Sloping math symbols in italic faces, is it normal?
Chris Lozos
Posts: 1,458
When creating an italic face, I have always sloped the math symbols along with the figures since this makes the most sense to me. But, I recently looked at Neue Haas Unica Pro Bold Italic, a recent release, and I was surprised to find that the math symbols were upright, as if they were upright roman! Is this odd? New thinking? Appropriate?
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Chris, this is interesting as I've had similar thoughts and questions about what other glyphs should not be italicized. There always seems to be a handful of other symbols, including math symbols that are not always italicized (e.g. integral, product, registered, copyright, bar, currency).0

Roman is the normal convention for general math symbols. During the years that I set type I never saw italicized general math symbols until the age of desktop. To me, anyone who italicizes all such symbols, including copyright, doesn't know anything about correct typography.
One online source that might help you is:
http://www.shearsoneditorial.com/2012/07/typographicalconventionsformathematics/
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General rule for book and editorial typography is that math operators are not italicised. In advertising and packaging typography they may be. Hence the design tends to depend on the nature of the typeface design, with most having upright math operators (but spaced slightly differently in the italic fonts).6

I’ve always italicized them in italic fonts.
They look silly otherwise in text that is predominantly italic.
Now that math symbols are included in basic encoding, there’s no need to have them independent of typefaces, as they were originally, roman only as an economy.
For complex math setting, roman fonts are the default anyway, for most characters, with some letters picked out (manually selected) in italic. So it’s not as if the math typographer would ever be in the situation of having to change italic operators to roman.
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I second @John Hudson & strongly recommend Johannes Küster’s PDF “Fonts for Mathematics”: http://www.typoma.com/publ/20041002atypi.pdf
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They look silly otherwise in text that is predominantly italic.
Unless, of course, one thinks they look silly — indeed, cease to look like what they are — when slanted. Especially the ×.
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Can't even the times glyph "look like what it is" in the context of figures? Mathematicians seem to love hand writing formulas on black boards with chalk. The writing appears to be in haste and without care for inclination. Their hands try to work as fast as their minds but they have no problem understanding the scrawl they have created?
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I’m pretty sure most people, i.e. nonmathematicians, would consider upright math symbols in an allitalic setting to be a mistake—if they were to notice.
I personally have no trouble italicizing the multiply glyph!
If a typographer is setting complex mathematics, of the sort described by Küster, they will be using a specialist, serifed math font.
Therefore, all other italic fonts should have sloped math operators, and that means all sans serifs.
If typographers simply must have “proper” upright operators, they can access them in the Roman font.
Both methods are available for Helvetica and Times.
Above, Neue Helvetica Italic and Times New Roman Italic.
Below, Helvetica Oblique and Times Italic.
And of particular note, the same distinction is present between Cambria and Cambria Math (I would have shown it, but don’t have the fonts).1 
Nick, in response to your illustrations, I'd have to say that the slanted math operators are the ones that 'look wrong'. But that's a subjective answer to a subjective question. I didn't offer my original observation
General rule for book and editorial typography is that math operators are not italicised. In advertising and packaging typography they may be. Hence the design tends to depend on the nature of the typeface design, with most having upright math operators (but spaced slightly differently in the italic fonts).
based on what I subjectively think looks right or wrong, but with regard to the conventions of various kinds of typography and, hence, various kinds of fonts.
I'll also note that Brill's typographers were not only clear that they wanted the math operators upright in their italic fonts, but also a lot of other symbols and all parentheses, braces and brackets.6 
I don't think most readers care, or even notice, if math symbols slant. But how many graphic designers will assume slanted math symbols are wrong and not buy a typeface that has them?1

