A Brief Dictionary of Phrases Used In
Mathematical Writing

Since authors seldom, if ever, say what they mean, the following glossary is offered to neophytes in mathematical research to help them understand the language that surrounds the formulas. Since mathematical writing, like mathematics, involves many undefined concepts, it seems best to illustrate the usage by interpretation of examples rather than to attempt definition.

ANALOGUE - This is an analogue of: I have to have some excuse for publishing it.

APPLICATIONS - This is of interest in applications: I have to have some excuse for publishing it.

COMPLETE - The proof is now complete: I can't finish it.

DETAILS - I cannot follow the details of X's proof: It's wrong.

DIFFICULT - This problem is difficult: I don't know the answer. (Cf. Trivial)

GENERALITY - Without loss of generality: I have done an easy special case.

IDEAS - To fix the ideas: To consider the only case I can do.

INGENIOUS - X's proof is ingenious: I understand it.

INTEREST - It may be of interest: I have to have some excuse for publishing it.

INTERESTING - X's proof is interesting: I don't understand it.

KNOWN - This is a known result but I reproduce the proof for the convenience of the reader: My paper isn't long enough.

LANGUAGE - PAR ABUS DE Language: In the terminology used by other authors. (Cf. Notation)

NATURAL - It is natural to begin with the following considerations: We have to start somewhere.

NEW - This was proved by X but the following new proof may present points of interest: I can't understand X.

NOTATION - To simplify the notation: It is too much trouble to change now.

OBSERVED - It will be observed that: I hope you have not noticed that.

READER - The details may be left to the reader: I can't do it.

REFEREE - I wish to thank the referee for the suggestions: I loused it up.

STRAIGHTFORWARD - By a straightforward computation: I lost my notes.

TRIVIAL - This problem is trivial: I know the answer. (Cf. difficult)

WELL-KNOWN - This result is well-known: I can't find the reference.

EXERCISES FOR THE STUDENT - Interpret the following:
1. I am indebted to Professor X for stimulating discussions.
2. However, as we have seen.
3. In general.
4. It is easily shown.
5. To be continued.

This article was prepared with the opposition of the National Silence Foundation.