I am a math major, but sometimes I read the stuffy language in these papers and I really crack up. The worst part is, when I start writing I do exactly the same thing. Certain phrases used over and over, that are used to make the paper sound more logical and academic, here is one:
We proceed to a further generalization, ... which incorporates information about two [arrangements of circles]... which naturally arises from an analogous result in spherical geometry, which is how we discovered it.
It is from one of my favorite papers on geometry, it has lot of nice picture . For everyone's sake, I have omitted lots of jargon and adapted a short paragraph into the above unwieldy sentence.
Math statements build on top of each other, and in this paper the different version of the same statement (about circles) are presented is towards increasing generality. The tone is appropriate for their audience - other mathematicians.
What is more common language explain such logical progressions? How do I explain that logical progression without sounding like I was born in the 18th century?
For reference, the original statement of the theorem was written as a poem. Soddy's A Kiss Precise:
For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.
Though their intrigue left Euclid dumb
There's now no need for rule of thumb.
Since zero bend's a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.