AN INTERVIEW WITH JACK K. HALE -- by Yingfei Yi November 18, 2003 in Atlanta
	Jack in his backyard in Atlanta, June 1992.

Foreword

Professor Jack K. Hale is a world renowned leader and among the most influential persons in the field of nonlinear dynamics in our age. He was an originator and pioneer in many important areas in the interface of dynamical systems and differential equations including nonlinear oscillations, stability and bifurcation theory, functional differential equations, and infinite-dimensional dynamical systems defined by parabolic and hyperbolic equations. Professor Hale's seminal work and leadership have played an important role in the development of these areas which are now widely studied and are being acknowledged as some of the most important branches of mathematics today. Professor Hale's influence in the field has gone far beyond his papers and books. By being a leading mathematician and a person of exemplary character, he has had tremendous impacts on the career developments of many people around him and has brought the best out of many of us working in the field. It seems only fitting that we begin the very first interview of the SIAM DSWeb Magazine with Professor Hale.

This interview is authorized by Professor Hale to publish on-line exclusively in the SIAM DSWeb Magazine. The published version of the interview has been proof-read by Professor Hale.

A brief biography of Professor Hale

Professor Jack K. Hale was born in Kentucky, USA, on October 3, 1928. He received his B.A. degree in Mathematics from Berea College in 1949, and the M.Sc. and Ph.D. degrees in Mathematics, in 1951 and 1953, respectively, from Purdue University. From 1954-57, Professor Hale worked as a Systems Analyst at Sandia Corporation. From 1957-58, he was a Staff Scientist at Remington Rand Univac and was involved in numerical analysis and the design of logic computers. From 1958-64, he was a permanent member of the Research Institute for Advanced Studies (RIAS) in Baltimore, Maryland. He joined the faculty at Brown University in 1964 as a Professor in the Division of Applied Mathematics for 24 years until 1988 and served as a Division Chair from 1973-76 and Director of the Lefschetz Center for Dynamical Systems for several years. He came to Georgia Institute of Technology (Georgia Tech) in 1988 as a Professor and was named a Regents' Professor in 1990 in the School of Mathematics. He was a co-founder of the Center for Dynamical Systems and Nonlinear Studies (CDSNS) at Georgia Tech and served as Director of the CDSNS from 1989-1998. Presently, he is a Regents' Professor Emeritus at Georgia Tech.

Professor Hale has written 15 books, over 200 research papers, and has supervised 48 Ph.D. students and numerous post docs. He has been a Chief Editor of the Journal of Differential Equations since 1981 and an editor of nine other high-level mathematical journals. He has given numerous plenary lectures and invited addresses at professional conferences including Equadiff (1962, 1973, 1987, 1989, 1991, 1993), the International Congress of Mathematicians (ICM, 1966), Louvain Summer School (1976), SIAM conference (1985, 1990), and meetings of the American Mathematical Society (1981, 1985), the Australian Mathematical Society (1977, 1993), the Canadian Mathematical Society (1985, 1993), C.I.M.E. (1972, 1974, 1983), and the Conference Board of Mathematical Sciences (1980). He has provided extensive services to the international mathematical community.

Professor Hale's professional accomplishments and contribution to the international mathematical society have been acknowledged with the highest academic distinctions. Among these are Honorary Doctorate Degrees from Universiteit Gent, Belgium (1982), Universität Stuttgart, Germany (1988), Instituto Superior Técnico Lisboa, Portugal (1991), Universität Rostock, Germany (1998) and Clark University, USA (2000). He is a Fellow of the American Academy of Mechanics since its founding, a Corresponding Member of the Brazilian Academy of Science (1979), an Honorary Fellow of the Royal Society of Edinburgh, Scotland (1987), and a Foreign Member of the Polish Academy of Sciences (1992). He received the Distinguished Alumnus Award from Purdue University (1991) and from Berea College (1992). He received the Chauvenet Prize (1965), Guggenheim Fellowship (1979-80), British Carnegie Fellowship (1986), McFarland Fellowship (1988-92), and the Sigma Xi Sustained Research Award at Georgia Tech (1991). He was a Guest of the Japanese Society for Promotion of Science (1976-77), the Rothschild Visiting Professor at the Isaac Newton Institute, University of Cambridge (1995), and the Kloosterman Professor at the Lorentz Center, University of Leiden (1997).

Jack and Hazel at the home of the father of Czeslaw, in Pincow, Poland, spring 1972.	Jack with Czeslaw Olech outside his home in Providence, mid 1980's.

