在 MIT 教了大半辈子书，他想跟你分享 10 条经验

Lesson One: You can and will work at a desk for seven hours straight, routinely.

第一课：你能且你要长期进行七个小时的伏案工作。

For several years, I have been teaching 18.30, differential equation, the largest mathematics course at MIT, with more than 300 students. The lectures have been good training in dealing with mass behavior. Every sentence must be perfectly enunciated, preferably twice. Examples on the board must be relevant, if not downright fascinating. Every 15 minutes or so, the lecturer is expected to come up with an interesting aside, joke, historical anecdote, or unusual application of the concept at hand. When a lecturer fails to conform to these inexorable requirements, the students will signify their displeasure by picking by their books and leaving the classroom.

若干年来，我一直在讲授 18.30，微分方程，麻省理工学院最大的数学课程，有 300 多名学生。授课是处理群众行为的良好培训。每个句子都必须完美地读出来，最好是两次。若非极度迷人，黑板上的例子必须是相关的。每隔 15 分钟左右，讲师要想出一个有趣的旁白、笑话、历史轶事，或手头概念的不寻常应用。当讲师不符合这些不可抗拒的要求时，学生就会拿起书本离开教室，以表示他们的不满。

Despite the lecturer’s best efforts, however, it becomes more difficult to hold the attention of the students as the term wears on, and they start falling asleep in class under those circumstances should be a source of satisfaction for a teacher, since it confirms that they have been doing their jobs. There students have been up half the night-maybe all night-finishing problem sets and preparing for their midterm exams.

尽管讲师尽了最大努力，随着学期的推移，吸引学生的注意力变得越来越困难；学生们在这种情况下开始在课堂上睡着…… 这其实应该是教师满意的原因之一，因为这证实了他们一直在做他们的功课。学生们已经熬了半夜 —— 也许是一整夜 —— 完成问题集，为期中考试做准备。

Four courses in science and engineering each term is a heavy workload for anyone; very few students fail to learn, first and foremost, the discipline of intensive and constant work.

每学期四门科学和工程课程对任何人来说都是一个沉重的工作负担；很少有学生学不会最首要的东西 —— 密集和持续工作的纪律。

Lesson Two: You learn what you don’t know you are learning.

第二课：你学到了自己不知道在学的东西。

The second lesson is demonstrated, among other places, in 18.313, a course I teach in advanced probability theory. It is a difficult course, one that compresses the material typically taught in a year into one term, and it includes weekly problem sets that are hard, even by the standards of professional mathematicians. (How hard is that? Well, every few years a student taking the course discovers a new solution to a probability problem that merits publication as a research paper in a refereed journal.)

除其他地方外，第二课在 18.313 中得到了证明 —— 这是我教授的高级概率论课程。这是一门困难的课程，它将通常一年的教学材料压缩到一个学期内，它包括每周的问题集，即使按照专业数学家的标准，也是很难的。（这有多难呢？好吧，每隔几年就有一个选修该课程的学生发现了一个新的概率问题的解决方案，值得作为研究论文发表在权威期刊上。）

Students join forces on the problem sets, and some students benefit more than others from these weekly collective efforts. The most brilliant students will invariably work out all the problems and let other students copy, and I pretend to be annoyed when I learn that this has happened. But I know that by making the effort to understand the solution of a truly difficult problem discovered by one of their peers, students learn more than they would by working out some less demanding exercise.

学生们联合起来做问题集，有些学生从这些每周的集体努力中获益更多。最优秀的学生总是会把所有的问题做出来，让其他学生抄袭，当我得知有这种情况发生时，我假装很恼火。但我知道，通过努力理解一个由他们的同伴发现的真正困难的问题的解决方案，学生学到的东西比他们通过锻炼一些要求不高的练习要多。

Lesson Three: By and large, “knowing how” matters more than “knowing what”.

第三课：总的来说，“知道如何做” 比 “知道是什么” 更重要。（授人以渔 vs. 授人以鱼）

Half a century ago, the philosopher Gilbert Ryle discussed the difference between “knowing how” courses are those in mathematics, the exact sciences, engineering, playing a musical instrument, even sports. “Knowing what” courses are those in the social sciences, the creative arts, the humanities, and those aspects of a discipline that are described as having social value.

