by Ian Stewart
The message here is, don’t assume things. Check them beforehand. Not just the layout of the lecture hall or the location of the building where you are supposed to be giving a talk, or the city in which your meeting is due to take place, or the date of that meeting . . . Recall Murphy’s law: “Anything that can go wrong, will.” Above all, remember the mathematician’s corollary to Murphy’s law: “Anything that can’t go wrong will go wrong too.”
This was brought home very clearly to a good friend of mine, also a mathematician, on a trip to a country that it would be best not to name. He was attending a conference and he was making a flight from his first port of entry to another, fairly distant, city. As he sat in the airplane scribbling some calculations, he noticed the pilot emerge from the flight cabin, shutting the connecting door behind him. A few minutes later the copilot did the same thing. Soon after that, the pilot returned, and tried to open the door to return to the cockpit. He seemed to be encountering some difficulty. The copilot tried to help, but neither of them could open the door. At this point my friend realized that the plane was flying on autopilot and no one could get to the controls. A female flight attendant joined the pilot and copilot, disappeared, and reappeared carrying a small hand ax. The pilot then attacked the door with the ax, made a hole in it, put his hand through, and opened the door. The flight crew then entered the cabin and closed the door behind them.
No announcement was made to explain these events to the bemused and distinctly frightened passengers.
My advice here really applies to the pilot and the copilot, not the passengers. If you go to conferences, you will sometimes have to fly on airlines that have been booked by the conference organizers. You can choose not to go, if you wish, but you can’t always choose not to travel on an airline with a dubious safety record or an aging fleet. There really is no way for a passenger to anticipate such a problem, or to help solve it or avoid it.
Let me revert to the topic of lecturing. Another useful piece of advice is to make sure that you have plenty of time to get to the lecture room. Avoid taking on unpredictable commitments immediately beforehand. I still have vivid recollections of arriving late to give a lecture on algebra. I lived in a village at that time, and another member of the math department owned a small farm in the same village, so we carpooled. One day when it was his turn to drive, he decided to drop a pig off at the local abattoir on the way to work. The pig, perhaps sensing that the trip would not be to its advantage, had other ideas. It refused to climb the plank into the back of the truck. It is difficult to remain professorial when explaining that you were late because you could not get a pig into a pickup truck.
One of the main ways you will interact with other mathematicians is by attending, and giving, talks. These might be seminars, specialist talks for experts in your research area; they might be colloquia, more general talks for professional mathematicians but not specialists in the area concerned; or they might be public lectures open to anyone who wants to turn up. All lectures are fraught with potential disaster.
There was, for instance, a prominent professor of number theory who had the habit of turning up at the start of a visiting speaker’s seminar, falling asleep within minutes of the talk starting, snoring loudly the whole way through, and then asking penetrating questions at the end when the audience’s applause woke him up. By all means, emulate the penetrating questions, but try to avoid the snoring if you possibly can; otherwise you will get a reputation for eccentricity.
If you are the person giving the talk, the opportunities for Murphy to strike are far more numerous, especially if you are using equipment. When I started lecturing, the only equipment we ever had was blackboard and chalk, and I confess to a continuing bias in favor of lo-tech visual aids, though I am capable of preparing the all-singing, all-dancing PowerPoint presentation with a video projector and moving graphics downloaded from the Internet if that is what is called for. I have used overhead projectors, whiteboards with those horrible pens that smell of solvent, even the businessperson’s ubiquitous flipchart.
Even chalk can go wrong. First, it may not be there. I developed a habit of taking my own box of chalk to lectures in case the previous lecturer had used it all, or the students had hidden it as a joke. Some chalk is very dusty and gets all over your clothes: I made sure I had the “antidust” kind with me. It still got on my clothes, but the cleaning bills were smaller. Many types of chalk can make horrible screeching sounds when you write, putting everyone’s teeth on edge. It takes practice to prevent that. And normal-sized chalk will not do if you are lecturing to five hundred freshman calculus students in a cavernous lecture hall. You need supersize.
Other types of equipment can go wrong more spectacularly. A good friend of mine was delivering a short talk at the British Mathematical Colloquium—the UK’s main mathematics conference, held annually—and he was intending to use an overhead projector to show lots of pictures on a projection screen. Unfortunately, when he tried to pull the screen down from the ceiling—it was on a roller and there was a string attached—it fell down on his head. He ended up projecting the pictures onto the wall.
Never believe your hosts when they tell you that all the equipment will work perfectly. Always try it for yourself before the lecture. I was giving a public lecture in Warsaw using a cassette of about eighty 35-mm slides. I was persuaded to hand the slides to the projectionist, who would set everything up for me, while my hosts took me for a quick coffee. As I entered the room to deliver the lecture, the projectionist put the slides into the projector, which was tilted at an alarming angle because of the high position of the screen. The cassette slid right through the projector and fell out the back onto the floor, where its contents were scattered far and wide. Many of the slides were sandwiched between thin sheets of glass, which broke. It took ten minutes to get everything back into some kind of order, in front of five hundred patient people.