I’m no mathematician, but the lines with slanted math symbols above definitely look wrong.
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My point is that you already have upright math symbols in the roman, why do you need another set of the same with the italic? You are forced to pick upright. Rather than forcing a user to do anything I may feel is correct, in general, I would rather give the user the option to choose the version that is correct in their thinking for their express purpose rather than tie their hands to my choice.
2 
Chris, the problem with that approach is that it a) requires users who want the upright math operators to selectively switch fonts within strings of numbers and operators, and b) does not provide for optimum spacing/kerning between upright signs and slanted numbers.
I can imagine providing slanted operators as a stylistic set in an italic font, but since I mostly make book types I'm not inclined to make them the default form.3 
There are situations where math symbols are used in non math situations. Like Google+ or band names like M+M, +/−. Equal signs are used in sentences. The movie title, E=mc2. Once you slant the plus and equal sign, where do you stop slanting? I think you have to go all the way.5

As a graphic designer who flirts with type design on the side, nonitalicized elements in an, otherwise, italicized block of text look mismatched to me. Consequently, I'd likely not buy or use an italic font that didn't contain italicized figures.In blocks of upright text, italics are used most often to draw attention to a particular word or phrase. If that italicized phrase happens to contain numbers, it would be frustrating and, possibly, misleading to the reader to have part of that phrase revert back to upright numerals.In numerical tabular data, I'd be unlikely to use italic figures unless, of course, I was trying to differentiate certain numbers from the others. And if this were the case, once again, I'd be frustrated to find that no italic figures existed in the font family.Old, obscure conventions hold no particular value in the absence of good, practical reasons supporting their continued use — especially when there are compelling reasons to the contrary.1

We often have conversations online and at conferences about typographic convention. We should have a way to ask graphic designers about this stuff. Some kind of annual typographic surveys conducted by design organizations around the world, with the results made public like the AIGA salary survey.2

We should have a way to ask graphic designers about this stuff.
And book designers, and information designers, and packaging designers....
Oh, and typographers, if you can find any.4 
I don't italicize the math symbols (or copyright, registered, currency...). An italicized degree symbol looks very wrong to my eyes.
2 
It may seem confusing for one font to share roman and italic attributes, but a mathematical symbol set includes all sorts of operators and bracketing characters that are never italicized.
1 
And book designers, and information designers, and packaging designers....We should have a way to ask graphic designers about this stuff.
We would probably get as many and as varied answers as here.
My experience is the same as what John observed above. And since my primary focus is also book and editorial text, I do not italicize math operators in an italic font.
Nor copyright, registered, and trademark. Nor vertical bar. And typically not degree (although I have been somewhat inconsistent on this last one).
4 
BTW, a specialized application of a math operator in a nonmath context that might not be on everyone’s radar is the use of the multiplication sign in the botanical names of hybrids. In some cases it is surrounded on both sides by space; in others it can occur without space directly before a genus or species name.
The rules are governed by the International Code of Nomenclature for algae, fungi, and plants (the current version of which is known as the Melbourne Code, adopted in 2011).
What is particularly worth noting in this context is the following recommendation from Article H.3 in the appendix about hybrids:H.3A.2. If the multiplication sign is not available it should be approximated by the lowercase letter “x” (not italicized).
That last part seems to indicate a clear preference, on the part of botanists anyway, not to have the multiplication symbol slanted in the context of an italic font. And this has borne out in my experience working with gardening writers & editors.
8 
Oh, and typographers, if you can find any.
A gem from John ;)
0 
Kent Lew said:That last part seems to indicate a clear preference, on the part of botanists anyway, not to have the multiplication symbol slanted in the context of an italic font. And this has borne out in my experience working with gardening writers & editors.The ICN considers the multiplication symbol as an operator within a name but not part of the italicized name itself. I doubt it's an indication of a broader preference for upright symbols in italic fonts.It's common convention for both the genus and species in binomial nomenclature to be italicized. However, botanists and zoologists differ in their approach to more complicated naming conventions. Even within subdisciplines of these fields styles differ. The American Ornithologists’ Union, for example, places hyphens in many common species names, like sagegrouse or seaeagle, which puts it at odds with both other biology style guides and common punctuation conventions.This all works fine for inhouse publications produced by those specialist organizations, but when general consumer publications run into conflicting style preferences, they typically defer to the Associated Press, Chicago Manual of Style, or their inhouse guidelines.Style guidelines shouldn't be interpreted as universal commandments. Instead, their main purpose is to ensure contextual consistency.More to the point, publications whose styles dictate nonitalicized figures will select fonts that correspond to their preferences. Publications without that requirement will likely regard an italic font lacking italic figures as reason to use another font. The decision by a type designer to include or not include italicized figures and symbols in a font isn't a matter of right and wrong. Instead, it seems more a matter of making a choice based on buyer preferences and, possibly, aesthetics.1

