Saturday, April 21, 2007

If you write clearly, then your readers may understand your mathematics and conclude that it isn't profound. Worse, a referee may find your errors. Here are some tips for avoiding these awful possibilities.

1. Never explain why you need all those weird conditions, or what they mean. For example, simply begin your paper with two pages of notations and conditions without explaining that they mean that the varieties you are considering have zero-dimensional boundary. In fact, never explain what you are doing, or why you are doing it. The best-written paper is one in which the reader will not discover what you have proved until he has read the whole paper, if then.

2. Refer to another obscure paper for all the basic (nonstandard) definitions you use, or never explain them at all. This almost guarantees that no one will understand what you are talking about (and makes it easier to use the next tip). In particular, never explain your sign conventions --- if you do, someone may be able to prove that your signs are wrong.

3. When having difficulties proving a theorem, try the method of "variation of definition"---this involves implicitly using more that one definition for a term in the course of a single proof.

4. Use c, a, b respectively to denote elements of sets A, B, C .

5. When using a result in a proof, don't state the result or give a reference. In fact, try to conceal that you are even making use of a nontrivial result.

6. If, in a moment of weakness, you do refer to a paper or book for a result, never say where in the paper or book the result can be found. In addition to making it difficult for the reader to find the result, this makes it almost impossible for anyone to prove that the result isn't actually there. Alternatively, instead of referring to the correct paper for a result, refer to an earlier paper, which contains only a weaker result.

7. Especially in long articles or books, number your theorems, propositions, corollaries, definitions, remarks, etc. separately. That way, no reader will have the patience to track down your internal references.

8. Write A==>B==>C==>D when you mean (A==>B)==>(C==>D), or (A==>(B==>C))==>D, or .... Also, always muddle your quantifiers.

9. Begin and end sentences with symbols wherever possible. Since periods are almost invisible (and may be mistaken for a mathematical symbol), most readers won't even notice that you've started a new sentence. Also, where possible, attach superscripts signalling footnotes to mathematical symbols rather than words.

10. Write "so that" when you mean "such that" and "which" when you mean "that". Always prefer the ambiguous expression to the unambiguous and the imprecise to the precise. It is the readers task to determine what you mean; it is not yours to express it.

11. If all else fails, write in German.