What is general style to write theorem and proof?

Question

In the amsthm LaTeX package guide -written by the American Mathematical Society-, there are three default styles to write Theorem | Proposition | Lemma | Corollary | Definition | Example | Exercise | Remark | Note | Case

• plain: italic text, extra space above and below; for Theorem | Proposition | Lemma | Corollary

• definition: upright text, extra space above and below; Definition | Example | Exercise

• remark: upright text, no extra space above or below, for Remark | Note | Case

So Are these styles are the default for all the prestigious scientific journals?

Or the question in another way, Is the style of writing Theorems consistent for all the prestigious scientific journals?

Answer 1

Typically each journal will provide their own style file. Sometimes these will provide pre-defined environments for theorems/definitions/etc, in which case they'll look however they look.

If the stylefile does not already include the environments, authors will usually import amsthm and use the environment styles provided there. However, it is not obligatory to use the environment styles in the way you've set out. My personal preference is to use the "definition"-style also for theorems etc, and this does not seem to be too weird of a position.