10 Lessons of an MIT Education

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. Thelectures have been good training in dealing with mass behavior. Everysentence must be perfectly enunciated, preferably twice. Examples onthe board must be relevant, if not downright fascinating. Every 15minutes or so, the lecturer is expected to come up with an interestingaside, joke, historical anecdote, or unusual application of the conceptat hand. When a lecturer fails to conform to these inexorablerequirements, the students will signify their displeasure by picking bytheir books and leaving the classroom.



Despite the lecturer'sbest efforts, however, it becomes more difficult to hold the attentionof the students as the term wears on, and they start falling asleep inclass under those circumstances should be a source of satisfaction fora teacher, since it confirms that they have been doing their jobs.There students have been up half the night-maybe all night-finishingproblem sets and preparing for their midterm exams.



Four coursesin science and engineering each term is a heavy workload for anyone;very few students fail to learn, first and foremost, the discipline ofintensive 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, acourse I teach in advanced probability theory. It is a difficultcourse, one that compresses the material typically taught in a yearinto one term, and it includes weekly problem sets that are hard, evenby the standards of professional mathematicians. (How hard is that?Well, every few years a student taking the course discovers a newsolution to a probability problem that merits publication as a researchpaper in a refereed journal.)



Students join forces on theproblem sets, and some students benefit more than others from theseweekly collective efforts. The most brilliant students will invariablywork out all the problems and let other students copy, and I pretend tobe annoyed when I learn that this has happened. But I know that bymaking the effort to understand the solution of a truly difficultproblem discovered by one of their peers, students learn more than theywould 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 thedifference between "knowing how" courses are those in mathematics, theexact sciences, engineering, playing a musical instrument, even sports."Knowing what" courses are those in the social sciences, the creativearts, the humanities, and those aspects of a discipline that aredescribed as having social value.



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



Tobe sure, the content of "knowing what" courses if often the mostmemorable. A serious study of the history of United States Constitutionor King Lear may well leave a stronger imprint on a student's characterthan a course in thermodynamics. Nevertheless, at MIT, "knowing how" isheld in higher esteem than "knowing what" by faculty and studentsalike. Why?



It is my theory that "knowing how" is reveredbecause it can be tested. One can test whether a student can applyquantum mechanics, communicate in French, or clone a gene. It is muchmore difficult to asses an interpretation of a poem, the negotiation ofa complex technical compromise, or grasp of the social dynamics of asmall, diverse working group. Where you can test, you can set a highstandard of proficiency on which everyone is agreed; where you cannottest precisely, proficiency becomes something of a judgment call.



Atcertain liberal arts colleges, sports appear to be more important thanclassroom subjects, and with good reason. A sport may be the onlytraining in "knowing how"-in demonstrating certifiable proficiency-thata student undertakes at those colleges. At MIT, sports are a hobby(however passionately pursued) rather than a central focus because weoffer a wide range of absorbing "knowing how" activities.



Lesson Four: In science and engineering, you can fool very little of the time. Mostof the sweeping generalizations one hears about MIT undergraduates aretoo outrageous to be taken seriously. The claim that MIT students arenaive, however, has struck me as being true, at least in a statisticalsense.



Last year, for example, one of our mathematics majors,who had accepted a lucrative offer of employment from a Wall Streetfirm, telephoned to complain that the politics in his office was "likea soap opera." More than a few MIT graduates are shocked by their firstcontact with the professional world after graduation. There is a widegap between the realities of business, medicine, law, or appliedenginering, for example, and the universe of scientific objectivity andtheoretical constructs that is MIT.



An education in engineeringand science is an education in intellectual honesty. Students cannotavoid learning to acknowledge whether or not they have really learned.Once they have taken their first quiz, all MIT undergraduates knowdearly they will pay if they fool themselves into believing they knowmore than is the case.



On campus, they have been accustomed topeople being blunt to a fault about their own limitations-or skills-andthose of others. Unfortunately, this intellectual honesty is sometimesinterpreted 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 and19th centuries) has done harm to education. It is demoralizing to givea young person role models of Beethoven, Einstein, and Feynman,presented as saintly figures who moved from insight to insight withouta misstep. Scientific biographies often fail to give a realisticdescription of personality, and thereby create a false idea ofscientific work.



