Best practices for typesetting a math document and its building blocks (definitions, theorems, lemmata)?

Question

This is admittedly a soft question and, to make things worse, the goal of my question might even be controversial. Please bear with me, though.

I'm writing a long math paper with hundreds of math blocks (definitions, theorems, lemmata, remarks, examples, …) and some – though not much – text in between. Let's call that text prose because its only purpose is to serve as rhetorical glue between the math blocks and to provide motivation and guidance. In contrast, the math blocks stand on their own and a reader could in theory only read those, i.e. follow the usual chain of definition – lemma – theorem – proof, and ignore the prose completely. (In particular, variables etc. introduced in the prose are not used in the math blocks and every math block carefully spells out its assumptions.)

Unfortunately, the default amsthm-like style of math papers written in LaTeX doesn't seem to lend itself well to this sort of logical separation since (at least in my opinion) there is little to no optical separation between math blocks and prose. Everything is often just one contiguous text.

For instance, in most papers I read, I find it extremely hard to tell upon first sight where a remark, an example, or a definition ends and where prose starts. In addition, corollaries, remarks and examples – which usually refer to / follow from the math block immediately preceding them – are not typeset in a way which makes this relationship clear. Finally, it is also quite hard sometimes to see which theorems are important and which less so.

I've been thinking about various ways to fix this, i.e. about how to use typography to highlight the overall logical structure and, among others, achieve clear optical separation between math blocks and prose:

• larger verticals margins between math blocks and prose
• separation of subsequent math blocks and/or prose by a horizontal line or by *** or some other typographic ornament
• highlight (some) math blocks with borders / frames
• different indentation/geometry for prose and math blocks
• always ending definitions/remarks/examples with an analogue of the QED tombstone ∎ to demarcate their end
• different fonts for math blocks and prose
• different \parindent for the first line of prose that immediately follows a math block
• start prose with an initial

None of these solutions seems ideal, though (what's best seems to depend very much on the situation – e.g. how many math blocks vs. how much prose), and I have yet to see a math paper where things are typeset beautifully. I am therefore looking for inspiration.

Hence my question:

Can you give examples of math papers or books that, in your opinion, are typeset in a beautiful, non-standard way (maybe even incorporate some of the above fixes) and thereby alleviate or even solve the above issues? Alternatively, are there any best-practice guides on how to solve the above issues typographically?

In the spirit of this question and that one I really hope my question is not off-topic. If it is, I would very much appreciate any help to make it on-topic.

Answer 1

I would second the recommendation for tcolorbox. The documentation has many examples, of which very few look like they would work in a Powerpoint presentation. The package also offers the \tcolorboxenvironment command, so that you can adjust the preamble of an otherwise "regular" document to add the boxes you want throughout the document. For example:

\documentclass{amsart}

\newtheorem{theorem}{Theorem}

\usepackage{tcolorbox}
\tcolorboxenvironment{theorem}{}
\tcolorboxenvironment{proof}{}

\begin{document}

Some text before.

\begin{theorem}
This is my theorem.
\end{theorem}

Some text between.

\begin{proof}
This is my proof
\end{proof}

Some text after.

\end{document}

Having told tcolorbox to box up theorem and proof (the second argument allows you to adjust the default options), you end up with:

Adjusting the default options allows you to color the boxes, or adjust the vertical spacing before, during, or after, or many other things.

Answer 2

Please think hard on what you are trying to do. "Officially" mathematics is all about definitions and proofs. In reality, all that is completely useless if it doesn't help understanding what is meant, how things hang together, why some definition is just so, how to use theorems, what the important problems are. And that requires a lot of text in between.

Think about it: An association of professional mathematicians offers their members (but more generally the whole world) a set of carefully designed tools for one of their principal tasks (writing up their results), and that tool works in a totally different way than what you want to do exactly that. Maybe they are all wrong, but I somehow doubt it...