英语翻译0.PrefaceThis is a subjective essay,and its title is misleading; a more honest title might be HOW I WRITE MATHEMATICS.It started with a committee of the American Mathematical Society,on which I served for a brief time,but it quickly becam

英语翻译0.PrefaceThis is a subjective essay,and its title is misleading; a more honest title might be HOW I WRITE MATHEMATICS.It started with a committee of the American Mathematical Society,on which I served for a brief time,but it quickly becam
英语翻译
0.Preface
This is a subjective essay,and its title is misleading; a more honest title might be HOW I WRITE MATHEMATICS.It started with a committee of the American Mathematical Society,on which I served for a brief time,but it quickly became a private project that ran away with me.In an effort to bring it under control I asked a few friends to read it and criticize it.The criticisms were excellent; they were sharp,honest,and constructive; and they were contradictory.“Not enough concrete examples” said one; “don’t agree that more concrete examples are needed” said another.“Too long” said one; “maybe more is needed” said another.there are traditional (and effective) methods of minimizing the tediousness of long proofs,such as breaking them up in a series of lemmas” said one.“One of the things that irritates me greatly is the custom (especially of beginners) to present a proof as a long series of elaborately stated,utterly boring lemmas” said another.There was one thing that most of my advisors agreed on; the writing of such an essay is bound to be a thankless task.Advisor 1:“By the time a mathematician has written his second paper,he is convinced he knows how to write papers,and would react to advice with impatience.” Advisor 2:“All of us,I think,feel secretly that if we but bothered we could be really first rate expositors.People who are quite modest about their mathematics will get their dander up if their ability to write well is questioned.” Advisor 3 used the strongest language; he warned me that since I cannot possibly display great intellectual depth in a discussion of matters of technique,I should not be surprised at “the scorn you may reap from some of our more supercilious colleagues.” My advisors are established and well known mathematicians.A credit line from me here wouldn’t add a thing to their stature,but my possible misunderstanding,misplacing,and misapplying their advice might cause them annoyance and embarrassment.That is why Idecided on the unscholarly procedure of nameless quotations and the expression of nameless thanks.I am not the less grateful for that,and not the less eager to acknowledge that without their help this essay would have been worse.“Hier stehe ich; ich kann nicht anders.”

英语翻译0.PrefaceThis is a subjective essay,and its title is misleading; a more honest title might be HOW I WRITE MATHEMATICS.It started with a committee of the American Mathematical Society,on which I served for a brief time,but it quickly becam
0.序言
这是一个主观篇文章,它的标题是误导;更诚实的标题可能记数学.它是由一个委员会由美国数学协会,我曾在一段短暂的时间内,但是,很快就一个私人的项目,带走了我.为了把火势控制住我问了他几个朋友来读它,批判.这些批评;他们的急剧、诚信、建设性的,他们也矛盾."不够具体的例子”一个人说;“不同意说更具体的例子是需要”另一个说.“太长”一个人说,“也许还需要another.说:“有传统的(和有效的最小化为目标等方法证明无聊乏味,如打破长期在一系列的lemmas”一个说,“其中的事情,这让我很是习惯(尤其是初学者)提出一个证实一长串的精心说,完全枯燥的lemmas”另一个说.有一件事情,大多数我的顾问们同意了;写这种一篇文章,必然会出现“费力不讨好”.顾问一声:“当一个数学家写了他的第二篇论文中,他相信他知道如何写的文件弄乱了,将对建议不耐烦.”顾问2:“所有的人,我想,觉得秘密,如果我们但打扰我们真的可以一流的expositors.谦虚的人对他们的数学将获得他们的皮屑,如果他们的能力,写好质疑.”顾问3用严厉的语言,他警告我,因为我不可能表现出极大的讨论知识深度技术的问题,我不应对此感到惊讶的轻蔑,你收”我们的更高傲的同事."我的顾问,建立了相应的众所周知的数学家.从我信用额度在这里不会加上东西向的头衔,但我的误解,遗忘,misapplying他们的建议可能使他们烦恼,尴尬.我