction is omitted or is the italicization just a pretty-printing convention for certain kinds of letters devoid of semantic content?

I like the ISO style in that it does not except Greek capital letters from italicization (in the American tradition, they are upright, while in the Russian tradition, Greek small letters are upright as well, and in the French tradition, Latin capital letters are upright as well), so it is quite consistent in this regard. (How about a sloping plus sign when discussing rings in general, then?) Even so, inconsistencies may occur: In the GUM, “Pr” for probability is written upright as one typically does not use multi-letter variables in mathematics (though two-letter symbols for characteristic numbers do occur in physics: Re) while “E” for expectation is written in italic – of course, probability could be denoted with a variable as well since there are various probability measures, what is used as a variable here really comes down to the number of letters …

In the TUGboat article Typesetting mathematics for science and technology according to ISO 31/XI (1997), Beccari writes that if both upright and sloping fonts were available, an upright π should indicate the numerical constant 3.1415…, while a sloping π should indicate the physical constant 3.1415… rad – this seems wrong to me, these are the same number. The crucial difference to me is that while mathematical constant symbols are purely mathematically defined, physical constant symbols are of empirical nature and one might imagine a different world where an empirical quantity has a different value. The TUGboat article also seems to confuse conventional values with true values. (“According to the ISO regulations […], italic symbols should be used only to denote those mathematical and physical entities that may assume different values, […] but also those physical ‘constants’ that are not really constant, because better measuring techniques may produce updated values.”)

Mr. X
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    I think the cause is pure laziness… – Bernard Jun 23 '20 at 11:44
  • I'm not really sure what the technical issue is here: one can choose to mark up pi, e, etc. and then make them appear however one likes – Joseph Wright Jun 23 '20 at 11:52
  • Most mathematicians I work with does not use upright letters for any of these unless they work in mathematical physics. So I'd also say it is tradition. – daleif Jun 23 '20 at 11:53
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    I find hilarious the justification that physical constants should be in italics because “their value might change”. According to the current theories, the speed of light in vacuum is constant; with c we denote the constant, not its value in some unit of measure. Why not simply say that “physical constants are set in italics, because so we decided”? However, since I don't want to pay the ISO in order to be taught how I should typeset mathematics, I trust mathematical authorities who typeset those symbols in italics. – egreg Jun 23 '20 at 12:03
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    The question is not really on topic here, note also that ISO 80000-2:2009, simply doesn't apply to most math documents, it formulates an (unusual) stylistic convention for use by a limited number of engineering/natural science disciplines that want to use a math notation. It does not apply to normal mathematical documents at all. – David Carlisle Jun 23 '20 at 13:05
  • Somewhat related: https://tex.stackexchange.com/questions/145926/upright-greek-font-fitting-to-computer-modern – John Kormylo Jun 23 '20 at 13:41
  • I frequently use the letter i in two completely different ways: as an index variable, or for the imaginary unit. I’m often mixing in words such as “if” as well. It makes sense to me to typeset those symbols differently from each other or the letter i in text. I like Euler for upright math symbols, but upright italics can work nicely. You can also use \imath. – Davislor Jun 23 '20 at 16:25
  • I’ve only once used π as a variable in a paper, when I was going through a lot of Greek letters and I definitely wasn’t using the constant. In practice, you’re never going to be using the letter π for anything but the constant, and if you did, the difference between upright and slanted π is going to be much too subtle to avoid confusing your readers. Especially in a serif font. – Davislor Jun 23 '20 at 16:31

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