Herbert Bishop Keller
SIAM News, Vol. 41 (July 2008), No. 6, p. 2.
By Michael Holst and Thomas Y. Hou

The applied mathematics community experienced a tremendous loss of one of its intellectual and spiritual leaders when Herbert Bishop Keller, a long-time Professor of Applied Mathematics at the California Institute of Technology, passed away unexpectedly on January 26, 2008 in his home in Pasadena, California. Herb (as he preferred to be called) would have been 83 years old on June 19. He had just returned from his regular 40-mile Saturday morning bike ride with friends when he suddenly passed away. Herb was a central figure in the numerical analysis community, although his work branched into a number of other areas in applied mathematics, including bifurcation theory, computational fluid dynamics, homotopy and path following methods, and parallel computing algorithms. He was the co-author (with Eugene Isaacson) of a textbook in numerical analysis in 1966 entitled ``Analysis of Numerical Methods'', which is considered a classic in the area and is still used in several leading graduate programs in computational and applied mathematics. Herb served as SIAM Vice-President during 1973-1974, SIAM President from 1975-1976, and was the recipient of SIAM's Von Karman Prize in 1994. He was a Guggenheim Fellow from 1979-1980, and was a Fellow of both the American Academy of Arts and Sciences and the American Association for Arts and Sciences. In addition to Herb's numerous professional achievements, he was simply adored by his many friends, colleagues, and students, and his passing is a tremendous loss to a very large personal and professional network of people. Herb is survived by his son Steve, daughter Debbie, former wife Loretta, and four grandchildren.

In the following article, the co-authors have tried to collect together some biographical information along with some entertaining and telling stories about Herb from a number of his close friends, colleagues, and family members.

Herb was born in Paterson, New Jersey, on June 19, 1925. He was born two years after his well-known sibling, Joe Keller, to his mother Sarah Bishop Keller and his father Isaac Keller; there were no other siblings. Both Herb and Joe were given their mother's maiden name, Bishop, as their middle name. Their father Isaac Keller was born in 1888, in the part of Poland then part of Russia, and he came to the US in 1905. Their mother Sarah was born in Hull, England in 1900, and came to the US that same year. Sarah's parents came from Russian Poland, and had lived in England for a few years.

Herb attended Public School 20 and Eastside High school in Paterson. Upon graduation he went to Georgia Institute of Technology in Atlanta, Georgia, where he majored in Engineering Physics. He also joined the Naval ROTC. Upon graduation he married and then entered the Navy as an officer. He became a gunnery officer, and his ship patroled the Atlantic. (The following anecdote was related by Joe Keller.) When it was time for him to be released from the Navy, he was told that he could not be released because there was no other gunnery officer on board. He was advised to teach a gunnery course to incoming officers, which he did, and one of his students was Jimmy Carter! He was then released from duty.

Herb returned to Georgia Tech where he began graduate study, but after a year he moved to NYU to study mathematics instead. (The following anecdote about this period of Herb's life was related by his brother Joe Keller.) When Joe received his PhD in 1948, he invited Herb to join him on a trip to Europe for two months. They bought bikes there and cycled a great deal. Once near Marseilles, they found the road lined with thousands of people, who cheered and applauded them wildly. It turns out that they had entered the route of the Tour'de France, and they were ahead of the pack. Herb enjoyed this biking trip to Europe a great deal, and as it turned out many years later he took his son Steve to Europe for a similar cycling trip. His love affair with bicycling really took off in 1985 after returning from trekking through the Himalayas for several weeks; he subsequently gave up smoking, became a biking "fanatic", and spent much of his time cycling with friends in cycling clubs in Pasadena and in San Diego.

After Joe became his advisor at NYU, they wrote several papers together on wave propagation and reflection. Joe thought it would not look right for him to be listed as his advisor, so he asked his colleague Wilhelm Magnus to sign Herb's thesis. Joe comments that this was a big mistake, since he turned out to be one of Joe's best students! Herb remained at NYU as a faculty member, and decided to work in numerical analysis and computing (Herb commented to various colleagues over the years that this decision was to allow him to make a mark in mathematics distinct from his brother Joe.) He ultimately became the Associate Director of the A.E.C. Computing and Applied Mathematics Center at the Courant Institute. Herb met and married Loretta during this period at NYU, and also spent time running the mathematics department at nearby Sarah Lawrence College from 1951 to 1953. He often spoke about his experience at Sarah Lawrence, and this remained with him throughout his career, influencing his approach to teaching at Caltech, and later impacting his development of the summer teaching programs as part of the NSF Center for Parallel Computation (CRPC) which he directed at Caltech from 1989 through his retirement in 2000.

