Summary: boldface came first, in print, and was widely used. Much later, some mathematicians started to write blackboard bold on blackboards (because actual bold would be very untoward to write on a blackboard). Then, the usage was backported to print.
I find it ugly, a sort of breaking "suspension of disbelief", I don't know how to explain why. Some sort of "anachronistic" feeling, like watching a movie about the roman empire and some soldiers wear watches.
EDIT: as for having "different symbols", this is not the case. They are exactly the same symbol, with different faces. Like when you write the letters "a" or "g" very different on a blackboard as they appear on print.
That's pretty typical for how typography develops. Majuscule and miniscule letters were just two different styles of writing the same letter. But eventually, people started using majuscule (i.e uppercase) letters to give emphasis to the beginning of sentences or certain words, like names.
Italic typefaces were created by Italian type designers to mimic the cursive handwriting of the time. They weren't meant to be mixed with roman style typefaces. However, typesetters who had access to both roman and italic fonts started to use italic for emphasis when typesetting texts in roman type.
And of course blackletter is also just a style that originally tried to mimic earlier handwriting.
> I’ve literally never heard anyone advocate your position until you did, just now
Many mathematicians concerned by typography use real boldface. For example: Terence Tao's blog, Donald Knuth, Paul Halmos (author of "how to write mathematics"), and the famous journal "Publications Mathématiques de l'IHÉS" which is the undisputed gold standard in mathematical typography. They use real boldface for the number sets N, Z, Q, T, R, C.
I've never seen a boldface R to mean a set different than the real numbers.
People use both, for reasons of tradition, ergonomics, practicality, available toolset. Boldface is obviously common in places where BB is unavailable, more restrictive, more difficult. Web publishing is a great example.
BB is common, in my experience, in hand-written text where bold isn't really an option. It is, to my tradition, the most common and recognizable way to indicate the most common field sets and also generally is a good stand-in for any "large category" of interest.
Bold is used intermittently in my experience, probably due to its inability to be hand-written. To me, it tends to mean "vector" or "matrix" much more than set. In hand-written forms, I sometimes see "arrow hats" instead, especially for vectors.
> "Publications Mathématiques de l'IHÉS" which is the undisputed gold standard in mathematical typography.
It is? Do you have any supporting evidence for this claim?
I just had a look at a bunch of recent articles, and I would very much dispute it. I saw nothing extraordinary, and found the fonts they used rather ugly (though of course that is highly subjective). The use of bold face to highlight theorem/definition/etc. numbers is IMHO very questionable. The boldface letters you praise stick out like a sore thumb, feeling as if they were being emphasized and highlighted when they clearly are not meant to be.
> It is? Do you have any supporting evidence for this claim?
I don't have any evidence to support this claim. I always thought about it as self-evident, because it was in that journal that Grothendieck published his work, and the same style is used in by the legendary Hermann editor from Paris and by Bourbaki. But I cannot find any non-partisan source of my claim. As for non-neutral sources, you have for example the congratulations on the typesetting by Dieudonnée [0] (who was a member of the IHES), or a more recent article by Haralambous about the Baskerville variant used by the institute [1]. I will retire my claim of "undisputed" if you find a source that says that the pinnacle of mathematical typesetting is something else :)
https://en.wikipedia.org/wiki/Blackboard_bold
Summary: boldface came first, in print, and was widely used. Much later, some mathematicians started to write blackboard bold on blackboards (because actual bold would be very untoward to write on a blackboard). Then, the usage was backported to print.
I find it ugly, a sort of breaking "suspension of disbelief", I don't know how to explain why. Some sort of "anachronistic" feeling, like watching a movie about the roman empire and some soldiers wear watches.
EDIT: as for having "different symbols", this is not the case. They are exactly the same symbol, with different faces. Like when you write the letters "a" or "g" very different on a blackboard as they appear on print.