半个世纪前，哲学家吉尔伯特·赖尔讨论了 “知道如何做” 的课程与数学、精确科学、工程、演奏乐器，甚至体育课程的区别。“知道什么” 的课程是指社会科学、创造性艺术、人文学科的课程，以及被称为具有社会价值的学科的那些方面。

At the beginning of each term, students meet with their advisors to decide on the courses each will study, and much of the discussion is likely to resolve around whether a student should lighten a heavy load by substituting one or two “knowing what” courses in place of some stiff “knowing how” courses.

在每个学期开始时，学生与他们的顾问会面，决定每个人将学习的课程，讨论的大部分内容可能是围绕学生是否应该用一两门 “知道是什么” 的课程来代替一些僵硬的 “知道如何做” 的课程，从而减轻沉重的负担。

To be sure, the content of “knowing what” courses if often the most memorable. A serious study of the history of United States Constitution or King Lear may well leave a stronger imprint on a student’s character than a course in thermodynamics. Nevertheless, at MIT, “knowing how” is held in higher esteem than “knowing what” by faculty and students alike. Why?

诚然，“知道是什么” 课程的内容往往是最令人难忘的。认真研究《美国宪法》或《李尔王》的历史很可能比热力学课程在学生的性格上留下更深刻的印记。然而，在麻省理工学院，“知道如何做” 比 “知道是什么” 更受教师和学生们的推崇。为什么？

It is my theory that “knowing how” is revered because it can be tested. One can test whether a student can apply quantum mechanics, communicate in French, or clone a gene. It is much more difficult to asses an interpretation of a poem, the negotiation of a complex technical compromise, or grasp of the social dynamics of a small, diverse working group. Where you can test, you can set a high standard of proficiency on which everyone is agreed; where you cannot test precisely, proficiency becomes something of a judgment call.

我的理论是，“知道如何做” 被推崇是因为它可以被测试。人们可以测试一个学生是否能应用量子力学，用法语交流，或克隆基因。要评估一首诗的解释、一个复杂的技术妥协的谈判，或对一个小型的、多样化的工作小组的社会动态的把握，则要困难得多。在可以测试的地方，你可以设定一个每个人都同意的高标准的熟练度；在不能精确测试的地方，熟练度就变成了一种判断的东西。

At certain liberal arts colleges, sports appear to be more important than classroom subjects, and with good reason. A sport may be the only training in “knowing how”-in demonstrating certifiable proficiency-that a student undertakes at those colleges. At MIT, sports are a hobby (however passionately pursued) rather than a central focus because we offer a wide range of absorbing “knowing how” activities.

在某些文理学院，体育似乎比课堂科目更重要，而且有充分的理由。一项运动可能是学生在这些学院进行的唯一 “知道如何做” —— 展示可认证的熟练程度 —— 的培训。在麻省理工学院，体育是一种爱好（无论多么热情地追求），而不是核心重点，因为我们提供了广泛的吸收性 “知道如何” 的活动。

Lesson Four: In science and engineering, you can fool very little of the time.

第四课：在科学和工程领域，你不大可能自欺欺人。

Most of the sweeping generalizations one hears about MIT undergraduates are too outrageous to be taken seriously. The claim that MIT students are naive, however, has struck me as being true, at least in a statistical sense.

人们听到的关于麻省理工学院本科生的一概而论，大多数都太离谱了，无法认真对待。然而，麻省理工学院学生很天真这一说法让我觉得是真的，至少在统计意义上是这样。

Last year, for example, one of our mathematics majors, who had accepted a lucrative offer of employment from a Wall Street firm, telephoned to complain that the politics in his office was “like a soap opera.” More than a few MIT graduates are shocked by their first contact with the professional world after graduation. There is a wide gap between the realities of business, medicine, law, or applied   enginering, for example, and the universe of scientific objectivity and theoretical constructs that is MIT.