The interview

(H = Jack Hale, Y= Yingfei Yi)

Y: Jack, thank you for your time with this interview for the SIAM DSWeb magazine. As a leader and a pioneer in many areas of dynamical systems, especially those related to differential equations, you have witnessed the entire development of modern dynamical systems. Your experience and views will certainly be valuable to those, especially younger ones, working in these areas. Below, I am going to ask you some questions about your career, experience, and your views on the areas, which I think would be of interest to our readers.

H: It is an honor to be asked to have this interview. I am glad to answer, to the best of my ability, any questions. Of course, the answers will reflect mostly my own personal experiences.

Y: I know you got your Ph.D. from Purdue (University) in 1953 with Professor Lamberto Cesari and you wrote your thesis on nonlinear oscillations. How did you become a student of Lamberto Cesari and what made you decide to do dynamics?

H: At that time at Purdue, there was very little opportunity to study differential equations and there was no course of the type that we see today dealing with qualitative questions. I had finished my preliminary exams and was ready to begin working with some professor. Lamberto Cesari had been at Purdue about a year, I had not taken any course with him and it did not occur to me to work with him because his interest was in surface area and calculus of variations. I was reading in the library one day and Lamberto Cesari came to me and asked if I would like to work with him on differential equations. He had done some work in the 1930's on stability of linear systems and had a contract to publish a book with Springer. Therefore, he wanted some students who would help him with the project. Having an interest in engineering and physics, I accepted.

Y: I can imagine that, with few references available, to get things off the ground must have been pretty tough.

H: At that time, the mathematical community in the US had very little interest in differential equations. I did not know of any serious book in the subject. However, after I had essentially finished my thesis, I discovered the 1947 notes of Lefschetz and the book of Minorsky on nonlinear oscillations. It was much later that I discovered the extensive research that the Russian mathematicians had been doing since the time of Poincaré and Lyapunov.

When Lamberto Cesari asked me to work with him, I informed him that I knew almost nothing about differential equations. His reply: `Don't worry. We will learn the subject together by reading the original work of Poincaré and Lyapunov.' This was like a reading course and was the best thing that happened to me because these two books laid the foundation for the present theory of differential equations. It also made it easy for me to read the Russian literature of the 1950's.

Y: Is your research experience in nonlinear oscillations the main reason for you to become interested in engineering problems after your Ph.D.?

H: As I mentioned before, I had a deep interest in engineering and physics. I also was interested in nonlinear analysis and the role of eigenvalues in the behavior of systems. For the public lecture that was required of all Ph.D. students at Purdue, I made use of a visual aid consisting of a real system, designed by an engineering professor, which would excite the first five modes of a steel bar. After the Ph.D., since there was almost no literature on nonlinear oscillations in mathematical journals, my reading was primarily in engineering journals.

Y: I know you joined the research group led by Lefschetz at RIAS in 1958 as a permanent member. How was this group formed, what was its main function, and who were among the initial members?

H: As you know, Lefschetz was originally an engineer and turned to mathematics after a serious accident which destroyed both lower arms. Of course, he is famous for his contributions to topology, but he had the background to keep abreast in subjects not in the mainstream of mathematics at that time. He was one of the few people in the US who was somewhat familiar with the contributions of the Russian community to differential equations and dynamical systems. He was responsible for bringing much of the Russian literature to the attention of the `Western' countries.

The following remarks about Lefschetz and RIAS may not be completely correct, but I think that they contain the essential ideas. Lefschetz did not start RIAS. It was already a research institute, but did not have a special group devoted to mathematics. After Sputnik was put into orbit, Lefschetz became very concerned about the fact that differential equations and dynamics was not a subject which was being pursued with vigor in the US. Robert Bass was working for the Martin Company at RIAS, he knew Lefschetz from previous visits to Princeton and also he was well versed in differential equations. This gave Lefschetz a contact at RIAS to attempt to form a group in differential equations and control under the umbrella of the Martin Company. The group was located in Baltimore about twenty miles from the company and had no obligations to the Martin Company except to allow visitors from their various locations to spend some time at RIAS, profiting in any way that they could.

There were a few permanent members of the group and many temporary visitors from around the world. This created an atmosphere in which ideas were exchanged freely. This helped in coordinating and accelerating the research in the subject, not only at RIAS, but at the institutions of the visitors. Most people in my age bracket working on the subject spent some time at RIAS.

RIAS was also conveniently located near Johns Hopkins University and the University of Maryland, which gave the opportunity to have close contacts with persons there. A journal, Contributions to Differential Equations, was formed jointly with the University of Maryland. It lasted only for a few years and was the predecessor to the Journal of Differential Equations which Prof. LaSalle began after we arrived at Brown.

