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Today I want to bring you 10 life advices brought by Professor Gian-Carlo Rota (Jian-Carlo Rota), the only professor of mathematics and philosophy at MIT so far.
Lesson One
You can and will work at a desk for seven hours straight, routinely.
You can and will long-term 7-hour desk work
For many years, I have taught 18.30, a differential course that also has the largest number of students in the MIT math department. To what extent? There are more than 300 students taking this course at any one time.
This course can train teachers to be more comfortable when facing many students. In this class, everything they say must be pronounced clearly and loudly—ideally twice, so that everyone in the audience can hear it. Even if the examples on the blackboard are not compelling enough, they should help students understand as much as possible.
Not only that, but teachers are ideally able to shake out a piece of baggage every 15 minutes or so, be it a digression, a joke, an anecdote from history, or an unusual application of the concept they are currently explaining. And when a teacher fails to meet these requirements, students respond by bringing books and leaving the classroom to express their displeasure.
However, despite the best efforts of teachers, as the semester passed, it became more and more difficult to keep students' attention in class, and more people began to fall asleep in class .
But from another point of view, this may also become a source of a sense of accomplishment for teachers, because it proves that they are not lazy as teachers-students are working all day long to solve heavy homework and mid-term exams Studying all night (not kidding).
Taking four science and engineering classes a semester is a lot of work for anyone. Because of this, almost all MIT students have learned this, and most importantly, the ability to perform high-intensity and continuous work.
Lesson Two
You learn what you don’t know you are learning.
You learn something without knowing it.
The second thing I learned from MIT can be illustrated with the example of another class I teach.
The course is 18.313, an advanced probability theory course. The course is difficult not only because it condenses into one semester what would normally be taught in a year, but also because it requires students to write a weekly homework assignment that would be difficult even for a professional mathematician ——It is so difficult that every few years students in this course can publish a journal paper when they find a new solution to the problem.
The students in the class worked together on this problematic assignment, and some of them benefited more from it than others. Those students who are the brightest can always complete all the exercises, and then let other students copy theirs.
I always pretend to be distressed by this, but in reality, I know that when students try to understand the solution to a really difficult problem from their classmates, they learn more More.
Lesson Three
By and large, “knowing how” matters more than “knowing what.”
Teaching a man to fish is worse than giving him a fish
Half a century ago, the philosopher Gilbert Lyell discussed the difference between those lessons of "know how" and those of "knowledge of facts".
"Know how" courses include exact sciences like math, engineering, playing an instrument, and even sports; while "factual knowledge" courses include social sciences, creative arts, humanities, etc., and those described as having "social value." subject.
At the beginning of each semester, students meet with their academic advisors to decide which courses they will take, and many times the discussion will focus on whether students should replace some "know how" courses with "Factual knowledge" classes, through which they can often take some of the course load off.
Admittedly, the "facts" lessons are sometimes more memorable. A serious study of the U.S. Constitution or King Lear is likely to leave a more profound impression on the character and conduct of a student than a course in thermodynamics. Nevertheless, at MIT, both teachers and students generally value "know how" classes more.
why? In my opinion, this is because "know how" courses are more likely to test students' mastery. We can test whether a student can apply quantum mechanics, communicate in French or clone a gene. However, it is much more difficult to assess a student's interpretation of a poem, the negotiation of a complex technical project, or the study of the social dynamics of a small and diverse working group.
In those subject areas that are easy to test, we can establish a high standard that everyone recognizes to evaluate everyone's mastery; while in those subject areas that are not easy to accurately test, whether a person has mastered and proficient in this knowledge depends It just depends on individual subjective judgment.
In some liberal arts colleges, outdoor sports are more important than some in-classroom academic subjects, and there are reasons for that. In these schools, outdoor sports may be the only training for students in "knowing how to do it"-it is only in this project that they can give accurate tests of mastery.
At MIT, sports are just a "hobby" (although many people love it madly), because our school provides students with many activities that train them to "know how to do it".
