Making a short summary before a set of paragraphs? Of late I noticed that recent books or long articles tend to make a short summary before every set of paragraphs. For example, we might have:

1. Introduction

We so and so ...

Therefore, so and so ....

What is so and so: Let us consider ...

Properties of so and so: We notice that ...

where every boldfaced phrases is followed by a set of paragraphs. For a real example: 
http://modular.math.washington.edu/edu/2011/581g/misc/Darmon-Diamond-Taylor-Fermats_Last_Theorem.pdf

My questions are:

1) Is this style of writing really a trend? 

2) Is it still a good idea if we are writing an article of moderate length such as a statement of purpose or a short report?

In my opinion, such style seems much more intelligible.
Ah, it's just LateX's \paragraph{} command.

It's not the most widespread style, but I think it's clearer, too, and I suggest you to go on using it.

What problems could there be? I can only foresee issues with journal articles, if you encounter overzealous copy-editors. A good card to play is "if your house style contains \paragraph{}, I am using it".