Herb visited the Applied Mathematics Group at Caltech for a year in 1965, at the invitation of Gerald Whitham. Herb returned to NYU for the academic year 1966-1967, acting as Associate Director of the A.E.C Computing and Applied Mathematics Center at the Courant Institute. However, he came to miss California, and after Caltech approached him during that year about returning to Caltech as a faculty member, he then returned as a Professor of Applied Mathematics in 1967, with a joint appointment in Mathematics. He remained at Caltech until retiring in 2002. Caltech allowed Herb's career in applied mathematics to blossom fully, which he recognized and appreciated throughout his professional career. He remained an enthusiastic believer in Caltech as an institution to the end of his life, donating his Pasadena home to Caltech to endow a lectureship.

During his time as a Caltech Professor of Applied Mathematics, Herb became a central figure in the numerical analysis and applied mathematics communities, and over his career he made fundamental contributions to a number of areas in applied mathematics, including bifurcation theory, computational fluid dynamics (CFD), homotopy and path following methods, and parallel computing. He is particularly well-known for his work on numerical methods for two-point boundary-value problems, and for his careful numerical analysis of nonlinear problems exhibiting folds and bifurcation phenomena. He is considered one of the pioneers of pseudo-arclength continuation and other numerical homotopy techniques for difficult parameter-dependent nonlinear problems. His work in numerical homotopy methods is a beautiful blend of ideas from numerical analysis, linear algebra, nonlinear analysis, differential geometry, and topology. (His elegant work in this area heavily influenced the first author of this article to choose numerical analysis as a field.) In the later part of his career, he and G. M. Shroff developed the Recursive Projection Method (RPM) to stabilize fixed point iterative procedures for solving nonlinear parameter dependent problems. This method has generated a great deal of interest in the scientific community, and has found many interesting applications in different scientific disciplines. Herb was honored for his work as a Fellow of the American Academy of Arts and Sciences, as a Fellow of the American Association for Arts and Sciences, as a Guggenheim Fellow (1979-1980), as a Distinguished Visiting Fellow of Christ's College in Cambridge (1993-1994), and finally with SIAM's Von Karman Prize in 1994.

Herb was exceptionally active in the scientific community, serving on the SIAM publications committee (1964-1971), on the SIAM Council (1965-1968), as SIAM Vice-President (1973-1974), as SIAM President (1975-1976), and was on the Science Policy Committee from 1986 until he retired. He also served on council for the National Research Council of the National Academy of Sciences Division of Mathematical Sciences (1969-1972), and was on the executive committee (1970-1971). He also served on the council (1971-1974) and on the Nominations Committee (1974-1975) for the Conference Board for the Mathematical Sciences. He was also active with the American Mathematical Society, serving on the Council (1974-1977), the Committee on Science Policy (1979-1982), and was the Chairman of the Gibbs Lecturer Committee (1975-1976). He served on the editorial boards (periodically as either Chief Editor or Associate Editor) of a number of the central journals in applied and computational mathematics, including SIAM J. Appl. Math., SIAM J. Numer. Anal., Numerische Mathematik, Journal of Computer and System Sciences, the International Journal of Mathematics and Mathematical Sciences, the Journal of Mathematical and Computer Modeling, the Japan Journal of Applied Mathematics, and Journal of the Ramanujan Mathematical Society, and Journal on Differential and Integral Equations, the ACM Monograph Series, Acta Numerica, the Springer Series in Computational Physics, and the North-Holland series on Studies in Mathematics and its Applications. Herb also served on a number of national panels and committees, including the Applied Mathematics Division Review Committee at Argonne National Laboratory, the Computing Facility Advisory Panel for NCAR, the Applied Mathematics Advisory Panel for NBS, the Regional Conference Panel for the Conference Board for the Mathematical Sciences, the Panel on Applied Mathematics Research Alternatives for the Navy, and the Science Council for the Universities Space Research Association. He lent his expertise to numerous corporations through consulting work, including Aerospace Corporation, Argonne National Laboratory, Batori Computer Company, Boeing Scientific Research Labs, CEIR Inc., General Electric Space Systems Division, General Applied Science Labs, Exxon, IBM, Los Alamos Scientific Labs, Maxon Corp., McDonnell-Douglas, North American Aviation, and the U.S. Army Signal Corps.
Herb wrote several seminal books and monographs during his career. His work on two-point boundary-value problems in the first part of his career appears in both a long Dover monograph and in a shorter SIAM monograph. His later work in bifurcation and path-following appears in a well-known monograph published by the Tata Institute. The 1966 textbook he co-authored with Eugene Isaacson, ``Analysis of Numerical Methods'', is a classic in the area and is still used in leading graduate programs in computational and applied mathematics. (One of the co-authors of this article uses it regularly, due to its careful treatment of a number of topics not covered in more modern surveys in the area, such as the constructive proof of the Weierstraus Approximation Theorem using Bernstein polynomials.)