Lesson Four
In science and engineering, you can fool very little of the time.
In science and engineering, it's hard to fish in troubled waters.
Most of the rumors people hear about MIT graduates are not that reliable. However, I realized that one of the rumors was true, and that was that MIT students were naive—at least in a statistical sense.
For example, last year, one of our mathematics graduates who was admitted by a Wall Street company called us and complained that his company's office "politics" was like a soap opera. And he was far from the only one who was shocked after his first contact with the workplace after graduation, but many MIT students.
The environment of MIT - an ideal world centered on scientific objectivity and theory construction - has to be said to have a considerable gap between it and the realities of industries such as business, medicine, law or applied engineering.
An education in science or engineering is an education of intellectual honesty. Among them, what students inevitably have to face is the fact of knowing whether they have learned or not. Especially after the quiz, all MIT undergrads know that if they cheat themselves into learning something they didn't learn, they will pay the price.
On campus, they are used to being unabashed and outspoken about their own or other people's faults and flaws. Unfortunately, this intellectual honesty is often dismissed as naive.
Lesson Five
You don’t have to be a genius to do creative work.
Geniuses are not the only ones who can do creative work.
Genius was an overemphasized concept during the Romantic era (late eighteenth to nineteenth centuries), to the detriment of our education today.
That era molded Beethoven, Einstein, Feynman and others into saints. They continued to succeed and never made mistakes in their insight into the world again and again, and today's young people take them as models. What about people getting discouraged? Those scientific biographies have always been unable to realistically describe the personalities of scientists, so that many people have misunderstood scientific work.
However, after coming to MIT, young people are quick to dismantle their own illusions about genius and correct these misconceptions. And when they, like other MIT students, start doing research with their professors, they learn the new positive lesson that their professors can act like bumbling idiots themselves.
At MIT, the quest for excellence and achievement is ubiquitous, and this atmosphere has a democratic effect that puts faculty and students on the same level and makes ability appreciated for its own sake, regardless of its source. Students will discover that many great ideas come from teams of scientists and engineers working together, and very little is attributed to a specific individual.
If you want to describe it, MIT's scientific work model is closer to the communication and fusion between artists in the large workshops of the Renaissance, rather than the image of a lonely romantic genius.
Lesson Six
You must measure up to a very high level of performance.
You must set high standards for yourself.
I can imagine some students and parents asking: "Why do I (my child) have to study calculus at MIT? Is the University of Wisconsin not good? No matter which school you study calculus, the concepts you learn are not the same. Is it the same? But it costs more to go to MIT.”
I've seen a few answers to this question, but none of them seem to hit the point. They may think:
You will learn more about calculus from someone who has devoted himself to the study of mathematical analysis than from someone who has never published in the field.
Some teachers who devote themselves to mathematical analysis will teach better than those who have never published in this field.
There are teachers who have never studied the subject in any depth, but do a better job than the most eminent mathematicians at conveying the ideas of the subject of calculus.
In my opinion, the above views are biased. Why do you have to study at MIT if you have the conditions? I think the most important point is that the teaching atmosphere of the subjects is different. A group of talented students studying together will complement each other and achieve each other.
Because of the halo of graduating from MIT, graduates will receive different scrutiny and expectations. The expectation of high standards is absorbed and accepted by students unconsciously, and it stays with them throughout their lives.
Lesson Seven
The world and your career are unpredictable, so you are better off learning subjects of permanent value.
The world and your career can be unpredictable, so it's best to study subjects that will last you a lifetime
Some students set foot on MIT's campus with a clear career plan in mind, and some didn't, but really, neither really matters. In this day and age, some of our most cutting-edge computer scientists have PhDs in mathematical logic, a branch of mathematics that was once considered the least likely to apply but is now a critical branch of software development. At the same time, many of the leading figures in experimental molecular biology started out as PhDs in physics.