例如，去年，我们的一名数学专业学生接受了一家华尔街公司的丰厚就业机会，他打电话抱怨说，他办公室里的政治 “像肥皂剧”。不止几个麻省理工学院的毕业生被他们毕业后与职业世界的第一次接触所震惊。例如，在商业、医学、法律或应用工程的现实与麻省理工学院的科学客观性和理论构建的宇宙之间存在着巨大的差距。

An education in engineering and science is an education in intellectual honesty. Students cannot avoid learning to acknowledge whether or not they have really learned. Once they have taken their first quiz, all MIT undergraduates know dearly they will pay if they fool themselves into believing they know more than is the case.

工程和科学方面的教育是一种智力诚实的教育。学生不可能不知道他们是否真的学到了知识。只要他们参加过一次测验，所有麻省理工学院的本科生都知道，如果他们自欺欺人地认为自己知道的比实际情况多，他们将付出沉重的代价。

On campus, they have been accustomed to people being blunt to a fault about their own limitations-or skills-and those of others. Unfortunately, this intellectual honesty is sometimes interpreted as naivete.

在校园里，他们已经习惯了人们对自己的限制或技能以及其他人的限制直言不讳。不幸的是，这种智力上的诚实有时被解释为天真。

Lesson Five: You don’t have to be a genius to do creative work.

第五课：你不一定非得是个天才才能做创造性的工作。

The idea of genius elaborated during the Romantic Age (late 18th and 19th centuries) has done harm to education. It is demoralizing to give a young person role models of Beethoven, Einstein, and Feynman, presented as saintly figures who moved from insight to insight without a misstep. Scientific biographies often fail to give a realistic description of personality, and thereby create a false idea of scientific work.

浪漫主义时代（18 世纪末和 19 世纪）阐述的关于 “天才” 的想法对教育造成了伤害。给年轻人树立贝多芬、爱因斯坦和费曼的榜样，把他们描述为圣人般的人物，说他们总是能准确无误地从一个洞见跨越到另外一个洞见，是极为令人丧气的。科学传记往往不能对人格进行真实的描述，从而造成对科学工作的错误认识。

Young people will correct any fantasies they have about genius, however, after they come to MIT. As they start doing research with their professors, as many MIT undergraduates do, they learn another healthy lesson, namely, a professor may well behave like a fumbling idiot.

然而，年轻人来到麻省理工学院后，会纠正他们对天才的任何幻想。当他们开始与教授一起做研究时，就像许多麻省理工学院的本科生一样，他们学到了另一个健康的教训，即教授很可能表现得像一个摸不着头脑的白痴。

The drive for excellence and achievement that one finds everywhere at MIT has the democratic effect of placing teachers and students on the same level, where competence is appreciated irrespective of its provenance, Students learn that some of the best ideas arise in groups of scientists and engineers working together, and the source of these ideas can seldom be pinned on specific individuals. The MIT model of scientific work is closer to the communion of artists that was found in the large shops of the Renaissance than to the image of the lonely Romantic genius.

在麻省理工学院随处可见的追求卓越和成就的动力，具有将教师和学生置于同一水平线上的民主效应，在这里，无论其出处如何，能力都会得到赞赏。学生们了解到，一些最好的想法产生于科学家和工程师的团体合作，而这些想法的来源很少可以归咎于具体的个人。麻省理工学院的科学工作模式更接近于文艺复兴时期大商店里的艺术家的交流，而不是孤独的浪漫主义天才的形象。

Lesson Six: You must measure up to a very high level of performance.

第六课：你必须为自己立下极高的标准

I can imagine a propective student or parent asking, “Why should I (or my child) take calculus at MIT rather than at Oshkosh College? Isn’t the material practically identical, no matter where it is taught, while the cost varies a great deal?”

我可以想象，一个潜在的学生或家长会问：“为什么我（或我的孩子）应该在麻省理工学院学习微积分，而不是在奥什科什学院？无论在哪里授课，教材不都是一样的吗，而费用却有很大的不同？”

One answer to this question would be following: One learns a lot more when taking calculus from someone who is doing research in mathematical analysis than from someone who has never published a word on the subject. But this is not the answer; some teachers who is doing research in mathematical analysis than from someone who has never published a word on the subject. But this is not the answer; some teachers who have never done any research are much better at conveying the ideas of calculus than the most brilliant mathematicians.