(The following amusing story about Herb, Eugene, and this textbook was related by Tony Chan, with some recollections added from the first author.) Apparently, Herb and Eugene were having a lot of trouble agreeing on the preface to their book, so one would rewrite it, pass it to the other, and then the other would completely rewrite it again. Finally Herb decided to embed a hidden message in the preface using an acrostic, which would mean that if Eugene modified the preface again, he would destroy the message. Eugene then gave in and told Herb that he would agree to that version of the preface, which is the one that eventually appeared in the book. (We challenge the reader to find the hidden message in the preface.)

After retiring from Caltech, Herb joined the Center for Computational Mathematics (CCM) within the Mathematics Department at UC San Diego as a Senior Research Scientist, and split his time between his home in Pasadena and a condo in Leucadia, about 17 miles north of UCSD. Herb was a regular attendee at the weekly Tuesday CCM Seminar, and was present the week before he passed away. He usually biked down to UCSD from his condo in Leucadia, a round-trip of 35 miles a day.

After Herb passed away on January 26th, a number of his close colleagues and friends gathered with his family on February 24th at the Athenaeum at Caltech to celebrate Herb's life with a memorial service. It was a wonderful event with all of Herb's family present, along with Herb's long-time friends and colleagues from Caltech, UCSD, and elsewhere in Southern California. Herb's daughter Debbie and her family organized the event, together with Sheila Shull, Herb's longtime friend and administrator in Applied Math at Caltech. The service was organized around a lunch, with the opportunity for anyone who wished to stand up and say a few words about Herb. Some of the individuals who spoke were Herb's brother Joe, his former wife Loretta, Sheila Shull, JoAnn Boyd (Herb's longtime administrative assistant for the CRPC Center), Tom Hou (Herb's colleague at Caltech), Michael Holst (former postdoc of Herb, now faculty at UCSD), and Tony Chan (former postdoc of Herb, now faculty at UCLA and NSF). Through recollections of events and anecdotal stories, Herb's wonderful appetite for life, generosity, sense of humor, and many other wonderful aspects of his personality were remembered. The "Keller Principle" was identified by a number of people as having been taught to them by Herb; this is a general approach to solving problems that involves "asking for forgiveness later" rather than "asking for permission first". The first author gave some examples of Herb's fearless approach to mathematics and science, and described him as having tremendous self-conficence and ``chutzpah'' to go after interesting problems regardless of field. This approach impacted and continues to influence his many students and postdocs to this day.

When it became widely known that Herb passed away in late January, a number of Herb's colleagues and friends came forward with various amusing and insightful stories and comments and Herb. We thought it most fitting to include most of these contributions, essentially verbatim.

Eugene Allgower: There was an incident about 30 years ago, which boosted my esteem for Herb sky high. It concerned referee's reports for a habilitation. This is much more critical than reports for a paper, it is more like a tenure decision which decides whether a career can proceed. To make a long story short, there was one report which was unfairly negative and had thrown the habilitation committee into uncertainty. Two more expert referees were called upon to give their opinion. Herb was one of them. Herb indicated in no uncertain terms that the habilitation paper was an excellent piece of work and he didn't understand why there could be any dithering over the matter. That settled that! In that regard, I always found Herb to be totally direct and fair as a referee or as a reference giver. I well remember a personal incident too. About 10 years ago, while attending a conference at IMA, I was walking on crutches, due to a broken hip. Herb and his partner, solicitously asked how I had broken my hip. When I told them that it resulted from a bicycling accident, they said that a real bicyclist would have broken his collarbone!

