1997 Timoshenko Medal Lecture by John R. Willis

Mechanics of Research
The text of the Timoshenko Medal Acceptance Speech delivered at the Applied Mechanics Dinner at the 1997 IMECE.
by J. R. Willis, University of Cambridge

The award of the Timoshenko Medal is a singular and unexpected honour. I thank my friends who exaggerated my case so successfully, and promise them that I shall do my best to justify their faith in the future, even if I have not managed it in the past.

I’m not sure if I should say this, but I will. I have attended one Applied Mechanics Division Dinner previously. Bernie Budiansky received the Timoshenko Medal. I was surprised that he spoke for so long! Now I realize why. It was no ordinary after-dinner speech but the Timoshenko Lecture, and its length is prescribed. Therefore, I can only advise now that you settle down and prepare to let your thoughts wander!

A technical exposition is clearly not required, and I sought inspiration, or at least examples of how to proceed, by reading the lectures of a few previous medallists. It seemed to me that I might try to follow, in some approximate way, the path taken by George Batchelor, who was also my boss at a formative time in my career. He was founder and head of the Department of Applied Mathematics and Theoretical Physics in Cambridge.

I was fortunate enough to hold junior posts there, between 1965 and 1972, and perhaps am now even more fortunate to hold a senior post in that department. George is no longer its head but he is there every day, providing an example of dedication to research and scholarship in mechanics.

This, in fact, will be my theme: how does a career develop, in which perhaps the most significant component is research? Naturally, this will relate to applied mathematics and mechanics, because that is all that I know.

The main focus of George’s lecture was how an institution should be organised to stimulate invention and research, and I shall try to address a somewhat similar question.

Yapa Rajapakse asked me the other night what would be the title of my talk. I told him that I hadn’t given one, but perhaps an appropriate title would be “Mechanics of Research”. My concern will be how an individual should position himself or herself, to do fruitful research. So, in particular, what should someone just starting out do, and expect?

To begin, it pays to be good at passing exams. Otherwise, acceptance in a good research school is likely to be difficult. It pays also to have a thesis adviser who has the right sense of what might be important in the future as well as tractable now, with the right amount of effort. This is not always so easy to achieve. Paul Matthews, a physicist of great distinction (I knew him when he was Vice-Chancellor of the University of Bath, where I spent many happy years as a Professor), told me that, when he was a young research student in the Cavendish Laboratory, he one day approached Paul Dirac and asked him if he might be willing to supervise his research. Dirac’s response, utterly sincere and modest, was that he didn’t need any help with his problems at that time.

Few of us have the opportunity to acquire such an anecdote. There is, however, an uncomfortable lesson to be learned by all at this stage. Being clever may be necessary, but it certainly is not sufficient! It is still more important to have commitment and true interest in what you are doing. While a bit of competitive spirit is surely no bad thing (and may be almost essential), the pleasure of achievement against your own standards should be -- probably has to be -- your main reward, since it is certain, whoever you are, that you will see people around you who have more talent, and have done much more significant research than you are ever likely to do yourself. I am reminded here of another story I was once told. I am not sure now whether it was told me by Jock Eshelby, or about him: as a young research student, he went to see a great elder statesman of solid state physics, and asked what were the really significant areas in which an aspiring researcher should concentrate. The reply was, “I don’t know. And if I did, I wouldn’t tell you!”. Or perhaps Jock was the elder statesman: those that knew him can surely imagine him making such a response, mixing humour with truth! The fact is that, unless you are exceptionally lucky, you have to have your own ideas and be satisfied with them.

Having done your first research, and obtained your PhD, the next problem is to find a position which will allow your research to flourish. I wish I could advise here. My own experience is useless, since when I was at that stage, there were more good jobs than there were people to fill them, and I remember with appreciation one of the services my thesis adviser, Maurice Jaswon, rendered at that time. He took sabbatical leave in the USA, and I was able to monitor some of his movements from job offers that I received. I actually took a post-doctoral position at the Courant Institute, New York, and had the benefit of learning from some of the greats of applied mathematics, including Joe Keller, another Timoshenko Medallist. There are two problems now, or so it seems to me.