对这一问题的一个回答是：“从一个正在进行数学分析研究的人那里学习微积分”，要比 “从一个从未发表过一个字的人那里学习同一个科目”，收获要多得多。可实际上这并不是正确答案 —— 这个比较有问题。一些从未做过任何研究的教师在传达微积分的思想方面要比最出色的数学家好得多。

What matters most is the ambiance in which the course is taught; a gifted student will thrive in the company of other gifted students. An MIT undergraduate will be challenged by the level of proficiency that is expected of everyone at MIT, students and faculty. The expectation of high standards is unconsciously absorbed and adopted by the students, and they carry it with them for life.

最重要的是教授课程的氛围；一个有天赋的学生会在其他有天赋的学生的陪伴下茁壮成长。一个麻省理工学院的本科生将受到挑战，因为麻省理工学院的每个人，包括学生和教师，都要达到精通的水平。对高标准的期望被学生不自觉地吸收和采纳，并使他们终生受益。

Lesson seven: The world and your career are unpredictable, so you are better off learning subjects of permanent value.

第七课：世界和你的职业是不可预测的，所以你最好学习具有永久价值的科目。

Some students arrive at MIT with a career plan, many don’t, but it actually doesn’t matter very much either way. Some of the foremost computer scientists of our day received their doctorates in mathematical logic, a branch of mathematics that was once considered farthest removed from applications but that turned out instead to be the key to the development of present-day software. A number of the leading figures in experimental molecular biology received their doctorates in physics. Dramatic career shifts that only a few years ago were the exception are becoming common.

有些学生来到麻省理工学院时有职业规划，很多人没有，但实际上这两种情况都不太重要。我们这个时代最重要的一些计算机科学家是在数理逻辑方面获得博士学位的，数理逻辑是数学的一个分支，曾经被认为是离应用最远的，但结果却成为当今软件发展的关键。实验分子生物学的一些领军人物都是在物理学方面获得的博士学位。几年前还属于例外的戏剧性职业转变正在变得普遍。

Our students will have a harder time finding rewarding jobs than I had when I graduated in the fifties. The skills the market demands, both in research and industry, are subject to capricious shifts. New professions will be created, and old professions will become obsolete with the span of a few years. Today’s college students have good cause to be apprehensive about future.

我们的学生将比我在 50 年代毕业时更难找到有价值的工作。市场所需的技能，无论是在研究领域还是在工业领域，都会发生反复无常的转变。新的职业将被创造出来，而旧的职业将在几年的时间内被淘汰。今天的大学生有充分的理由对未来感到忧虑。

The curriculum that most undergraduates at MIT choose to follow focuses less on current occupational skills than on those fundamental areas of science and engineering that at least likely to be affected by technological changes.

麻省理工学院大多数本科生选择的课程不太注重当前的职业技能，而是注重那些最不可能受到技术变革影响的科学和工程的基本领域。

Lesson Eight: You are never going to catch up, and neither is anyone else.

第八课：你总是跟不上，其他人也一样。

MIT students often complain of being overworked, and they are right. When I look at the schedules of courses my advisees propose at the beginning of each term, I wonder how they can contemplate that much work. My workload was nothing like that when I was an undergraduate.

麻省理工学院的学生经常抱怨工作过度，其实，他们是对的。当我看到我的建议者在每个学期开始时提出的课程表时，我想知道他们怎么能考虑那么多工作。我在读本科时的工作量与此完全不同。

The platitudes about the disappearance of leisure are, unfortunately, true, and faculty members at MIT are as heavily burdened as students. There is some satisfaction, however, for a faculty member in encountering a recent graduate who marvels at the light work load they carry in medical school or law school relative to the grueling schedule they had to maintain during their four years at MIT.

不幸的是，关于休闲消失的陈词滥调是真实的，麻省理工学院的教职员工和学生一样负担沉重。然而，对于一个教员来说，遇到一个刚毕业的学生，惊叹于他们在医学院或法学院的工作负担比他们在麻省理工学院的四年中不得不保持的艰苦的时间表要轻，是有一些满足的。

Lesson Nine: The future belongs to the computer-literate-squared.

第九课：未来属于（懂电脑的人^2^）。

Much has been said about computer literacy, and I suspect you would prefer not to hear more on the subject. Instead, I would like to propose the concept computer-literacy-squared, in other words computer literacy to second degree.