It's becoming more and more common for people to change career directions dramatically in just a few years.
Finding meaningful work is easier than it is today than it was in the 1950s when I was looking for a job. The skills needed in the marketplace, both in research and industry, are highly variable. New jobs are created and old ones are eliminated. In this way, today's college students do have reason to feel uneasy about the future.
Therefore, I suggest that most MIT undergraduate students should not choose those current popular vocational skills that are more likely to be changed by technology when making major choices, but should choose basic fields such as science or engineering.
Lesson Eight
You are never going to catch up, and neither is anyone else.
You can never catch up with others, and others can't catch up with you.
Students at MIT often complain that the coursework is too heavy, and in all fairness, they are right. Every time before the start of a semester, as an instructor, when I see the timetable made by the students, I always sigh how they complete such a heavy coursework. I think back then when I was still an undergraduate, my workload was not so heavy at all. Many people say that in this era, leisure in our lives is gone forever. Sadly, it's true that MIT's faculty is just as heavily burdened as the students above. But maybe there are some good things, like when a faculty member recently met with MIT grads who went on to medical or law school and said that compared to the hardships of the past four years at MIT, the workload of medical school and law school is surprisingly small. They feel much more relaxed.
Lesson Nine
The future belongs to the computer-literate-squared.
The future belongs to the "square computing power".
So much has been said about computer power before this that I guess you don't want to hear more. So what I want to propose here is the concept of "squared computing power", in other words, higher order computing power. It is well known that many undergraduates at MIT are majoring in computer science, and many of them also have computer skills that can be applied to other fields if they do not major in this major. And by the time these people reach their sophomore year, they will find that the required computer science courses in school do not provide all the content of this discipline. ——This is not to say that there are gaps and deficiencies in the syllabus. On the contrary, MIT's computer science courses are probably the most advanced and advanced in the world. This is to say that students will also discover their own "hidden lessons" while studying the required courses. These courses contain new ideas and techniques that have just been applied, and these ideas and techniques spread and spread like wildfire, and soon bring new and unexpected applications, which will eventually be included in the in the school's official curriculum. If a computer scientist wants to maintain a leading position in this field, he must constantly update these "hidden lessons" and keep pace with the times. And those who don't have the "square computer ability" to become computer scientists end up only programmers applying other people's ideas.
Lesson Ten
Mathematics is still the queen of the sciences.
Math still trumps all science.
In the first nine principles, I tried to look at MIT as a whole from an objective and fair perspective, and finally, I decided to make an advertisement for my own field-mathematics as a summary. Whenever an undergraduate student asks me if they should major in mathematics instead of any other arbitrary major X, I always reply with the following line: "If you major in mathematics, you can change majors at any time learning, but vice versa, it won’t work.”
- Attached to the original text:
10 Lessons of an MIT Education
by Gian-Carlo Rota
Lesson One: You can and will work at a desk for seven hours straight, routinely. 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.
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.
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.
Lesson Two: You learn what you don’t know you are learning. 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.)
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.
Lesson Three: By and large, “knowing how” matters more than “knowing what.” 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.
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.
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?
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.
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.
Lesson Four: In science and engineering, you can fool very little of the time. 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.
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.
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.
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.
Lesson Five: You don’t have to be a genius to do creative work. 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.
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.
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.
Lesson Six: You must measure up to a very high level of performance. 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?”
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.
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.
Lesson seven: The world and your career are unpredictable, so you are better off learning subjects of permanent value. 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.
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.
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.
Lesson Eight: You are never going to catch up, and neither is anyone else. 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.
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.
Lesson Nine: The future belongs to the computer-literate-squared. 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.
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.
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.
Lesson Ten: Mathematics is still the queen of the sciences. 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.
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.”
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.
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.
From the Association of Alumni and Alumnae of MIT April 1997
- References:
10 Lessons of an MIT Education by Gian-Carlo Rota
10 things he learned from teaching at MIT for most of his life