Conferences organized by RIAS in 1959 in Mexico and 1961 in Colorado Springs were to my knowledge the first ones devoted to differential equations in the West. There were visitors at these conferences from Eastern Europe and Russia, which led to much closer personal as well as professional contacts.

The original permanent members of RIAS were S. Lefschetz, J.P. LaSalle, R. Bass, R. Kalman, H. Kushner, S. Schwartzman, me, and, I think, J. Auslander and B. Rinehart. As mentioned, there were always several visitors. During our last year in 1964, the number of people doing research was approximately 30.

Y: You have given me a copy of your first book `Oscillations in Nonlinear Systems' which was published in 1963. When did you start working on the book and what was your motivation for writing it?

H: The material in this book had been an important part of my research on nonlinear oscillations which I began in my thesis together with the new knowledge gained by reading much literature and my introduction to invariant manifolds through Bogoluibov and Mitropolski. Many people were working on nonlinear oscillations, but it was my feeling that the engineers were not aware of much of the information that could be of assistance in understanding some of their problems. I felt strongly that they should be exposed to this information and decided to write the book.

Y: Is it also at RIAS that you began to work on functional differential equations (FDEs) and what was the status of the area back then?

H: My motivation for studying delay differential equations came from the simple observation that delays occur in so many engineering systems. At that time, there was almost no serious effort on the part of engineers (Minorsky was an exception) who would incorporate delays into their models even though it was clear that they should be there. There was much literature on linear systems and some results on stability and instability of equilibria. For a delay equation for \(x \in \mathbb{R}^n\), the analysis was always restricted to analyzing the solution in \(\mathbb{R}^n\).

Such an approach was a severe limitation on the development of any type of qualitative dynamics. Periodic solutions did not look like closed curves, there was no hope for something like a geometric classification of stable and unstable manifolds of equilibria, etc.

I began to make progress after studying (in Russian) the book of Krasovskii on stability. He made it clear that one should consider the state space as the function space consisting of the initial data on a delay interval and then consider such equations as evolutionary equations in this function space. This approach changed the subject completely and led eventually to the theory that we have today.

Y: How do you view the progress of FDEs as it is now, after forty years of development, and what do you think the future directions of the area should be?

H: There has been tremendous progress. The qualitative theory began with retarded functional differential equations with finite delay (RFDEs). These were the simplest because the dynamical system becomes compact after the time exceeds the delay. In addition to showing that many of the results for ordinary differential equations in \(\mathbb{R}^n\) (ODEs) are valid for RFDEs, new ideas arose in trying to understand the global limiting behavior of solutions. By exploiting this compactness, the concept of a compact global attractor was introduced for dissipative RFDEs in 1971. In my opinion, the progress in RFDEs had a big influence on the development of the qualitative theory of parabolic PDEs as we know it today.

In the middle of the 1960's, a qualitative theory was also initiated for a special type of neutral functional differential equations (NFDEs) for which the derivatives occur linearly and with delays. These equations do not have the smoothing property and are more like hyperbolic PDEs. The dynamical system generated by such equations was shown in the late 1960's to have special properties, which were special cases of asymptotically smooth dynamical systems. With dissipation, these equations also have compact global attractors.

Once these concepts were introduced, it led to many natural questions about the finite dimensionality of the attractor, the discussion of special types of equations for which one could describe the flow on the attractor, etc.

Some references for many more ideas are the books of Hale and Verduyn Lunel (Springer, 1993), Hale, Magalhães and Oliva (Springer, 2002), and Diekmann, van Gils, Verduyn Lunel, and Walther (Springer, 1995). There is now also a theory for partial functional differential equations of retarded type and the beginnings of a the theory for neutral type as shown in the book of Wu (Springer, 1996). There are many challenging problems in all of these areas as one can easily see by scanning the above references.

Jack with Waldyr Oliva in Brazil, mid 1980's.

Y: I noticed that during the 1970's, you begin your interests in dynamics of PDEs and dissipative systems in general. What was the area like in that period?

H: I became very interested in the fact that our work in FDE was playing a role in a qualitative theory of quasilinear parabolic PDEs, which Dan Henry, a former student of mine, began to develop in 1971, culminating in his book in 1981. In the late 1970's, some of my students were working in this subject.

I became even more interested when I encountered a nice paper of Babin and Vishik (1983) on the existence of attractors for linearly damped hyperbolic wave equations on a bounded domain. Their definition of attractor was more restrictive than the one we gave for NFDEs. It turned out that the theory that we had developed for NFDEs worked equally well for this situation and we could obtain the strong attractor. The difficulties encountered by Babin and Vishik were of similar nature to the ones we had encountered with NFDEs in the 1960's.

