学专业英语－How to Write Mathematics?
How to Write Mathematics?
------ Honesty is the Best Policy
The purpose of using good mathematical language is, of course, to make the understanding of the subject easy for the reader, and perhaps even pleasant. The style should be good not in the sense of flashy brilliance, but good in the sense of perfect unobtrusiveness. The purpose is to smooth the reader’s wanted, not pedantry; understanding, not fuss.
  The emphasis in the preceding paragraph, while perhaps necessary, might seem to point in an undesirable direction, and I hasten to correct a possible misinterpretation. While avoiding pedantry and fuss, I do not want to avoid rigor and precision; I believe that these aims are reconcilable. I do not mean to advise a young author to be very so slightly but very very cleverly dishonest and to gloss over difficulties. Sometimes, for instance, there may be no better way to get a result than a cumbersome computation. In that case it is the author’s duty
to carry it out, in public; the he can do to alleviate it is to extend his sympathy to the reader by some phrase such as “unfortunately the only known proof is the following cumbersome computation.”
Here is the sort of the thing I mean by less than complete honesty. At a certain point, having proudly proved a proposition P, you feel moved to say: “Note, however, that p does not imply q”, and then, thinking that you’ve done a good expository job, go happily on to other things. Your motives may be perfectly pure, but the reader may feel cheated just the same. If he knew all about the subject, he wouldn’t be reading you; for him the nonimplication is, quite likely, unsupported. Is it obvious? (Say so.) Will a counterexample be supplied later? (Promise it now.) Is it a standard present purposes irrelevant part of the literature? (Give a reference.) Or, horrible dictum, do you merely mean that you have tried to derive q from p, you failed, and you don’t in fact know whether p implies q? (Confess immediately.) any event: take the reader into your confidence.
There is nothing wrong with often derided “obvious” and “easy to see”, but there are certain
minimal rules to their use. Surely when you wrote that something was obvious, you thought it was. When, a month, or two months, or six months later, you picked up the manuscript and re-read it, did you still think that something was obvious? (A few months’ ripening always improves manuscripts.) When you explained it to a friend, or to a seminar, was the something at issue accepted as obvious? (Or did someone question it and subside, muttering, when you reassured him? Did your assurance demonstration or intimidation?) the obvious answers to these rhetorical questions are among the rules that should control the use of “ obvious”. There is the most frequent source of mathematical error: make that the “ obvious” is true.
It should go without saying that you are not setting out to hide facts from the reader: you are writing to uncover them. What I am saying now is that you should not hide the status of your statements and your attitude toward them either. Whenever you tell him something, tell him where it stands: this has been proved, that hasn’t, this will be proved, that won’t. Emphasize the important and minimize the trivial. The reason saying that they are obvious is to put them in proper perspecti e for the uninitiated. Even if your saying so makes an occ
asional reader angry at you, a good purpose is served by your telling him how you view the matter. But, of course, you must obey the rules. Don’t let the reader down; he wants to believe in you. Pretentiousness, bluff, and concealment may not get caught out immediately, but most readers will soon sense that there is something wrong, and they will blame neither the facts nor themselves, but quite properly, the author. Complete honesty makes for greatest clarity.
                                                    ---------Paul R.Haqlmos
vocabulary
flashy 一闪的                            counter-example 反例                   
unobtrusiveness 谦虚                    dictum 断言；格言
forestall 阻止，先下手                  deride嘲弄
anticipate 预见                          subside沉静
pedantry 迂腐；卖弄学问                  mutter出怨言，喃喃自语
fuss 小题大做                            intimidation威下
reconcilable 使一致的                    rhetorical合符修辞学的
gloss  types是什么意思掩饰                              pretentiousness自命不凡
alleviate 减轻，缓和                    bluff 欺骗
implication 包含，含意                  concealment隐匿               
notes
1.      本课文选自美国数学学会出版的小册子How to write mathematics 中Paul R.Halmos. 的文章第9节
2.      The purpose is smooth the reader’ way, to anticipates his difficulties and to forestall them. Clarity is what’s wanted, not pedantry; understanding, not fuss.

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