One is that jobs are scarce. The other is that there is pressure to behave immediately as though you are a great leader, attract research funds and perhaps have more graduate students than is comfortable for you or them. I do believe that foundations have to be laid, by personal study and contemplation. Better to become a motivator and facilitator later! And in any case, you won’t survive long-term as a generator of ideas, unless you are doing quite a bit of research personally. Clearly, these days, some compromise is necessary. I would like to think that talent is recognised not only by amounts of money attracted, or numbers of publications, though it would be quite wrong to infer that independence from these activities as demonstrated by failure to deliver necessarily implies true commitment, or ability, or depth. A positive aspect of the grant culture is that research driven by practical concerns can have fundamental significance and, even when it does not, involvement in such research can provide a perspective from which important generic or fundamental problems may be identified.

Assuming that you keep going successfully, and achieve a senior position either in a University or a Research Department, you surely will acquire wider responsibilities. These are likely to include responsibility for the welfare (and livelihood) of others, and may also involve administration concerning the research infrastructure of your discipline.

I think particularly here of activities relating to publishing. We almost all act as referees (except for those — some very distinguished — who just don’t respond!) and some of us act as journal editors.

I have to admit that I sometimes suspect that people these days write more than they read -- including, in some cases, papers upon which the person’s name appears as author! But enough of that, and back to the functions of an editor. This is not a research activity, but (I do my best to remind myself) it does make an important contribution to the collective scientific endeavour. Furthermore, although you certainly can’t please everyone all the time, it is my experience that the job can make you more friends than enemies. The thing to remember is that you can’t know everything, so you must take the best advice that you can find and then (even when the advice is inadequate, as it can be on occasions!) take a decision in as honest a fashion as you can. Just occasionally, you may have the opportunity to promote some of the first work of someone destined to be a star. This is a real satisfaction. And this reminds me of something else that goes with age and seniority: if you become a head of department -- or similar -- and have the opportunity to make appointments, you must never be afraid of appointing someone you suspect may be better than yourself. I have done this many times. Not only is it essential for the well-being of your unit, but you actually derive credit as well as benefit for your own research.

I realize that I started with the intention of making general comment but have lapsed into personal reminiscence. Now I would like to do this still more explicitly. Certainly the progress of my career has been influenced greatly by various colleagues that I have had. After NYU, I went to Cambridge on the initiative of Rodney Hill.

Of course he is impossible to emulate, but I saw an example towards which to aspire. Also at Cambridge, I interacted with Jock Eshelby, whose papers had already been one of the foundations of my education. I always knew that my main contribution would be mathematical, and I learned important lessons from Gerard Friedlander and Edward Fraenkel in particular.

When I was still relatively young, I moved to the then new University of Bath. Over the next few years, I had the great good fortune to appoint outstanding colleagues, and I learned some more mathematics particularly from John Toland. I also had several excellent students and post-docs. In particular, David Talbot was my student more than 20 years ago. He is still a major collaborator and I am happy to acknowledge my debt to him. One of my best post-docs was Pedro Ponte Castañeda.

Again, we have interacted over the succeeding years to my distinct advantage. When I first returned to Cambridge, I was fortunate to have Pedro as one of my early visitors. Another was Walt Drugan, who was never my student or post-doc but I wish he had been. This is one of the advantages of working in a location that others consider attractive. In the three and a half years I have been back, I have had the benefit of a succession of distinguished long-term visitors including, besides Pedro and Walt, Huajian Gao and Zvi Hashin. I have also, in recent years, done my own share of travelling, and my most frequent single destination has been the laboratory of Sia Nemat-Nasser, where there is always something new and exciting for me to learn.

Travelling and editing a journal do not form an ideal mixture, and would have been much more difficult to combine if I had not had the fortune to have Ben Freund as an outstanding co-editor of JMPS. During periods that I am away, he continues -- I expect -to feed copy to the press, so that short absence is not a problem.

One of the most significant world events of the last few years had impact on me and my research too: the demise of the Soviet Union made available many researchers of great ability, prepared to take more junior positions than objectively they deserved. In my case, I had successively as post-docs Sasha Movchan, Valery Smyshlyaev and Natasha Movchan. I can only liken working with them to driving a powerful car: you touch the accelerator and really move! They all three now have secure positions and do not need me, but still we collaborate, and I get (some of) the credit for their hard work and talent.

This, perhaps, leads me to my final piece of advice: when you get the chance, collaborate with talented younger researchers as much as you can. Few activities can be more rewarding. In my case, this goes a long way towards explaining my presence this evening. Now I would like to conclude, expressing my deep gratitude to all those with whom I have had the good fortune to interact during my career so far, coupled with keen anticipation of more in the future.