Remember that there is an alternative to revision and

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likely to produce inconsistencies. Remember that there is an alternative to revision and rewriting. It is called omission. If something does not fit in with the flow of the essay or reads badly however often you rewrite it then, perhaps, it should not form part of the essay. The hardest thing for an author to do is to leave out a passage over which he or she has sweated blood — but often it is the right thing to do. How many lectures have you heard which were too short and 7 Since the effect of replacing sin by cos is to produce ‘cosce the effect of replacing cos by cos’. 8 On the other hand a spell checker is invaluable when used with a good dictionary. 9 But keep a copy of the original in case you change your mind. 22
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how many too long? How many books on your shelves are too short and how many too long? 5.9 Know yourself Halmos is one of the great mathematical expositors. Here is some advice from his essay How To Write Mathematics [4]. In the first draft . . . I recommend that you spill your heart, write quickly, violate all rules, write with hate or with pride, be snide, be confused, be ‘funny’ if you must, be unclear, be un- grammatical — just keep on writing. When you come to rewrite, however, and however often that may be necessary, do not edit but rewrite. It is tempting to use a red pencil to indicate inser- tions, deletions, and permutations, but in my experience it leads to catastrophic blunders. Against human impatience, against the all too human partiality everyone feels towards his own words, a red pencil is much too feeble a weapon. You are faced with a first draft that any reader except yourself would find all but un- bearable; you must be merciless about changes of all kinds and, especially, about wholesale omissions. Rewrite means write again — every word. This is attractive advice until you realise that Halmos rewrote (that is wrote again — every word) each of his books three times and followed this by a massive revision. (This is an underestimate, parts of his books were rewritten six or seven times.) Every book that Halmos wrote was a success and some were outstanding. The problem with his advice is that most mathematicians dislike writing, hate revising and consider rewriting a confession of failure. The word processor encourages endless minor changes but discourages root and branch revision. Under these circumstances my advice is as follows. Revision, however thorough you believe it to be, leaves most things unaltered. You may haul large chunks of prose from one place to another but the patterns embedded in those chunks re- main unchanged and the overall structure is altered only in the crudest way. However hard you wield the red pencil most of your sentences will retain the the form you originally gave them. Thus the last draft that you write out in full (and for most mathematicians this will also be the first) must be as perfect as you can make it. If you are dissatisfied with anything, rewrite 23
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it before starting revision. Once you start revision you will find
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