Tony Chan I was Herb's postdoc from Jan 1978 to Aug 1979. But even before that, my academic life had already been highly influenced indirectly by him. First, I used his Isaacson-Keller book in my undergraduate course on numerical analysis at Caltech. Near completion of my PhD at Stanford, I was referred to the postdoc with Herb by Joe Keller (Herb's older brother), who had just recently arrived at Stanford as a faculty member. Given my background on computational linear algebra, it was natural that the first problem that Herb asked me to work on was on the iterative solution of singular linear systems, which quickly brought me to the source of these problems, namely bifurcation problems where the Jacobian matrices are singular at critical points. This opened up a whole area of math that I had no previous exposures to before and for this I am always indebted to Herb. Shortly afterwards, Achi Brandt was visiting Caltech, and out of that visit we started working on multigrid methods for singular and indefinite elliptic systems, which I pursued for a number of years afterwards. I continued my interest on multiscale methods for many more years. It all had its beginnings with Herb. Herb was a very intensive, and some may say competitive, person, whether it is work or play (tennis was his main game back then and we often played at the Athenaeum). He was confident, set high standards for himself and people he worked with, and wanted to be the world leader in whatever he was working on. That certainly had a lasting effect on my own career. Yet he always had a sense of humor. The best (but may be not as well known) example is the "hidden" message in the Preface of Isaacson-Keller. That mischievous and rebellious sense of humor is so quintessential Herb. For a young person starting out, just knowing that even a revered senior role model can be a bit of fun in work was a revelation. I'll remember him dearly.

Ellis Cumberbatch: Herb was an informal advisor when the mathematics clinics were inaugurated at Claremont Graduate University and Harvey Mudd College in the 1970s. Subsequently he was a frequent visitor when students presented their project results at the end of the academic year. He was interested in the problems that industry had set and in the approaches the teams adopted, but he was also on the lookout for talent to attract to the Caltech program. He was valued member of the CGU Math Board of Visitors from the mid-90s, giving generously of his time and experience. He came to a BOV dinner in Claremont in December 2007, bringing a bike in his Prius and pedaling 28 miles before the wine session. Claremont is also an attractive bike ride out for a number of Caltech faculty; it has a pleasant downtown boasting a high-end bike shop and a first-class bakery - a frequent Sunday morning venue for Herb and his bike group.

Sebius Doedel: I was introduced to Herb by Jim Varah (UBC) who had held a position at Caltech. Herb offered me a postdoc in Applied Math at Caltech (1975-1977). It was during this time that I learned about bifurcations and their numerical analysis in a graduate course that Herb gave and in many discussions with him. During this period I also implemented Herb's ideas in a program for computing bifurcating solution families in nonlinear ODE boundary value problems. This period was extraordinarily exciting for me: I felt that I was being introduced to something very important and very useful. When I got a job at Concordia University in Montreal in 1979 I started working on the continuation of periodic solutions, their bifurcations, and related topics. This work, which led to the software AUTO, was greatly influenced by Herb's fundamental work. When Herb found out about AUTO he invited me for return visits to Caltech, not just for a few days, but in fact for several years total time! These visits led to work on applications of continuation methods, which in turn resulted in improved algorithms in the AUTO software. I have fond memories of Herb: not only did he provide me with key ideas, but he was also always extremely supportive of my work in many ways. I greatly admired his originality, his incredible energy, and his courage to try out totally new ideas. Moreover, I deeply valued the personal friendship; the many bike rides with him, his company during visits to France, The Netherlands, and many other places.

Donald Estep: Herb Keller had an enormous impact on both my personal and professional lives. Much of my personal interactions with Herb revolved around cycling. Indeed, Herb and another mutual friend decided to play matchmakers and they introduced me to my future wife on a ride to Claremont. Eighteen years and 3 children later, we still enjoy riding together, thanks to Herb. Many of my best memories of Herb, and still the subject of stories when we get together with mutual friends, are the times we spent together on our bicycling trips around the US and Europe. Those trips illustrate Herb's best qualities. For example, we had the fun of cycling through The Alps with Herb in the summer of 1992. We would plan a route for the day and sometimes ride together and sometimes someone would ride ahead, but wait for the rest, at a decision point in the road. Herb, with his absolute confidence in his sense of direction, would often keep going. One afternoon in Austria, we lost track of Herb in a village with a lot of winding streets. We waited for an hour in the next town as the weather turned worse, hoping he would come past so we could ride to the hotel together. Finally, we rode along dispiritedly to the hotel, only to be greeted by Herb relaxing in a chair outside the hotel bar. He had cleverly fallen in with a local group of riders who rode fast to a bar in another town a few miles away, where they proceeded to treat Herb to a feast. After a lot of food and a few toasts, Herb became a little worried about going the last few miles to our hotel. But as he stepped outside with the group of his new friends, one beckoned to a limousine, which pulled up. As it turns out, these were very wealthy bicyclists (including the sports minister of Austria), and they gave Herb a ride to his hotel. Herb seemed never to hesitate at the crossroads and by virtue of his personality, generosity, cleverness and positive attitude; things seemed to work out for him. Professionally, it is hard to describe the impact that Herb had on my career. Languishing in a poisonous "pure versus applied" climate at my own department as an assistant professor, Herb gave me two precious years at Caltech in which I could find my own direction. By providing me with the example of his own scientific courage, he taught me to pursue new ideas without fear of failure and that the key to a successful, and fun, career in a university is to always keep scientific issues paramount. But, I was just one of many young people that Herb helped in this way. My last memory is listening to Herb answer the endless questions of my son about the motion of waves while we sat on the beach outside his San Diego condominium. Seeing Herb infuse yet another young person with the joy in science and mathematics is a fitting way to keep him in mind.

