 Commutative diagrams:
This is surely rather hard to do in TeX. But that is because this
is rather a picture than math text. It would be desirable too to
have an easy way to do some similar things in TeX, e.g. writing in
Frege's Begriffsschrift (if only for historical reasons). So TeX is
surely confined here or at least complicated to use, but as for
diagrams: they could be done in MetaPost quite easily. May be only
a set of the needed arrows (arrowheads and arrowtails) is missing
here (or at least a standard for them). Anyway this is far better
than the approach via TeX directly, as it seems almost impossible
to have a set of glyphs for all things demanded here (arrows at the
right lenght, with the correct inclination, correct placement of letters
relative to the arrows). So this doesn't seem to be a strong point
against TeX to me.
 Other systems: Writing with a typewriter doesn't seem to be a serious
alternative, and I doubt that it will be faster in most cases. And as
for the other systems I can't find any point against TeX here other than
"complicated to use" or "too timecomsuming". That is too commonplace
as long as no better way is given explicitly. I simply doubt that other
systems are superior here when one wishes to get the same quality as with
TeX. So please give explicit examples, then these points could be considered.
Of course, some mathematicians don't type at all (e.g. Erd"os never did
it), but somebody has to do the work, and still seeing books done in
typewriter means fear and loathing time for me. I don't know why any
publishing house should still allow this.
 Rules for mathematical typography: Hans Abergs arguments here esentially
boil down to "most mathematicians don't know about rules for typography,
if they would know, they wouldn't like to follow them, and they couldn't
care less about typography anyway". This seems rather true to me, but
it is certainly nothing to be proud of. And it is nothing that this list
should be concerned with in the first place. Typography is not about
personal taste (or only to a very limited extent), so the position of
most mathematicians always reminds me of someone always setting "j"
instead of "e" in plain text, just because he likes it better this way,
thus greatly increasing the readability. Of course, a mathematician
could use his very own special symbols in his handwriting, even may be
in a lecture, but when it comes to printing and publication, he should
be well aware of existing standards and rules, only leaving them when
appropriate because of a mathematical necessity.
If mathematicians prefer systems other than TeX, quite well, as long as
they achieve at least equally good typography and readability. If not,
this seems to be rather ignorance than better knowledge.
What we should be concerned with here is how to make LaTeX easily
usable for those mathematicians who would like to follow good rules
and traditions, and may be how to trick the unknowing mathematicians
to use them rather unwillingly (e.g. by supplying appropriate control
sequences, but this doesn't seem very realistic). We can't make TeX
foolproof or DAUproof (Duemmster Anzunehmender User, cf.
The New Hacker's dictionary), TeX can't keep mathematicians from
misusing it and from misusing their own symbols, but it shouldn't
support them in doing so, as far as possible.
Johannes Kuester

Johannes Kuester [log in to unmask]
Mathematisches Institut der
Technischen Universitaet Muenchen
