For example, his opening paragraph "One of the main problems..." seems fine to me for setting the context, but I would immediately want him to follow with "Let ..." and state the proper definition. All of the extra fluffiness means I have to do two translations - from the fluffy part to the actual maths and then back again - each time to understand what he is getting at.
In my opinion, great maths writing is both rigourous and engaging. I would use "Calculus" by Michael Spivak as an example. It's really lovely to read but also concise and elegant and the beauty of (and love for) the maths comes through on every page. The author isn't trying to turn it into a short story and it's not padded out with additional rhetorical bullshit like "And now we come to a key player: the group of deck transformations." That sentence makes me want to puke just a little bit.
But all of the above is a matter of opinion. This, for me is a hard nope:
This may require “watering down” the results being described — stating corollaries or special cases instead of the full theorems in their maximal generality. Sometimes you may even need to leave out technical conditions required for the results to really be true.
Like if you want to give a simpler version of something, you can by all means do:
This is known as seanhunter's theorem, which is usually stated as, if blah blah blah...
When x is a real number greater than zero this can be simplified as follows:
If x is the number of minutes spent in a meeting and p is the number of participants, then the expected value of the meeting is given by
v= r/sqrt(x^3p^2) r~N(mu, sigma^2)
... or whatever.
So you give the real version and then the "special case" version that is actually useful most of the time. Like when people give you Fermat's little theorem[1] and they say a^p is congruent with a mod p but that is equivalent to saying if p does not divide a then a^(p-1) congruent with 1 (which is the one you're going to actually use most of the time).