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