6. WRITE EXPOSITORY
When I was in graduate school, one of my teachers
told me: "When you write a research paper, you are afraid that your
result might already be known; but when you write an expository
paper, you discover that nothing is known."
Not only is it good for you to write an expository
paper once in a while, but such writing is essential for the
survival of mathematics. Look at the most influential writings in
mathematics of the last hundred years. At least half of them, from
Hilbert's Zahlbericht on down, would have to be classified as
Let m tell it to you in the PR language that you
detest. It is not enough for you (or anyone) to have a good product
o sell; you must package it right and advertise I properly.
Otherwise, you will go out of business.
Now don't tell me that you are a pure mathematician
and that therefore you stand above and beyond such lowly details. It
is the results of pure mathematics, rather than those of applied
mathematics, that are most sought after by physicists and engineers
(and soon, we hope, by biologists as well). Let us do our best to
make our results available to them in a language they can
understand. If we don't, they will someday no longer believe we have
any new results, and they will cut off our research funds. Remember,
they are the ones who control he purse strings, since we
mathematicians have always proven to be inept at all political and
7. DO NOT SHOW YOUR QUESTIONERS TO
When an engineer knocks at your door with a
mathematical question, you should not try to get rid of him or her
as quickly as possible. You are likely to make a mistake I myself
made for many years: to believe that the engineer wants you to solve
his or her problem. This is the kind of oversimplification for which
we mathematicians are notorious. Believe me, the engineer does not
want you to solve his or her problem. Once, I did so by mistake
(actually, I had read the solution in the library two hours earlier,
quite by accident), and he got quite furious, as if I were taking
away his livelihood. What the engineer wants is to be treated with
respect and consideration, like the human being he or she is, and
most of all to be listened to in rapt attention. If you do this, he
or she will be likely to hit upon a clever new idea as he or she
explains the problem to you, and you will get some of the credit.
Listening to engineers and other scientists is part
of our duty. You may even occasionally learn some interesting new
mathematics while doing so.
8. VIEW THE MATHEMATICAL COMMUNITY
AS A UNITED FRONT
Grade school teachers, high school teachers of
mathematics, administrators, and lobbyists are as much
mathematicians as you or Hilbert. It is not up to us to make
invidious distinctions. They contribute to the well-being of
mathematics as much or more than you or many other research
mathematicians. They are right in feeling left out by snobbish
research mathematicians who do not know which way their bread is
buttered. It is in our best interest, as well as in the interest of
justice, to treat all who deal with mathematics, in whichever way,
as equals. By being united we will increase the probability of our
9. ATTACK FLAKINESS
Now that communism is a dead duck, we need a new
Threat. Remember, Congress reacts only to potential or actual
threats (through no fault of their own; it is the way the system
works). Flakiness is nowadays creeping into the sciences like a
virus through a virus through a computer system, and it may be the
greatest present threat to our civilization. Mathematics can save
the world from the invasion of the flakes by unmasking them, and by
contributing some hard thinking. You and I know that mathematics, by
definition, is not and never will be flaky.
This is perhaps the biggest chance we have had in a
long while to make a lasting contribution to the well-being of
science. Let us not botch it like we did with the other few chances
we have had in the past.
10. LEARN WHEN TO WITHDRAW
Let me confess to you something I have told very
few others (after all, this message will not get around much): I
have written some of the papers I like the most while hiding in a
closet. When the going gets rough, we have recourse to a way of
salvation that is not available to ordinary mortals: we have that
mighty fortress that is our mathematics. This is what makes us
mathematicians into very special people. The danger is envy from the
rest of the world.
When you meet someone who does not know how to
differentiate and integrate, be kind, gentle, understanding.
Remember, there are lots of people like that out there and, if we
are not careful, they will do away with us, as has happened many
times before in history to other very special people.
And believe yours as ever,