数学专业英语(Doc版).10.docVIP

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抯 wanted, not pedantry; understanding, not fuss. 牋 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抯 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 搖nfortunately 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: 揘ote, however, that p does not imply q? and then, thinking that you抳e 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抰 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抰 in fact know whether p implies q? (Con