Roland Glowinski: I met Herb several times in the seventies and had a friendly relation with him but no real scientific cooperation. Things changed when he came to INRIA, in France, in the early eighties, to spend a sabbatical year in the research group (called MENUSIN) I was directing at the time. We started working together, merger his knowledge on the mathematical and numerical aspects of bifurcation theory with our own knowledge of finite element and variational methods. This led to the doctoral thesis of Laure Reinhart on the computation of the post-buckled solutions of the Von Karman (another Caltech hero) for plates and to a joint paper by Herb, L. Reinhart and myself, published in SISCC in 1985. Thanks to him, we demystified bifurcation, continuation methods, non monotonic nonlinearities. Indeed, he made us interested in the Gelfand-Bratu problem, and in the late nineties, my colleague J. He and I dedicated an article to him, published in JOTA on the chattering boundary control of the time dependent Bratu equation. Working with him was a real pleasure, due his knowledge, his enthusiasm, his predilection for difficult problems and the creative way he had at looking at things. He was instrumental at bringing me to Caltech for a semester in 1988/1989, as a Fairchild scholar. In 2006, I asked him to be part of the thesis committee of my PhD student F. Foss; since the thesis was about nonlinear eigenvalues and arc length continuation for some elliptic operators, he accepted with enthusiasm, making the defense of the thesis a most memorable event. We will miss him.

Arieh Iserles: My close interaction with Herb was at the stage of my own mathematical journey when, in late 1980's, I've "discovered" computational dynamics and attempted to use ideas from dynamical systems to understand the behavior of numerical methods. Herb was already the central person in computational dynamics. It is indeed no exaggeration that his work defined the subject: from bifurcation theory to continuation methods, the AUTO package etc. It was natural to talk with him and so our contact started in earnest and I valued his feedback and encouragement. In 1989 I've organized a conference in Bristol with the memorable title of "Dynamics of Numerics and Numerics of Dynamics" and Herb was one of the main speakers. In a flash of true genius, I persuaded him and Steve Smale to spend the preceding summer with me in Cambridge, and it was a memorable time indeed and an opportunity to learn a great deal, witness some great mathematical discussions and hear some great stories. Of course, Herb arrived from the airport on a bike and left to Bristol on a bike. A few years later Herb came to Cambridge for a year. We have many visitors in Cambridge but Herb was unique. Firstly, he was fun and a true character. The year was 1995 and the big event commemorating 50 years since the end of World War II was held at the American Cemetery at Madingley, outside Cambridge. Herb, needless to say, attended with his bike, in a stars-and-stripes biking outfit. Next day "Cambridge Evening News" carried two huge photographs on its front page: one of President Clinton and Prime Minister Major, the other of an "American visitor" with white beard and a cycling helmet. Besides being fantastic company and a phenomenal story teller, Herb also weaved among us his mathematical magic. He gave a graduate course from which we learned degree theory, differential geometry and homotopy methods, something that was just in time for my own evolving research concerns and also influenced others of my colleagues. He was a Distinguished Visiting Fellow of Christ College and immensely enjoyed the college life and fellowship privileges. Within a year he became a real Cantabrigian and we were immensely sad when he, his bicycle and his stories returned to South California. Since then I've seen Herb for various amounts of time: from a couple of months at MSRI to a couple of weeks at Durham, shorter amounts of time all over the world, from Park City to Rio de Janeiro, Toronto, Beijing, Minneapolis... And, perhaps most importantly, Pasadena (where once, foolishly, I allowed Herb to persuade me to join him on a bike ride: after several hours I, his junior by more than twenty years, was panting like a beached fish, while the Cycling Master hardly broke sweat) and Cambridge. The last time was in Cambridge last November. I did not know it was to be the last time and I realize with immense sadness that I'll never see him again.

