The 1970 paper of Halmos entitled "how to write mathematics" is
a bit old, preposterous to the TeX era, but I think that many of
his advices still make sense today. To summarize what he says,
"use well chosen words instead of plethora of symbols.". "Think
about the alphabet". And don't hesitate to associate a
meaningful symbol to a piece of formula that makes sense by
itself, so as to keep your calculation as compact as possible.
In particular, when there is some constant at the end of the
computation, that comes from an agregation of many constants
appearing during the computation, just call it C through the
whole calculation, and at the end, give its actual value. "The
value of the constant C is..." (I think I read that trick in
some paper by Krantz). "Use words correctly". Explain what is
going on. Irrelevancy should be avoided. Writing "Now applying
the Cauchy-Schwarz inequality leads to...", and just giving the
result, may be better than actually applying it in the middle of
the computation without menti