Ten rules for the survival of a mathematics department

Gian-Carlo Rota

Times are changing, and mathematics, once the queen of the sciences and the undisputed source of research funds, is now being squalidly shoved aside in favor of fields which are (wrongly) presumed to have applications, either because they endow themselves with a catchy terminology, or because they know (better than mathematicians do or ever did) how to make use of the latest techniques in PR. The present note was written as a message of warning to a colleague who insisted that all is well and nothing can happen to us mathematicians as long as we keep proving deep theorems.


I know that your frequently (and loudly, if I may add) disagree with your colleagues about the relative value of fields of mathematics and about the talents of practicing mathematicians. All of us hold some of out colleagues in low esteem, and sometimes we cannot help ourselves from sharing these opinions with our fellow mathematicians.

When talking to your colleagues in other departments, however, these opinions should never be brought up. It is a mistake for your to think that you might thereby gather support against mathematicians you do not like. What your colleagues in other departments will do instead, after listening to you, is use your statements as proof of the weakness of the whole mathematics department, to increase their own departments' standing at the expense of mathematics.

Departments at a university are like sovereign states: there is no such thing as charity towards one another.


When a dean or a provost receives a letter from a distinguished faculty member like you which ignores your chairman's opinion, his or her reaction is likely to be one of irritation. It matters little what the content of the letter might be. You see, the letter you have sent forces him or her to think on matters that he or she thought should be dealt with by the chairman of your department. Your letter will be viewed as evidence of disunity in the rank and file of mathematicians.

Human nature being what it is, such a dean or provost is likely to remember an unsolicited letter at budget time, and not very kindly at that.


You are not alone in believing that your own field is better and more promising than those of your colleagues. We all believe the same about our own fields. But our beliefs cancel each other out. Better keep your mouth shut, rather than making yourself obnoxious. And remember, when talking to outsiders, you shall have nothing but praise for your colleagues in all fields, you shall have nothing but praise for your colleagues in all fields, even for those in combinatorics. All public shows of disunity are ultimately fatal to the well-being of mathematics.


Once, when spending a year at a liberal arts college, I was assigned to teach a course on what some like to call "Mickey Mouse Math." I was stung by a colleague's remark that the course "did not deal with real mathematics." It certainly wasn't a course in physics or chemistry, so what was it?

We tend to use the word "mathematics" in a valuative sense, to denote the kind of mathematics we and our friends do. But this is a mistake. The word "mathematics" is more correctly used in a strictly objective sense. The grocery bill, a computer program, and class field theory are three instances of mathematics. Your opinion that some instances may be better than others in most effectively verbalized when you are asked to vote on a tenure decision. At other times, a careless statement of relative values is likely to turn potential friends of mathematics into enemies of our field. Believe me, we are going to need all the friends we can get.


Mathematics is the greatest undertaking of mankind. All mathematicians know this for a fact. Shocking as it may sound to us, many people out there do not share this view. As a consequence, mathematics is not as self-supporting a profession in our society as the exercise of poetry was in medieval Ireland. Most of our income will have to come from teaching, and the more students we teach, the more of our friends we can appoint to our department. Those few colleagues of ours who are successful atteaching undergraduate courses should earn our thanks, as well as our respect. It is counterproductive to turn our noses at those who bring home the dough.

When Mr. Smith dies and decides to leave his fortune to our mathematics department, it will be because he remembers his good teacher Dr. Jones who never made it beyond associate professor, not just because of the wonderful research papers you have written.


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.


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.


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.


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.


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,

Gian-Carlo Rota.