Is there a way to improve the readability of equations in research papers?

Question

I read a lot of computer science papers, and have to understand a lot of equations. Most of the time the concept is so easy, that someone could explain it to me in 5 minutes. I one the other hand need up to an hour to get it.

It is difficult for me to search for the variables in the text, and often I print the paper out and write the meanings of each variable down on the side.

My questions:

So why is it not common to make equations and algorithms more readable?

Is there some PDF reader plugin which highlights the variables in text? Any tips on how to improve in reading such papers?

Why do authors not add an additional list to each equation with a list and explanation of each variable. Should I do that?

Answer 1

I do not believe that the problem is fundamentally about space, but rather is a cultural problem that stems from three things:

1. Reviewers do not demand clarity in their mathematics
2. There is often a perception that "fancy" or "difficult" math means more important science (related to #1)
3. Really clear presentation of mathematics is difficult and takes a lot of work ("I would have written a shorter letter, but I did not have the time.")

Ultimately, a community tends to get what it rewards. There is no reason that math must be impenetrable. Even if one is faced with a space problem, you can play the same sort of games that you do with figures and data in order to fit. Right now, however, it is typically understood and accepted that you don't have to do that with your mathematics. In fact, some scientific communities will punish a researcher for presenting mathematics more clearly, because it makes the work look "less significant."

Technology cannot help solve this, because ultimately it is a problem of human communication. Anyone who is bothered by mathematical impenetrability can, however, take their own small steps towards changing this culture:

In your own work:

1. Include tables and clear explanations in your papers.
2. Use as few symbols as possible, and choose the symbols to improve clarity, e.g., matching the symbol to the first letter of its description.
3. Buffer your equations with explanatory prose that restates their content in plain English.

When considering other people's work:

1. Call out mathematical impenetrability as a reviewer
2. Ask for tables, clear prose, etc. in the papers that you review
3. View the mathematical impenetrability of a work as a flaw rather than a good thing.

This is a very difficult problem, and unlikely to change any time soon, but it can be made better one paper at a time. Moreover, it is my belief (and experience), that clearer mathematics can make for a higher impact and better cited paper, so it will likely be valuable to you in the short term as well, unless you are in a community that has a toxic relationship to mathematical impenetrability.

Answer 2

So why is it not common to make equations and algorithms more readable?

The simple reason is paper space constraints. You can only add so many reference tables and clearly separated equations into a paper before the page limit runs out. And given that many CS papers do not only consist of maths, but also need to have some space for a good evaluation, comprehensive related work, and various other sections, paper space is often at a premium, even at journals.

(and, given that most authors are really used to writing papers this way, they often also keep up the same style in those journals without an explicit page limit)

Is there some PDF reader plugin which highlights the variables in text? Any tips on how to improve in reading such papers?

I doubt that there is a plugin for that, but doing what you are already doing (keeping notes with the meaning of the more important definitions and assumptions) seems like a pretty good start to me.

Why do authors not add an additional list to each equation with a list and explanation of each variable. Should I do that?

If you have the space in your manuscripts, sure - whatever helps the readability of the paper.

Answer 3

I love the LaTeX package \hyperref. There you can link every variable to its definition. (If you use \usepackage[hidelinks]{hyperref} it does not change the visual appearance of your text, but makes variables clickable or you can color the links.)

You can link other symbols to their definition too (e.g. see http://docdro.id/HZMP7Uy from https://tex.stackexchange.com/a/360871/128042). See https://www.overleaf.com/read/mbbqrdpwbqfk for a simple code-example.

The advantage of this solution is that there is no additional distracting content that might annoy experienced reader that are familiar with the used notation, but those reader who forgot the meaning of a certain variable can just click on it.

Additionally, I personally think, sometimes there would be even more possibilities to improve readability by using

1. \underbrace to explain certain terms,
2. \overset like $a\overset{\text{Th. 1}}{=}b+c$ to indicate that a=b+c holds true because of Theorem 1.,
3. highlithing/lowlingthing to indicate more, and less important parts of complicated equations,
4. and probably many other ideas ...,

but every time you do something creative/unconventional, you will have opponents. I use many of this tools and often get very positive feedback in return, but some people don't accept unconventional things which definitely makes it harder to get accepted to certain journals.

At least \hyperref is accepted or even recommended by the majority of the scientific community.