Michael Holst: Shortly after I moved to UCSD in 1998, Herb purchased a condo in Leucadia and started spending close to half his time in San Diego. We appointed him as a research scientist at UCSD when he retired from Caltech around the year 2000, and he quickly became a full member of our Computational Mathematics group in the UCSD mathematics department. He was still very active; he was a regular at our Tuesday 11am seminars and at the faculty club lunch that followed, and he was with us the Tuesday before he passed away. It should be noted that Herb usually commuted to UCSD from Leucadia (about 17 miles north of UCSD) on his bicycle; he was always in tremendous physical condition, which is why his sudden passing caught many of us by surprise. It should be noted that I never once managed to beat him in either tennis or ping-pong. Besides being my postdoctoral advisor at Caltech, he had become one of my closest friends and colleagues over the last ten years. He was very generous and supportive of young people. When I was trying to figure out the logistics of how to take part in the numerical relativity visitor program at Caltech in 2003, at the same time that my wife Mai was pregnant with our first child Mason, he simply gave me the keys to his house in Pasadena so that Mai could stay in San Diego and so that I could go up to Caltech whenever it worked out. Herb had also become close with my wife Mai and our children Mason and Makenna over the last several years; we had him over for our holiday dinner just a few weeks before he passed away. Herb had a large impact on many lives, especially mine, both professionally and personally. I admired him tremendously; he was just fearless, both with regard to things like biking (those who kept track of his numerous bicycling accidents have some insight into this), and with regard to mathematics and science. Our interactions during my postdoctoral (1993-1997) and sabbatical (2003-2005) years at Caltech with him changed the way I thought about mathematics and science, and also changed the way I thought about myself. He had tremendous confidence in his own abilities, and refused to be limited by anyone's opinion of where he exactly fit in science, instead working on any problem that he felt to be particularly interesting. The paper sitting on his desk at UCSD when he passed away was one of Perleman's papers on Ricci flow; Herb was extremely interested in this work, was confident that he could learn the area, and was methodically working through the paper. He and I had a number of discussions about this in the months before he passed away. His influence and example led directly to my own work in mathematical physics, quite far from my original dissertation work in numerical analysis. It fills me with great sadness that we are no longer going to have the honor and pleasure of his company. He will be missed.

Debbie Keller: When I was little my dad used to take me to the driving range. I loved the wire bucket the balls came in. I loved handing Dad balls from the bucket and watching him practice his swing with a passion that consumed him. I was always sorry when it was time to go home. If you were to ask me to describe my dad in a single word, that's the word I'd use: passionate. Whatever it was that interested him, passion drove Dad to both excel in and relish it. Numerical analysis, cycling, reading the blurbs next to the paintings in the Norton Simon Museum, whatever. Once, when my kids were little, Dad took us on a nature walk in Pasadena. It was just a walk, but along the way we passed an archery range. Next thing you know the lone archer and Dad were best friends. An hour passed. We all got archery lessons and my kids were sent home with souvenir arrows, which they still have. One thing Dad relished was athletics. He was proud of himself and readily shared his accomplishments - he rode X miles on his bike that day, swam X number of laps, did X number of sit-ups, weighed X pounds and therefore had to lose Y pounds. I thought this constant stream of numbers was Dad boasting of his prowess, but I was wrong. I discovered the truth last summer. Herb was visiting us in Sacramento and we'd gone out dinner. The streets were crowded and we had to park some blocks away from the restaurant. Being the athlete he was, we knew Dad wouldn't mind the walk. He clasped his hands behind his back, leaned forward, and set forth, mumbling numbers as he went. My son asked if he was working on a problem. Dad stopped and looked up. "No. No problem," he said, smiling. "Just counting the number of steps to the restaurant so we can compare them to the number of steps back." Dad was a numbers man. Numbers were his passion in every facet of his life. The X miles he rode, the score of his arrows, the length of his golf drives, and he probably counted the number of balls in the wire bucket, too. I love that about my dad.

At the memorial service on February 24th, it was decided by a number of Herb's close colleagues that they would organize a 1-day Symposium in his honor at Caltech in Fall 2008. This will be held on September 12 at Caltech, and some of the speakers will be Tony Chan, Roland Glowinski, Tom Hagstrom, Michael Holst, Arieh Iserles, and Peter Lax.