Post by William F HammondPost by Marc van Dongen...
I agree entirely with your suggestion that one shouldn't put _such_
math into section titles. But I don't buy the argument that (at least
in this case) people shouldn't do it because "it" doesn't work for
bold math. In my opinion, the argument should be that you shouldn't do
it because we have no accepted conventions of how to typeset math in
section titles. That's all.
Absolutely.
All that I may say is that I'm completely stunned. Are we discussing
haiku collections, or books on political science? (La)TeX has more
applications that this.
Let me recall that (according to Littlewood) Kronecker (?) said that a
"quality" of mathematicians should be measured by the quantity of bad
texts they have written. The work of initial discoverers is very hard
to read. There is a certain flavor of "major" math book which are,
essentially, incomprehencible (without a substantial mental effort)
since their purpose is to completely change the reader's existing
point of view on phenomena.
Usually, in 20-30 years, an alternative more user-friendly approach
might be found. On the other hand, in that time the new paradigms
might have "been percolating through osmosis", so it is not only an
effect of "better text", but also of "more prepared readers". Anyway,
reading such books is an unalienable part of life of mathematicians.
For most mathematicians, a significant part of their life is spent
trying to fight their way through such life-changing excercises.
(AFAIK, in all other vocations, the rate of such events is at least an
order of magnitude smaller.) And many "lesser" texts are written in
similar styles, because using "soft glove" approach, while feasible,
would bloat the text, so would make the understanding yet harder.
Having a semester-long group effort to work through a short paper is
not unheard of. (And, often, these papers are extremely
well-written.)
Ergo: in a book on math (as opposing to a book USING math) the primary
objective is to provide as much help to the reader as possible.
Following typographical conventions (most of which were honed on books
in different subjects!) is a distant second goal. And having PROPER
sectioning with APPROPRIATE names is one of the major ways to simplify
comprehention without bloating the volume. (Both of a way to
comprehend the large-block architecture of the arguments, AND a way to
navigate starting from the ToC.) For a large proportion of headings,
this means using math in names. And in parts of math where bold is
very significant, this may mean using bold in math in header names.
Post by William F HammondBeyond the absence of such conventions is the situation with online
versions of LaTeX documents. A section title, particularly a first-order
section title, comes to be regarded as meta-date and thereby becomes a
candidate for processing by robots incapable of dealing with math.
Moreover, article section titles are imported as meta-data as a means
of conveying the contents of an article for casual scanning, and in
that context mathematical markup, even when properly rendered, is usually
not articulate.
Even if an author does not understand this, an editor should.
This argument looks as wild to me as saying: since people may make
spelling mistakes when they write, all communication should be
restricted to oral form.
Yours,
Ilya