Do not confuse the projection screen with a whiteboard and write on it in permanent ink. Many people do this, and their lecture is preserved for eternity, along with their mistake.
The famous physicist Richard Feynman once learned Spanish because he was going to give a lecture in Brazil. Check the local language.
If you are hosting a visitor, and they are giving a talk, make sure that you have the key to the projection room. On one occasion I had to improvise my lecture because the slide projector, though visible to us all inside a wonderfully equipped room, might as well have been located on the moon because the room was locked and no one knew how to get the key.
Do not forget that your visitor may not know the local geography. I was once abandoned inside a Dutch mathematics department building when my hosts went off to the parking garage to go to a restaurant. I had to make my escape through a window, setting off a burglar alarm. I did manage to catch up with them in the garage, which was a good thing because I had no idea where the restaurant was, or even what its name was.
Avoid wandering around strange buildings, especially in the dark. A biologist friend was visiting an institution with a strong marine biology department, and it had an aquarium. The entrance was down a short flight of stairs. Alone in the building, late at night, he tried to enter the pitch-black room, felt for the light switch, and accidentally hit the fire alarm instead.
Six fire engines turned up, lights blazing, sirens blaring.
He had called the fire station to explain his mistake, but according to the rules, they could not return to base without checking for a fire.
Committees are another place where you can easily make dreadful mistakes. Universities tend to run as a network of interlocking committees and subcommittees, some with real teeth, some window dressing. Most exist for a reason, and many tackle low-level but essential activities such as grading tests or sorting out course regulations. You will undoubtedly be involved in committee work, and you should be. A university is a complicated place, and it will not function well if everyone is left to make things up as they go along. E
very academic has to be something of an administrator, and to some extent the converse holds, especially at senior levels.
Not being a committee animal myself, I can’t offer much useful advice on how to “work” a committee so that it reaches the decision you favor. But I do know how not to. The following story is typical. An important committee was debating a major decision about some particular action. The mathematician on the committee saw immediately that taking the action concerned would lead to disaster, and spent five minutes explaining the logic behind this view, which was unassailable. His analysis was clear and concise, and left no real room to doubt his conclusions; no one contradicted him. The debate continued, however, because the other members of the committee had not yet had their say. After an hour or more of further discussion—to which the mathematician did not contribute, having already (he assumed) made his point—the committee voted. It decided to take precisely the action that the mathematician had warned it not to.
What was his mistake? It was not in the analysis, nor in its presentation, but in its timing. In any committee discussion, there comes a pivotal moment when the decision can be swayed either way. That is the time to strike. If you make your point too soon, everyone else will have forgotten it; if you are lucky, you may be able to remedy this with a timely reminder. But if you make your point too late, there is no way it can have any effect.
The other thing not to do in committees is to keep making your point when you have already won it. You may lose support merely because you keep banging on about what has by now become obvious to everyone. If you have further ammunition, save it in case it is needed later.
Which advice I will now take myself.
20
Pleasures and Perils of Collaboration
Dear Meg,
Yes, it is a bit of a dilemma. Tenure and promotion depend on your own personal record of teaching and research, but there are attractions in working with others as part of a team. Fortunately, the advantages of collaborative research are becoming widely recognized, and any contribution that you make to a team effort will be recognized too. So I think you should focus on doing the best research you can, and if that leads you to join a team, so be it. If the research is good, and your teaching record is up to scratch, then promotion will follow, and it won’t matter whether you did the work on your own or as part of a joint effort. In fact, collaboration has definite advantages; for instance, it’s a very effective way to get experience in writing grant proposals and managing grants. You can start out as a junior member of someone else’s team, and before long you will be a principal investigator in your own right.
Attitudes are changing, fast. In the past, mathematics was mostly a solo activity. The great theorems were discovered and proved by one person, working alone. To be sure, their work was carried out alongside that of other (equally solitary) mathematicians, but collaborations were rare and papers by three or more people were virtually nonexistent. Today, it is entirely normal to find papers written by three or four mathematicians. Something close to ninety-eight percent of my research in the last twenty years has been collaborative; my record is a paper with nine authors.
This is small potatoes compared to other branches of science. Some physics papers have well over a hundred authors, as do some papers in biology. The growth of collaboration has sometimes been derided as an adaptation to the “publish or perish” mentality, whereby tenure and promotion are determined by how many papers someone has published in a given period of time. An easy way to increase your list of publications is to get yourself added to somebody else’s paper, and the payback is simple: you add them to yours.
But I really don’t think this tit-for-tat behavior is responsible, to any significant degree, for the growth of coauthorship.
