6. WRITE EXPOSITORY PAPERS
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 expository.
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 financial matters.
7. DO NOT SHOW YOUR QUESTIONERS TO THE DOOR
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 survival.
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,