# [texhax] math notation

Michael Barr mbarr at math.mcgill.ca
Wed May 10 18:45:59 CEST 2006

A bit of history might help here.  In traditional typesetting, variables
were put in italics and constants upright.  So clearly the differential d
and the base e of the natural logarithm are constants.  Was this tradition
adhered to, say 50 years ago when I took calculus?  I don't know.  I can
look up some old books when I get to my office, but I'll bet not.  What
happened was that most of the "constants" used multi-character
identifiers.  Such as sin, log, arg, and so on.  I don't believe that
mathematicians ever used a multi-character identifier for a variable.
Enter computer science and later TeX.  CS uses multi-character identifiers
for variables all the time.  You should, by the old rule, put them into
italics.  But then the spacing is wrong.  If you have, say, deffn f = ...,
you want the deffn spaced as a word (with a ligature in most fonts).  You
could use textit, of course, but mostly typesetter used an upright font.
In fact, by that time, I expect that the rule had changed and the new rule
was that single character identifiers were put in slant and
multi-character ones were upright.  And I found this new convention must
more helpful to me since it makes the distinction between a string and a
character, much more important than that between a constant and a
variable. (Which is often utterly arbitrary in any case---it is the rare
constant that never varies.  I once asked the question: in what L^p space
is \pi minimized? (Answer: p = 2, no surprise there.  It is 4 at both
extremes.))

So while the ISO is formally correct, I think the modern usage is better
as well as easier.

Michael



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