Avoid Words

Many readers will skim over formulas on their first reading of your exposition. Therefore, your sentences should flow smoothly when all but the simplest formulas are replaced by “blah” or some other grunting noise. - Donald Knuth

As a graduate student, I am reading several papers a week trying to keep up with the mathematical physics literature. However, often many interesting papers are so full of linguistic dead weight that the author's intended meaning is obscured. The catchphrases over and over in papers in place of something more unique and memorable; it seems like laziness on part of the author. I'm trying to compile a list of "avoid" words, explain why I think they are bad and how to fix them.

Besides morbid curiousity, there are also linguistic reasons to try an experiment like this. What are words like "let" and "get" - which are ubiquitous - doing in the math lexicon? Mainly, their function is to make math precise, but many other disciplines achieve precise language without becoming quite so baroque.

The Following

It takes two connected ideas and separates them at an arbitrary place. This phrase can be eliminated from almost any sentence without changing the meaning.

Clearly, Obviously, Simply, Trivially

Don't make your readers feel stupid, even if it is clear simple or obvious. To the author and to other experts of field, a statement not require explanation but for outsiders - other mathematicians or scientists outside of math - such a statement might require some thought.

I've found scientific papers move faster than books, meaning they often suppress intermdiate steps in a calculation for the sake of space and clarity.

This book was conceived as a slim monograph, but grew to its present size as I attempted to set down an account of two-dimensional lattice models in statistical mechanics, and how they have been solved. While doing so, I have been pulled in opposite directions. On the one hand I remembered the voice of the graduate student at the conference who said "But you've left out all the working, how do you get from eq (81) to (82)?" On the other hand I knew from experience how many sheets go into the wastepaper basket after even a modest calculuation: there was no way it could all appear in print. - Nick Baxter, preface from ``Exactly Solved Models in Statistical Mechanics"
Sometimes, I wonder if "simply" or "exercises" are meta-information about the complexity of the solution. It's not always easy to tell when something is self-evident and when it isn't.

Thus, Therefore, It Follows That

These connectives try to establish causality between the sentence before and the sentence after. Sometimes, an explanation is lacking. Usually, at this point I'll break out a pencil and paper.

Let, Suppose, Consider

I want to cry when a proof introduces 10 variables names and expects me to keep track of them. Which is easier to read?

Version A

Let X be a manifold, f,g be C functions. Let T and V vector fields on M. Let Φ be a differentiable map from X to Y.

Version B

f,gC functions
T,Vvector fields on M
Φdifferentiable map from X to Y

The Above/Below, See eq. 3.158

Please don't make me run around the paper. If it's worth referening, it may be worth re-iterating. You don't waste that much ink printing the same equation twice and suddenly the paper is more readable.

Intensely Studied, Well-Known, Classical", Well-Studied", Extensively Studied"

Should I be enouraged for discouraged that a theorem is "well-known" or a field is "extensively studied"? How long does it take for something to be "classical"? 5 years, 10, 20 or 50? I feel like you can only hurt the tone of your paper by using these words. What are you trying to tell your readers this way?

"Quick" or "Rapid" Introduction.

Both of these are synonyms for "inadequate".

More words I hate [discussion to be added]:

I'm also devoting an entire section to things "we" do and "one" does in a math paper.

Face it. We all use these words and they are essential to mathematical writing. In fact, it is impossible to write a paper without these words. Still, they suck all the fun out of reading a math paper. I would argue an author loses one reader for every time he uses the word "let". Often, these "avoid words" are crutches put lieu of clearer explanations of our ideas. I read expressions like these as a sign the author don't really get what's going on or how to communicate it. Stronger language ultimately makes for stronger papers.