Re: What annoys you in mathematical text?

On Sat, 01 Jul 2006 01:15:49 GMT, Stephen Montgomery-Smith
<stephen@xxxxxxxxxxxxxxxxx> wrote:

Toni Lassila wrote:
I was thinking of ways to improve one's mathematical writing and went
through some essays on what certain authors preferred with regards to
style (rather than grammar). Many of the suggestions are of course
contradictory, so I think that rather than trying to be clever and
please everybody, it would just be better to avoid the common
annoyances that people run into in mathematical texts. The risk is to
become bland, but at least you'll be bland and inoffensive.

So what particular things annoy you when reading a mathematical paper
or a book? I would also appreciate hearing about people's annoyances
that are somewhat non-standard. I mean, everybody hates things like
the overuse of "it's easy to see" and "clearly". What is your pet
peeve of which you'd like to see authors rid themselves?
[...]
I dislike the use of Gothic letters, or any other kind of letters which
are hard to distinguish from each other.

I agree with this. Why are some computer scientists for one so
enamored with special fonts and symbols?

Style for style's sake (like grammar or spelling) are not things I worry
about (well you can see that fairly quickly from my posts), so if you
put a math symbol at the beginning of a sentence I am not going to get
bent out of shape. But I really do appreciate it when the author makes
a very genuine effort to make his or her arguments easy to follow, and
also makes the effort to make the whole argument flow nicely. If it is
a choice between clarity and good style, go for clarity.

One thing I've been thinking about is proper ordering of lemmata and
theorems. Some books like to prove a bunch of lemmata before getting
to the main result as an easy corollary, while others start by giving
the statement of the theorem plus an explanation of what needs to be
proved first before tackling the lemmata.

Neither approach seems flawless to me.

In books, I prefer it when the author tries to use somewhat standard
terminology or notation. I particularly like it when I can start
reading page 150 without reading the previous 149 pages. If you do
insist on non-standard terminology or notation, at least make sure that
you have a very good index. If its a choice between using the standard
but perhaps imperfect notation, or reinventing a much more consistent
new notation, generally you should stick to the old.

This perhaps depends on the subject. If you're writing on a well-known
topic that has been around for a while, then stick with the old
notation (provided there is one). But there have been cases in the
history of mathematics where a topic was first introduced with frankly
horrible notation, and only later someone came up with a sane way to
present things.
.

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