# Interview with Herbert B. Keller

By Hinke Osinga
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## Herbert Bishop Keller

by Hinke Osinga
University of Bristol, UK

In March 2005 DSWeb Magazine had the splendid opportunity to do an interview with Herb Keller when he visited Bristol to attend the workshop Qualitative Numerical Analysis of High-dimensional Nonlinear Systems. Herbert Bishop Keller, who was born in 1925 in Paterson, New Jersey, turns 80 this year ("Yes, in June... If I last that long"). Starting at the age of 20, he has been working in mathematics for almost 60 years and it would be impossible to convey the entire breadth and depth of his work in one article. This interview particularly focuses on his contributions in Dynamical Systems Theory.

 Herb got a Bachelor in Electronic Engineering from Georgia Tech in 1945. "This was a special program during the war years, where you took three semesters in one year for an otherwise four-year program. I did it in two years and eight months and so I was only 20 years old then." Herb got to Georgia Tech as part of the Naval Reserve Officer Training core program. He was trained as a fire control officer and he was on a battleship preparing for the invasion of Japan. There is a certain matter-of-fact-ness about it: "I got my diploma, and the next day I got married, and the next day I was off to war." From this point of view, one can understand the elation Herb felt when the bomb was dropped: Herb to Hinke: "I got my degree and the next day I got my comission as an Ensign in the Navy, and the next day I got my Georgia peach!" (March 24 2005, photographer Bernd Krauskopf) it meant he could go home. "They had a point system: you could get discharged as soon as you had enough points." However, when Herb had collected the required number of points a few months later, he was told that he couldn't possibly leave! "I was their only qualified catapult officer, they couldn't lose me." As suggested by a fellow officer, Herb put a message on the notice board Catapult class, 8am Monday morning' and, indeed, four young men showed up. "They were all from Annapolis, and one of them was Jimmy Carter! After two weeks of training them, I could go home."

In 1946 Herb was back at Georgia Tech and trying to decide what to do. His two-year older brother Joe was by then a Faculty member at the Institute for Mathematics and Mechanics at New York University, which later was to become the Courant Institute of Mathematical Sciences. "I was interested in Engineering and Physics, so naturally I was good at Mathematics, but I had never thought about a career in Mathematics. Through my brother I began to believe that Mathematics might be interesting." Joe arranged for Herb to meet Courant. Obviously, an interview with Courant himself was a serious matter, and Herb decided to wear his Navy Whites. "I had worn that uniform only twice before, when I tried it on, and when I got married. It seemed appropriate to wear it again." It is unclear whether the uniform did it. Courant certainly was not much impressed with Herb's mathematical skills. "At one point he looked up and down the big windows in his office and asked: Do you know how to wash windows?' But he hired me anyway and, fortunately, he found something else for me to do!" So that was that. Herb went to New York and studied for his Master's, which he got in 1948.

 Herb wrote papers with his brother on scattering theory and the reflection and transmission of electromagnetic and sonic waves. Part-time he also taught at Sarah Lawrence College in Bronxsville, New York. "There were 360 mostly wealthy and good-looking girls at this school, and I was the Math Department. That was a pretty nice job." As Herb was looking for a topic for his PhD, he realized that he should not work too closely with his brother. He decided to move away from scattering theory into computing. "I decided to become a Numerical Analysist." He wrote a thesis On systems of linear ordinary differential equations with applications to ionospheric propagation with Wilhelm Magnus as his advisor and received his PhD in 1954. From then on, he was a full-time member of the faculty at NYU. Joe and Herb Keller on la Tour Eiffel in 1948.

NYU was an extremely active place. The Institute officially became the Courant Institute in 1960, with Niels Bohr as the dedication speaker. "Everyone from Europe who traveled to the US came through Courant. The institute was well known and I got to meet lots of people." In the late 1950s NYU bought the third UNIVAC. This is a 1000-word memory mercury delay line computer, the first commercially available high-speed computer. They founded the AEC Computing and Applied Mathematics Center, of which Herb was the associate director and Peter Lax was the director. "This was the beginning of Scientific Computing. I think I was very fortunate to be getting into the numerical business at the right time. Numerical Analysis really took off. The main problem was how to solve big systems on small computers. It is changing now, because there is so much good software. We didn't even know the term software!"

Research in the early 1960s always had a strong military flavor. "We had the cold war with Russia. We wanted to know how to protect people from bombs." Together with Bob Richtmeyer, Herb set up a research group working on nuclear reactions and the effects of atomic weapons. "We were interested in Mathematical Physics in much the same way as Los Alamos, but our stuff was not classified. We worked on the theory of nuclear reactors for naval power reactors. These were diffusion problems and transport problems. It was all done numerically."

 At the same time, Herb was interested in fluid flow problems. "At Courant there was lots going on about fluid flow. You simply couldn't help being part of it. It really was the area where I started to work on computational things." He studied Von Karman swirling flow between rotating disks, Taylor-Couette flow, flows in channels and over airplane wings. "Oh yeah, and satellite re-entry problems. That is simply the flow around a sphere when entering the atmosphere at hypersonic speeds." Herb and Joe Keller at Iguassue Falls in Brazil, 1985.

## Developing a taste for Dynamical System Theory

At some point, Herb started working with Ed Riess, who was interested in solid mechanics at Courant, on the buckling of spherical shells and rods and so on. "We treated it as an equilibrium phenomenon, while it was a bifurcation problem. But we didn't know that at the time. We realized it had dynamics, but didn't do much about it."