My interest in the dynamics of PDEs continues.

Y: How do you view the importance of evolutionary PDEs as dynamical systems and how do you view the future directions of the area?

H: It is extremely important to develop the qualitative theory of PDEs and to exhibit interesting classes of equations for which we are able to understand the complete dynamics. This has been accomplished for scalar dissipative quasilinear parabolic PDEs on a bounded interval. The structure of the flow on the attractor is completely understood. The complete understanding of such a simple problem suggests the types of questions that should be asked in more complicated problems.

It is very important to isolate classes of equations which will exhibit new phenomena and, at the same time, to be amenable to a complete understanding of the dynamics. Such systems are beginning to appear in the literature dealing with systems of PDEs. The nonlocal interaction in such equations introduces many new phenomena. There is a considerable literature now dealing with the qualitative theory of dynamical systems related to parabolic systems, effects of cross diffusion, the Navier-Stokes equation, solitary equations, and effects of time dependence in these systems. In modeling as well as numerics of evolutionary PDEs, one encounters lattice dynamical systems, an actively investigated area at the present time.

Y: What other directions in the dynamics of differential equations do you feel need more attention?

H: My own interests at the present time are in trying to understand transition layers in singular parabolic problems, the role of the shape of the boundary of the domain of definition on the dynamics, the effects of time dependence in the equations. I also would like to understand singular problems for which the equation has parabolic structure and the singular limit is hyperbolic. This seems to be a very challenging problem which occurs very often in applications.

Y: Given the natural connections of dynamical systems with many applied disciplines, what role do you think we mathematicians should play when working on applied problems?

H: I have heard a conversation that someone was having with Lefschetz where he was asked: `What is applied mathematics?' Lefschetz replied that all mathematics is applied, some spelled with a capital `A' and some with a capital `M.' I think that we gain many new ideas from studying applications but mathematicians should emphasize capital `M.' It is our obligation to discover the mathematics and we cannot rely on the applied people to give us mathematical problems. We must find them. Even though my work has always been on the theoretical level, much of my motivation has come from applications.

Y: What is your standard for good research in dynamics of differential equations or how do you value mathematical research in general?

H: The measure of good research has nothing to do with the field. The things that I find most interesting are the ones that involve some new ideas. Most of the papers that do not contain a new idea but are just using standard things in an obvious way to improve a result do not push the field forward very much. On the other hand, such results may be beneficial in applications.

I think that my research has been guided by my own discovery of something that seemed interesting and that I wanted to understand. It did not matter to me if other people were interested or not. I was told several times that what I was doing was uninteresting. After many years, it turned out that some of the things were interesting. I guess that I was following some advice given to me by Lefschetz at RIAS, when I asked him if what I was doing was of any interest. His reply was: `Does it bother you?' Of course, my answer was yes. His answer was: `Then keep at it until it does not bother you.' To me, this is a good philosophy to follow. We should not work on anything unless it excites us and results in satisfaction.

Jack Hale in his office at Brown in 1988 after the celebration for his 60th birthday.

Y: What is your advice for young persons who wish to begin research in dynamical systems?

H: At the beginning of a research career, it is very unusual to be able to recognize fundamental problems. Therefore, we do what we can, which is usually to make small modifications to existing results. However, one should not continue to do this and one must spend considerable energy in diversifying his or her interest in other areas. There is then the possibility of recognizing something that one feels is fundamental and to which he or she will be committed for several years.

Y: As you know, there is a global pressure on young persons to publish papers and to obtain fundings. What is your opinion on this? And what steps should the community as a whole take to help improve the situation?

H: It is unfortunate that we have created an academic community which requires to publish or perish. It has led to young people focusing entirely on a subject which is directly related to problems of their thesis and there has been no time to either broaden their interests or delve deeply into the subject. Promotions are often based on the number or weight of publications without critical evaluation of content. A person may only publish one paper every two years, each of which is excellent with many new ideas, but will be put lower in the scale than a prolific publisher whose papers have little content. One way of correcting this is for the members of the academic community to take the job of evaluation of personnel more seriously.

For a long time, external funding has been given to members of the faculty of universities. This has allowed an increase in the number of faculty, but has also made universities dependent upon this external funding. As a result, the direction of research is being determined by a few members of the granting agencies who often have a very focused view of what is important. It is not what we usually consider to be a university where there is complete freedom of research. There should be emphasis at the university on scholarship and there should never be a penalty based on external funding.

