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.