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In Memory of David I. Gottlieb



On December 6, 2008, the worldwide community of computational mathematicians and scientists lost one of its most respected and original members when David Gottlieb, Ford Foundation Professor and Professor of Applied Mathematics at Brown University, passed away. He was 64. He is survived by his wife, Esty, their three children, Sigal, Zuki, and Adi, and four grandchildren.

David was a central figure in the development of high-order and spectral methods for the solution of partial differential equations, with a particular interest in issues related to time-dependent problems and stability. His classic 1977 SIAM monograph (with S. Orszag), Numerical Analysis of Spectral Methods: Theory and Applications, represented the first attempt to systematically analyze these relatively new methods. This work would shape the careers of a number of young researchers as the field quickly matured during the following decades. He made numerous important contributions to the related areas of approximation theory and post-processing methods, compact finite difference methods, splitting methods, shock-capturing techniques, and absorbing boundary conditions.

David was born in Tel Aviv, Israel, on November 14, 1944, and lived as normal a life as was possible during the formation of the state of Israel following the end of the Second World War. He enjoyed telling the story of how he had come to study mathematics by pure chance. By his own account, he did well in mathematics in school, but his real love and interest were in literature and, even more, history. It was therefore natural that, while serving as a sergeant in the Israeli army, David sought admission to Tel Aviv University to pursue studies in history. He was sorely disappointed on learning that the admission deadline had passed, and his application therefore declined. As he walked through the university campus on his way home, an elderly gentleman approached him and asked about the reason for the sad face. The gentleman, later identifying himself as Professor Posner and chair of the mathematics department, invited David to join that department to explore and develop his talents in this subject. The rest is, as they say, history. David graduated with an MSc in 1969, under Shlomo Breuer, and with a PhD in 1972, as the first student of Saul Abarbanel and, indeed, as the very first PhD of the Department of Mathematics at Tel Aviv University.

After graduation, David went to MIT to continue his studies with Gilbert Strang. Also at MIT at the time was a young researcher, Steven Orszag, who had begun some exciting work on spectral methods. Strang proposed that David talk to Orszag to see if they had some common interests. This was the beginning of a very productive collaboration, culminating in the classic 1977 SIAM monograph.

This was also the time of an initiative that would come to play a central role in David’s scientific life: creation of the Institute for Computer Applications in Science and Engineering at NASA Langley Research Center in 1972 David became an associate member in 1974, when ICASE was just a few years old, and he would visit annually for the next 28 years, until ICASE closed in 2002. During its long history, ICASE became a global focal point for many of the major developments in computational mathematics for partial differential equations and optimization. The summer program, in particular, was legendary for bringing together an outstanding group of leading researchers, and David was in the midst of it, continuing his work on high-order and spectral methods and demonstrating the effectiveness of these methods on complex problems to the NASA community.

In 1975, while maintaining a close connection to ICASE and spending every summer there, David returned to Tel Aviv University as a senior lecturer; he rapidly rose to the rank of full professor (in 1982) and served as Chairman from 1983-1985.. This was a period of intense scientific activity because of the rapid growth and interest in spectral methods following the 1977 monograph. Around 1980, David was invited to France to give several lecture series; those lectures marked the beginning of intense activity in France and Italy that would result in the development of a rigorous approximation theory for spectral methods and the infusion of modern functional analysis into the topic. While not a major contributor to this approach, David understood the value of this alternative direction and provided persistent and consistent encouragement to a group of young people, mainly in France and Italy, who would lay the foundation for rigorous error analysis of spectral methods.

In 1982, Peter Lax led an investigation for the National Science Board that culminated in a report titled Large Scale Computing in Science and Engineering. The report documents what is now recognized as the first major study to predict the future importance and impact of large scale computing. At Brown University, it prompted the Division of Applied Mathematics to seek to create a new activity area in scientific computing and numerical analysis. In 1985 David arrived at Brown to develop and lead this new initiative and related research activities.

From 1985 until his death, David was a member of the Brown faculty---as a professor and then, beginning in 1993, as Ford Foundation Professor, and, from 1996 to 1999, as chair of the Division of Applied Mathematics. During this time, he built a renowned program at Brown University with the focus on high-order methods for the solution of time-dependent partial differential equations---a topic that is now more relevant and important than ever. Most leading experts from all over the world spent time at one point or another with David and his colleagues at Brown. Among the many major advances he led during these years are fundamental results in shock capturing using spectral methods, the Gegenbauer polynomial-based approach for overcoming the Gibbs phenomenon, the development of a stability theory for compact finite difference schemes, a novel analysis of perfectly matched layer methods for absorbing boundary conditions, and the development of penalty methods for the weak imposition of boundary conditions.