Y: What is your philosophy for being a good intellectual?

H: I think that my attitude toward research has been dealt with before. As part of the academic community, our primary job is to train young people. We should instill in the student the excitement associated with learning and discovery. We should always participate in the formation of policies at our institution and we should serve the professional community when asked.

Y: Let me change to a different subject. When the mathematical group at RIAS moved to Brown in 1964, is that when the Lefschetz Center for Dynamical Systems at Brown started?

H: No. We formed a Center for Dynamical Systems (CDS) with Lefschetz, LaSalle, Kushner and myself coming from RIAS. Other appointments were made soon after arriving. The Center was named the Lefschetz Center in 1974 at a special meeting at Brown that we had planned in his honor. Unfortunately, he died two years before the meeting at the age of 88.

The Center received some funding from the University and we also secured some from external sources. At that time and for several years later, it was possible to obtain funding from the Defense Agencies to work on fundamental problems in areas without specific instructions to make a contribution in a special application.

Y: Were there other dynamical systems centers in the US during that time?

H: Not to my knowledge.

Y: As a former director of the Lefschetz Center, how do you view the role the Lefschetz Center played in the global development of dynamical systems; in particular, dynamics of evolution equations?

H: In my opinion, the Lefschetz Center made and is still making an important contribution to the development of dynamical systems. During my tenure, there were many excellent students who obtained their Ph.D. working with members of the Center and are now professors at various good universities inside and outside the US. The vitality of the Center was also enhanced by an average of two post-docs each year and the many visitors who came with their own funding. I can say that many directions in dynamical systems were influenced in a significant way by this program.

Y: You moved to Georgia Tech in 1988 with Shui-Nee Chow to start the Center for Dynamical Systems and Nonlinear Studies. To what extent do you feel an engineering environment like Georgia Tech has helped the development of applied dynamical systems at the Center?

H: The interaction between mathematics and engineering and the physical sciences has been much more extensive at Georgia Tech than at Brown. We have had many close interactions especially with Aerospace, Electrical and Mechanical Engineering, Materials Science and Physics. This interaction has had a very positive influence on all parties. It is continuing and should definitely be encouraged.

Y: You have been a director for two dynamical systems centers in the US for many years. In your view, what are the main factors leading to the success of a center on dynamical systems?

H: I think that I have answered that before - strong people working on good problems, good students, regular communication through seminars, and making sure that there is a program involving long term visitors.

Jack at his sister's home in 1988 with his father and Hazel.	Jack with his brother Gene in 2003 at the home of Gene, in Charlottesville, Virginia.

Y: Towards the end of this interview, I'd like to ask you something more personal and I hope you don't mind.

H: It is okay.

Y: I know that you have had opportunities other than being a professor when you were young. Some said that you even had a good opportunity to be extremely wealthy. Have you ever felt regret for choosing not to take those opportunities?

H: Everyone always has the opportunity to choose several directions for his or her professional career. After obtaining my Ph.D., I spent some years away from the university at Sandia Corporation in Albuquerque, New Mexico, and Remington Rand Univac in St. Paul, Minnesota. In St. Paul, I had the possibility to become wealthy when friends in our department asked me to join them in forming a new company, called Control Data. I knew that we were not smart enough to make money and, of course, I was wrong.

I was beginning to think that an academic career was more appropriate for me. When Lefschetz asked me to be a permanent member of RIAS, I did not hesitate and I have expressed to you what a great influence this had on my future. Of course, there are no regrets.

Y: What is your philosophy of life?

H: Try to be a responsible member of society, respect people for what they are, have good friends and do every task to the best of your ability.

Y: After you retired in 1998, you seem to be even busier. Do you feel your life style has changed some after retirement?

H: The only change that I see is that I am not on any university committees and do not teach or have students. There is more time for concentration on my research and writing. Retirement also has made it possible for me to spend more time with my wife, Hazel, and to participate more in the things that she enjoys.

Y: What do you do in your spare time?

H: I have always liked to read and travel and, in retirement, there is more time for this. Hazel and I both enjoy theater, museums and `playing in the dirt' in our garden.

Y: What is your plan in the next few years with respect to your research and other academic activities?

H: Professionally, I will probably be doing the same things that I have always done - try to understand new things, communicate things that I know through writing and lecturing.

Y: Well, Jack, thank you very much for sharing your life, your career experience and your views with us. I am sure that our readers will enjoy reading this interview. Finally, my best wishes to you and Hazel. Please give my best regards to Hazel. She has been like a mother to many of us and we all love her.

H: It was a pleasure.