The reason for the huge cast of authors on some physics papers is straightforward. In fundamental particle physics, the joint work of a huge team, carried out over several years, is typically condensed into a paper of perhaps four journal pages. The team will include theorists, programmers, experts in the construction of particle detectors, experts in pattern recognition algorithms that interpret the extremely complex data obtained by the detectors, engineers who know how to construct low-temperature electromagnets, and many others. All of them are vital to the enterprise; all fully deserve recognition as authors of the resulting report. But the report is usually short and to the point. “We have detected the omega-minus particle predicted by theory: here is the evidence.” Someone may get a Nobel Prize for those four pages. Probably whoever is listed first.
Big science involves big numbers of people. The same goes for gigantic biology projects such as genome sequencing.
Something similar has been going on throughout science. The root cause is that science and mathematics have become increasingly interdisciplinary. For example, you’ll recall that one area of interest to me is the application of dynamics to animal movement, and my early papers were all written in collaboration with Jim Collins, an expert in biomechanics. They had to be: I didn’t know enough about animal locomotion and Jim wasn’t familiar with the relevant mathematics.
My nine-author paper summed up two three-year projects to apply new methods of data analysis to the spring and wire industries. More than thirty people were involved in this work; for publication we reduced the list of authors to those who had been directly responsible for a significant aspect of the results. Some of us worked on theoretical aspects of the mathematics; some worked out new ways to extract what we needed from the data we could record; others carried out the analysis of those data. Our engineers designed and built test equipment; our programmers wrote code so that a computer could perform the necessary analysis in real time. Interdisciplinary projects are like that.
For the last twenty years, funding bodies worldwide have advocated the growth of interdisciplinary research, and rightly so, because this is where many of the big advances are being made, and will continue to be made. At first they didn’t get it quite right. The idea of interdisciplinary research was praised, but whenever anyone put in a proposal for such work, it went to the existing single-discipline committees, who of course did not understand substantial parts of the grant application. For example, a proposal to apply nonlinear dynamics to evolutionary biology would be turned down by the mathematics committee because they and their referees had no expertise in evolution, and then it would be rejected by the biology committee because they didn’t understand the math. The result was that the funding agencies encouraged interdisciplinary research in every way except kicking in funds.
No one, mind you, was doing anything wrong. It was virtually impossible to justify a decision to spend money on the dynamics of evolution when that took money away from top-class projects about algebraic topology or protein folding, say. To the credit of those involved, the system has changed, for the better, and one can now obtain funding for science and math that straddles several disciplines. An important consequence is the creation of entirely new disciplines, such as biomathematics and computational cosmology. Another is the blurring of traditional subject boundaries.
Setting these political factors aside, there is another reason why collaborative publication has increased dramatically. A social reason. Working in groups, with colleagues, is a lot more fun than sitting in your office with your computer. To be sure, sometimes you need solitude, to sort out a conceptual problem, formulate a definition, carry out a calculation. But you also need the stimulus of discussions with others in your own area, or in areas where you wish to apply your ideas. Other people know things that you don’t. More interestingly, when two people put their heads together, they sometimes come up with ideas that neither of them could have had on their own. There is a synergy, a new synthesis, something that Jack Cohen and I like to call complicity. When two points of view complement each other, they don’t just fit together like lock and key or strawberries and cream; they spawn completely new ideas. As your career progresses, you may well come to appreciate the deli
ghts of collaboration, and value the help, interest, and support of colleagues whose minds complement your own.
Unfortunately, there can sometimes be a downside to collaboration. Choosing the wrong collaborator is a surefire recipe for disaster. Unfortunately, this can happen with entirely reasonable and competent people; it’s a matter of personal “chemistry,” and not always easy to predict. The main thing is to be aware of the possibility, and to leave yourself an exit strategy.
Some years ago two mathematicians that I know were coauthoring a book. They had no trouble agreeing on the mathematical content, or the order in which the material was presented. They just couldn’t agree on the punctuation. It got to a stage where one of them would go through the entire manuscript putting in commas, and then the other would take them all out again. And round and round it went. The book did get written, but they have never collaborated on another one. They remain the best of friends, though.
Everyone involved in a collaboration must bring something useful to it. They don’t have to do the same amount of work; one person may be the only one who knows how to do a big calculation, or write a complicated program for the computer, while another may contribute a crucial idea that ends up as two lines in the middle of a proof. As long as everyone contributes something essential, that’s fair. No one objects to all coauthors getting some of the credit for the final result. But if one of the participants is just along for the ride, which occasionally happens, then it makes everyone else happier if their name does not appear on the final paper, book, or report. And it often makes the person concerned happier, too. This need not be a sign of laziness; sometimes the project changes direction in a way that could not have been anticipated, and a contribution that originally looked essential may turn out not to be needed.