David’s research style was legendary: He truly preferred to work at the blackboard, working through questions one by one, discussing out loud how to take the next step. Many offices have been left coated in thick layers of chalk dust after such sessions. David never took notes during or after these discussions, but rather relied on his memory and insight, insisting that the work would be repeated during the following session. He believed strongly that if the results were not immediately repeatable, the original work was faulty and it was necessary to start over---hence the dispensability of notes.

Working at the blackboard, David would show his unique ability to penetrate a complex problem and condense it to its essence, resulting in a much simpler problem that would be amenable to analysis and insight.  It was this remarkable ability that enabled him to make progress on problems otherwise believed to be out of reach. He spent many hours impressing the value of this approach on his students and collaborators.

His informal and insightful style was also in evidence in the classroom. David loved teaching and firmly believed that thorough understanding of the core material was superior to superficial knowledge of a vast body of material. For this reason his classes would often appear to progress very slowly. On occasion, young and ambitious students were surprised at first, coming to appreciate only later the depth of understanding he had given them through this approach. David had the ability to take a complicated proof and explain the heart of it in a straightforward and relevant manner, along with plenty of examples. True to his love of history, his lecture topics were often presented not only with their scientific context but with their historical context as well. His would often litter his lectures with jokes, making an often difficult and serious subject seem light and enjoyable.

In addition to the classic monograph of 1977, David published more than 125 papers on a wide range of topics and an additional book (with S. Gottlieb---his daughter---and me) titled Spectral Methods for Time-Dependent Problems (2007). He served on the editorial boards of many journals over the years, including SIAM Journal on Numerical Analysis, SIAM Journal on Scientific Computing, and Journal of Scientific Computing. As a member of numerous review and visitor committees for universities, funding agencies, and national laboratories, he played a central role in the ongoing development of scientific computing as a discipline in the U.S. He was one of the founders of the International Conference of Spectral and High-Order Methods (ICOSAHOM)---an international conference that has been running successfully since 1989 and continues to be the primary venue for the growing community of people working in these areas.

In the course of his career, David had 22 PhD students (3 in Tel Aviv and 19 at Brown) and served as a mentor for numerous postdoctoral researchers, many of whom have gone on to become leaders in their field both domestically and internationally.

In recognition of his originality and scientific impact, David received honorary doctorates from the University of Paris VI (1994) and Uppsala University (1996), and was elected to the U.S. National Academy of Sciences (2006) and the American Academy of Arts and Sciences (2007). In 2008 he gave the SIAM John von Neumann Lecture at the 2008 SIAM Annual Meeting; titled "The Effect of Local Features on Global Expansions," it was, sadly, to be his last public lecture.

While the scientific value and lasting impact of David’s body of work are undisputed, his qualities as a human being have had an even more profound impact on the community that developed around him. This quality is perhaps appropriately expressed, given David’s deeply rooted commitment to the Jewish faith, by the Yiddish word "Mentsh"---a person of integrity and honor, combining kindness, responsibility, and dignity. Those of us who were fortunate enough to get to know David came to appreciate his sincerity, his openness, his insightfulness, and, above all, his genuine interest in the well-being of others.

David was proud of his accomplishments, and recognition by his peers was very important to him. On the other hand, this recognition inevitably left him in a difficult situation, as his first thought was always with those he felt to be more deserving than he was.

In May 1997, David was diagnosed with kidney cancer---for which the forms of treatment available at the time were very limited and the chances of survival poor. When the disease returned in late 1999, he was given eight months to live; fortunately for all around him, the medical doctors were wrong. In an act of defiance---so typical of David in his dealings with his illness---he began to study mathematical models of tumors and tumor diagnosis, and this topic formed the core of the thesis of his last student.

The illness and the many experimental forms of treatment he went through took a tremendous toll on his physical well-being, yet he always gave the impression that all of this was secondary and minor. Never did he complain, and he always had time for people seeking his help, advice, or comfort. His courage in fighting this illness will serve as an inspiration to all of us when we face hardship in our lives.

On January 25, 2009, a significant number of David’s close colleagues, friends, and former students gathered with his family at the Brown Hillel Center to celebrate David’s life with a memorial service. Many took advantage of the opportunity to say a few words about David, expressing their deep respect and appreciation for his kindness, his complete lack of selfishness, his courage, and his total devotion to his family.

With his deep interest in history, David Gottlieb often expressed the wish to study this subject in greater depth. Ironically, his fortuitous departure into computational mathematics not only became a part of history but also allowed him to shape history itself through his work and his qualities as a human being.

His departure has left a gaping hole in the community. The absence of his kindness, his insight, and his generosity has left many of us with a tremendous sense of loss.

--Jan S. Hesthaven, Division of Applied Mathematics, Brown University, with the help from many of David’s friends, colleagues and students

Please also visit a special blog established in Professor Gottlieb's memory.  Your reflections are most welcome.