关于计算机扫盲已经说得太多，我猜你不想听到更多关于这个问题的内容。不过，我倒是想提出 “懂电脑的人^2^” 的概念，换句话说，就是把计算机当作第二学位。

A large fraction of MIT undergraduates major in computer science or at least acquire extensive computer skills that are applicable in other fields. In their second year, they catch on to the fact that their required courses in computer science do not provide the whole story. Not because of deficiencies in the syllabus; quite the opposite. The undergraduate curriculum in computer science at MIT is probably the most progressive and advanced such curriculum anywhere. Rather, the students learn that side by side with required courses there is another, hidden curriculum consisting of new ideas just coming into use, new techniques and that spread like wildfire, opening up unsuspected applications that will eventually be adopted into the official curriculum.

麻省理工学院有很大一部分本科生主修计算机科学，或者至少获得了广泛的计算机技能，这些技能适用于其他领域。在第二年，他们意识到计算机科学的必修课程并没有提供全部内容。不是因为教学大纲中的缺陷；恰恰相反。麻省理工学院的计算机科学本科课程可能是任何地方最进步和最先进的此类课程。实际上，学生们了解到的是，在必修课程的旁边还有另一个隐藏的课程，由刚刚投入使用的新想法、新技术组成，它们像野火一样传播，开辟了未曾预料的应用，最终将被纳入正式课程。

Keeping up with this hidden curriculum is what will enable a computer scientist to stay ahead in the field. Those who do not become computer scientists to the second degree risk turning into programmers who will only implement the ideas of others.

跟上这种隐藏的课程，才能使计算机科学家在该领域保持领先地位。那些没有成为第二学位的计算机科学家有可能变成只会实施别人想法的程序员。

Lesson Ten: Mathematics is still the queen of the sciences.

第十课：数学仍然是科学中之王。

Having tried in lessons one through nine to take an unbiased look at the big MIT picture, I’d like to conclude with a plug for my own field, mathematics.

在第一至第九课中，我试图以不偏不倚的眼光看待麻省理工学院的大局，最后我想为我自己的领域 —— 数学 —— 做一个总结。

When an undergraduate asks me whether he or she should major in mathematics rather than in another field that I will simply call X, my answer is the following: “If you major in mathematics, you can switch to X anytime you want to, but not the other way around.”

当一个本科生问我，他或她是否应该主修数学而不是另一个领域，我将简单地称之为 X，我的回答如下。“如果你主修数学，你可以随时转到 X 专业，但反之则行不通。”

Alumni who return to visit invariably complain of not having taken enough math courses while they were undergraduates. It is a fact, confirmed by the history of science since Galileo and Newton, that the more theoretical and removed from immediate applications a scientific topic appears to be, the more likely it is to eventually find the most striking practical applications. Consider number theory, which only 20 years ago was believed to be the most useless chapter of mathematics and is today the core of computer security. The efficient factorization of integers into prime numbers, a topic of seemingly breathtaking obscurity, is now cultivated with equal passion by software desigers and code breakers.

回访的校友无一例外地抱怨他们在读本科时没有修够数学课程。自伽利略和牛顿以来的科学史证实了这样一个事实：一个科学课题看起来越是理论性强、越是远离直接应用，就越有可能最终找到最引人注目的实际应用。考虑一下数论，仅在 20 年前，它被认为是数学中最无用的一章，而今天则是计算机安全的核心。将整数有效地分解为素数，这个似乎令人叹为观止的话题，现在被软件设计者和代码破解者以同样的热情所包围。

I am often asked why there are so few applied mathematicians in the department at MIT. The reason is that all of MIT is one huge applied mathematics department; you can find applied mathematicians in practicially every department at MIT except mathematics.

经常有人问我，为什么麻省理工学院的系里的应用数学家这么少。原因是，整个麻省理工学院是一个巨大的应用数学系；除了数学之外，你几乎可以在麻省理工学院的每一个系都找到应用数学家。

From the Association of Alumni and Alumnae of MIT  April  1997

来自麻省理工学院校友会和校友会的消息 1997 年 4 月