To clarify, no one is suggesting having nonitalicised figures (numerals) in italic fonts. We're just talking about the typical subset of math operator symbols for basic arithmetic included in typical text and display fonts.2

Not much, and in the early days of DTP Adobe fonts used to leave those code points glyphless, IIRC. Taking that as a cue for their irrelevance, I filled up those spots with other goodies such as extra ligatures (before Phinney and Hudson had drummed into me the error of my ways).
It would help if Multiply and Divide, rather basic math symbols, appeared on the North American keyboard, instead of ASCII tilde and ASCII circumflex.
At least, as font producers, we can make the En dash glyph identical to Minus—although that won’t keep most people from using the Hyphen.
3 
John Hudson said:To clarify, no one is suggesting having nonitalicised figures (numerals) in italic fonts. We're just talking about the typical subset of math operator symbols for basic arithmetic included in typical text and display fonts.Thanks for the clarification, John. I somehow embarrassingly missed that critical distinction. I need to pay more attention.Still, I can think of no compelling logic for italicizing numerals in an italic font but not italicizing the various operators that accompany them. If this is just an esoteric convention born out of economy during the metal type era, at least it was historically understandable. Today, however, I see little reason for it.I'm not a mathematician, but I remember from a few college physics courses that mathematical conventions assign meaning to italicized glyphs in ways that differ from everyday use. In these instances it makes sense to follow the conventions because doing so conveys information. If mathematical texts never use italicized operators, then there's no need to include them in math fonts, but in an italic typeface designed for broad, general use, their absence might be seen as a shortcoming.3

Still, I can think of no compelling logic for italicizing numerals in an italic font but not italicizing the various operators that accompany them.
As Kent and I both noted previously, this is the norm in book typography and has been for a very long time. It derives ultimately from the typography of mathematics, to which you refer, in which operators and other symbols have normative forms that are not subject to styling of weight or slant, and in which, conversely, stylings of weight and slant of alphanumeric characters have semantic connotations. The logic of not italicising mathematical operators is simply this: the identity of the symbols is in both their shape and their orthogonal relationship to the baseline. And after many years working designing and setting these symbols, I really do read them that way: they just look wrong if they're slanted. I'd put italicised math symbols in the same category as 'sloped romans', a kind of contradiction in terms.
I'm no absolutist. I recognise a place for even sloped romans, and as noted above there are kinds of typography, and hence kinds of fonts, in which slanted math symbols make sense. If one is doing that kind of work, then I can clearly see that the lack of them in a font would be 'seen as a shortcoming'. My book publishing clients were equally clear that they viewed the slanting of math symbols in an italic font as a shortcoming.
If a font doesn't contain what you need to do the kind of work you're doing, use a different font. It's not like there's a shortage of the bloody things.8 
The decision by a type designer to include or not include italicized figures and symbols in a font isn't a matter of right and wrong.
To be clear, I wasn’t intending to argue right or wrong. I was just providing some perspective in response to Chris’s original questions: Odd? New thinking? Appropriate?
No, not in my opinion; certainly not; for some audiences, yes.
Instead, it seems more a matter of making a choice based on buyer preferences and, possibly, aesthetics.
Exactly. And John and I have both explained how we see our buyers’ preferences (which I also take to be general preferences). But, like John, I don’t necessarily consider this to be absolute.
Others should do as they see fit.
3 
I see it this way: Being symbols, they only have one appearance. Italicize them would be like slanting a logo. Now why would you do that? This applies to trademark, copyright, degree, registered, etc.  aswell.3

Tobias Kvant said:I see it this way: Being symbols, they only have one appearance. Italicize them would be like slanting a logo.
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