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



The drive for excellence and achievement thatone finds everywhere at MIT has the democratic effect of placingteachers and students on the same level, where competence isappreciated irrespective of its provenance, Students learn that some ofthe best ideas arise in groups of scientists and engineers workingtogether, and the source of these ideas can seldom be pinned onspecific individuals. The MIT model of scientific work is closer to thecommunion of artists that was found in the large shops of theRenaissance 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 (ormy child) take calculus at MIT rather than at Oshkosh College? Isn'tthe material practically identical, no matter where it is taught, whilethe cost varies a great deal?"



One answer to this question wouldbe following: One learns a lot more when taking calculus from someonewho is doing research in mathematical analysis than from someone whohas never published a word on the subject. But this is not the answer;some teachers who is doing research in mathematical analysis than fromsomeone who has never published a word on the subject. But this is notthe answer; some teachers who have never done any research are muchbetter at conveying the ideas of calculus than the most brilliantmathematicians.



What matters most is the ambiance in which thecourse is taught; a gifted student will thrive in the company of othergifted students. An MIT undergraduate will be challenged by the levelof proficiency that is expected of everyone at MIT, students andfaculty. The expectation of high standards is unconsciously absorbedand 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 itactually doesn't matter very much either way. Some of the foremostcomputer scientists of our day received their doctorates inmathematical logic, a branch of mathematics that was once consideredfarthest removed from applications but that turned out instead to bethe key to the development of present-day software. A number of theleading figures in experimental molecular biology received theirdoctorates in physics. Dramatic career shifts that only a few years agowere the exception are becoming common.



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



The curriculum that most undergraduates at MIT choose tofollow focuses less on current occupational skills than on thosefundamental areas of science and engineering that at least likely to beaffected by technological changes.



Lesson Eight: You are never going to catch up, and neither is anyone else. MITstudents often complain of being overworked, and they are right. When Ilook at the schedules of courses my advisees propose at the beginningof each term, I wonder how they can contemplate that much work. Myworkload was nothing like that when I was an undergraduate.



Theplatitudes about the disappearance of leisure are, unfortunately, true,and faculty members at MIT are as heavily burdened as students. Thereis some satisfaction, however, for a faculty member in encountering arecent graduate who marvels at the light work load they carry inmedical school or law school relative to the grueling schedule they hadto maintain during their four years at MIT.



Lesson Nine: The future belongs to the computer-literate-squared. Muchhas been said about computer literacy, and I suspect you would prefernot to hear more on the subject. Instead, I would like to propose theconcept computer-literacy-squared, in other words computer literacy tosecond degree.



A large fraction of MIT undergraduates major incomputer science or at least acquire extensive computer skills that areapplicable in other fields. In their second year, they catch on to thefact that their required courses in computer science do not provide thewhole story. Not because of deficiencies in the syllabus; quite theopposite. The undergraduate curriculum in computer science at MIT isprobably the most progressive and advanced such curriculum anywhere.Rather, the students learn that side by side with required coursesthere is another, hidden curriculum consisting of new ideas just cominginto use, new techniques and that spread like wildfire, opening upunsuspected applications that will eventually be adopted into theofficial curriculum.



Keeping up with this hidden curriculum iswhat will enable a computer scientist to stay ahead in the field. Thosewho do not become computer scientists to the second degree risk turninginto 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 atthe big MIT picture, I'd like to conclude with a plug for my own field,mathematics.



When an undergraduate asks me whether he or sheshould major in mathematics rather than in another field that I willsimply call X, my answer is the following: "If you major inmathematics, you can switch to X anytime you want to, but not the otherway around."



Alumni who return to visit invariably complain ofnot having taken enough math courses while they were undergraduates. Itis a fact, confirmed by the history of science since Galileo andNewton, that the more theoretical and removed from immediateapplications a scientific topic appears to be, the more likely it is toeventually find the most striking practical applications. Considernumber theory, which only 20 years ago was believed to be the mostuseless chapter of mathematics and is today the core of computersecurity. The efficient factorization of integers into prime numbers, atopic of seemingly breathtaking obscurity, is now cultivated with equalpassion by software desigers and code breakers.



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



From the Association of Alumni and Alumnae of MIT April 1997

Powered by ScribeFire.