# why are math fonts (traditionally) italic/slant? and Greek non-italic?

why is it usually the case that mathfont = italic/slant? [in my post, I am not distinguishing between slant and italic. I believe the two can be different, but let's not distract from my real question, here.] what is this convention based on? did Knuth originate it, or does it have a longer history? what are the views about this today?

we are struggling with this.

should all/most numbers be typeset as math, then? "when you subtract 13 from $x$ you get $x-13$." here, the solo-number 13 should presumably also be in math-mode, too. (the same should then be for all percentages, dollar amounts, etc.) but then, we often have many cells of regression output in tabulars. should it all be set as math, too?

worse, I have seen output in which math-mode digits were italic, too (font limitations?); and some in which the math-mode digits were non-italic. having all-italic is weird in a big tabular that displays regression output. but, then again, if I do not use italic in the tabular, then we get inconsistent treatment of numbers in text vs number in regressions.

so, let's say I want to dispense with slant for math. I prefer to use mathastext.sty . (this is not available in mathjax, so we probably have to wrap \text{} around all symbols, which we can do with a program.) but what about mixing greek and latin characters? are greek characters in math themselves more "italic/slant", designed to look well with italic latin, are they neutral (the italic does not apply...but, then, there is a slant, e.g., in some tex-gyre), or how can I choose "non-slant-italic" greek in TeX.

/iaw

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When you see math mode digits in italics, it's a clear sign a word processor has been used. – egreg Mar 1 '14 at 18:35
on whether you should use 13 or $13$ see my answer here (and the link to D Knuth's article that barbara gives in the comments) tex.stackexchange.com/questions/162411/… – David Carlisle Mar 1 '14 at 19:01
Note that there are digits designed specifically for use in tabulars and that these should probably not match those in regular text or maths in the sense of being exactly the same. That is, if the font you are using provides tabular figures, these will match the non-tabular figures but will be designed specifically for tabular material. Latin Modern, for example, includes tabular and proportional versions of both lining and oldstyle figures, as well as some further sets for other purposes. I don't really know what you'd use tabular osf for, but tabular lining work well though not for text. – cfr Mar 1 '14 at 23:16
I realise you are asking about a different dimension - italic versus upright. I'm just noting this to show that the assumption that figures in text, maths etc. should all be the same might be mistaken. Of course, you wouldn't want figures from different families but figures in different styles from a single family is a different story. – cfr Mar 1 '14 at 23:19
@cfr Are LM tabular figures automatically activated in tabular and similar environments? Regular users probably never learn about their existence. – marczellm Mar 2 '14 at 13:42

Italic math has a long history, essentially since it was first typeset/printed.

Greek lowercase is italic; uppercase is not. Again, tradition. The first Greek printing fonts had upright uppercase, italic lowercase.

Numerals in math have always been printed upright.

Knuth, in designing TeX and the fonts to be used by TeX, took great pains in determining "best practices" according to such authorities as Oxford University Press (see below) and his own careful examination of books and journals published in the early years of the 20th century, when Monotype composition was at its best. You can read about it in his article Mathematical typography, based on his invited Josiah Willard Gibbs lecture presented at the 1978 annual meeting of the AMS.

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Greek lowercase is traditionally upright in french mathematics, as are capital latin letters. A number of fonts for TeX have this as options, most notably fourier, kpfonts, mathdesign and MinionPro. – Bernard Mar 1 '14 at 20:20
just posted---is there an easy way to get a matching math font for times.sty and mathastext.sty that uses upright lowercase greek? – ivo Welch Mar 2 '14 at 20:59

The tradition surely pre-dates TeX, although like many math typesetting conventions TeX has standardised and normalised it and most of us can't remember pre-Tex typesetting. You ask at the end how to get non sloped math Greek in TeX, the answer is you select the appropriate font. There isn't a standard command for it as the classic Computer Modern font set only has lower case Greek in the math italic font, and only has uppercase Greek in the Roman (or italic) fonts (and only those Greek letters that do not look like Roman ones). Other font sets have wider choice, in particular Unicode has a full alphabets of upright and slanted (and sans serif and bold) in the U+1D400 block so unicode-math together with a suitable font (eg STIX) gives access to more naturally encoded Greek alphabets in xetex/luatex.

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The answer I have dates back from some 30 years ago when I was involved in typesetting a physics textbook. As far as I know, the typographical rule is the same in French (my language) and in English.

So the rule is:

• constants (whether a number or a letter which stands as a constant, such as PI): roman character (i.e. straight)
• variables: italics
• vectors: bold

There was a debate as to whether vectorial variables (the force F) should be simply in bold or in bold italics.

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It hs been established that the practice of using italics has a long history, but no one has said why this is the case. I have always assumed that it is to make it clear when you are talking about variables, so that "the value of a is always positive" would not trip you up (it looks like a word is missing; the value of a what is positive). When it is "the value of a is always positive", it is clear that the "a" is being treated differently and not as a normal word in the sentence.

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that would be an awful lot of italics (with ambivalent later distinction for such entities as vectors and digits) for the sake of avoiding two single-letter words in English (and none in German). – ivo Welch Mar 2 '14 at 19:55
It is not just for those two, but also things like "the monomial ax", and in general makes it visually apparent for any mathematics so that it is easier to scan the sentence. As for numbers, these are already distinct from the letters, so there is no need to italicize them, and vectors being bold distinguishes them. – Davide Cervone Mar 2 '14 at 22:58
however, a variable a in a theorem environment can be confusing, which is why knuth created the cmmi font with different metrics (mainly a slight increase in width) to help ameliorate this problem, and also provided the \mathsurround concept, so that a change of font (where there is no shape distinction between italic text and italic math letters) could provide a hint in the form of extra space around math. it's still not perfect, of course, and from what i've seen, many users aren't aware of (or don't like) the \mathsurround possibility. – barbara beeton Mar 3 '14 at 13:28
math should have been set in a specific color, like blue ;-). – ivo Welch Mar 4 '14 at 5:06