This was also the time when Herb moved from the Courant Institute to the department of Applied and Computational Mathematics at Caltech. He had visited Caltech in 1965, but went back to NYU in 1966. "Courant came to see me and told me that it would be so much better for me to come back to NYU. I agreed with him. I mean, they had much more powerful machines than at Caltech. But when I came back to New York, I knew it was a mistake and I left for Caltech again in 1967 and have been there ever since."

 Herb Keller and Tony Chan (right) in China.

At NYU, Herb had alternated teaching Numerical Analysis with Eugene Isaacson, who was quite a bit older than Herb. Wiley asked them whether they were interested in writing a book about it from the lecture notes. "We had a really good collaboration going, working on this book together. This continued while I was at Caltech, which is quite something, because we didn't have email at the time. I remember writing the preface of the book. I found it really difficult and wanted to get it over with. But when I sent it to Eugene, he responded that it was terrible and had all sorts of suggestions on how to change it. That's when I decided to work in my secret message. Do you know what an acronym is? You go and figure it out. And when you think you should give up, keep on reading! When Eugene saw it, he never complained again." [When Herb told me this, we were enjoying a sparkling Chardonnay at a nice restaurant, and I couldn't wait to get back to my office and read the preface. It's worth it.]

As Herb worked on the book with Eugene Isaacson, he got too carried away on two-point boundary value problems. "It was too much material and I decided to write a monograph on it separately. The techniques explained in that book really were the start of the continuation setting." At Caltech, in 1967, Herb learnt about Lyapunov-Schmidt methods, which made a big impression on him. It was then that he started doing serious bifurcation theory and path continuation. "The real turning point only came in 1976, when I was asked to speak at the Advanced Seminar on Applications in Bifurcation Theory, organized by Paul Rabinowitz and Mike Crandall. The army had a big center for research at the University of Wisconsin and they organized a series of meetings every year with a book for each. In my paper "Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems" for this book, I invented the term pseudo-arclength continuation. It is my most popular paper ever. Rabinowitz was very thankful, because the popularity of my paper meant that his book was very popular."

 Stig Larsson, Simon Tavener, Herb Keller, Alastair Spence, Ridgway Scott, and Don Estep hiking in the Rocky Mountains outside of Fort Collins, Colorado, May 2001.

While research in Applied and Computational Mathematics at Caltech, which grew out of Aeronautics, was primarily focused on Fluid Dynamics, Herb brought in a strong numerical component. He built up a group of people working in Numerical Analysis, including Heinz-Otto Kreiss, Bengt Fornberg, Jens Lorenz, Tony Chan, Jim Varah, Eitan Tadmore and others. However, the core group at ACM was built by Gerald Whitham (a student of Lighthill's), and included Philip Saffman (who had worked with G.I. Taylor), Paco Lagerstrom (a topologist by training who worked on asymptotics in Aero), Julian Cole (also from Aero), Don Cohen (a student of Joseph Keller), and, of course, Herb himself. "In addition, I've had tons of excellent students and postdocs. You know, if you get garbage in, you get garbage out, but if you get good students in... It was a pleasure! Yes, in a sense I was lucky, being at such fantastic places and all that. I was influenced by the many good people around me. However, you cannot fake it in this business."

## Retirement

In contrast to many other countries, there is no longer forced retirement in the US. In 1983, an old senator from Florida who himself was in the 90s, passed a law that one should not force people to retire just because of age. As a transition period, it was decided that in the following ten years, one must retire when reaching the age of 70. "I was lucky. My brother turned 70 just before the end of those ten years, but I didn't."

 For many of the younger mathematicians, especially those who are still looking for a permanent job, it can be frustrating to see grey old men (mostly, isn't it!) sitting on precious academic posts. Herb ponders the possible benefits of forced retirement: "In fact, we did have a discussion at Caltech about how to get rid of the dead wood, but we decided that, at Caltech, we did not have to worry about it." Caltech has an appealing early retirement program, offering a two-year scholarly leave with full pay and no teaching (like a two-year sabbatical), at the end of which one should retire. "I think that good people do not hang on by the skin of their teeth. When they feel they do not pull their weight as compared to the people around them, they will pull out." Herb Keller with his grandson Milo at San Diego Zoo.
 Herb retired from Caltech in 2001. He is now a research scientist at UC San Diego and also kept his office at Caltech, which he also visits regularly. "Aging has effects on your research. You need to do lots of calculations and I find it harder to do. It used to be fun, but it is not as much fun anymore and it certainly does not go as fast." Herb also got tired of teaching. "It is a big commitment and I certainly was not very good at it. I probably could have been more stimulating." Caltech annually awards the Feynman Prize for Excellence in Teaching. The winner is chosen by the students, and the prize consists of a cash award of \$3,500 and an equivalent raise in the winner's salary. Jim Bunch, Herb Keller, and Randy Bank at UCSD, drinking beer. Herb has never won that prize ("Oh no, I didn't even come close!"), but he did ask advice on teaching from Harry Gray, the Beckman Professor of Chemistry, who is a very popular teacher." He told me that you should never start lecturing straight away. The first five to ten minutes the students are not ready for you yet. Furthermore, they cannot concentrate for more than 15 minutes and it is impossible to have them absorb more than one new idea in a lecture. Well, I think he had quite a low opinion of the students, but he worked very hard at teaching professionally. I never thought about it. My concerns were how to best present the material and how to present the proofs." There is a second aspect: the rate at which the course content changes is often slow compared to the changes in technology. "You work so hard on getting the course material, you cannot keep up, certainly not if you ever want to get any research done."

"I must say that it feels great to be retired. We old guys thought we were irreplacable, but we're not. We have been replaced and the young mathematicians are good. However, I do miss having students. That I miss most."

Those who know Herb well know that he hardly ever goes anywhere without his bicycle. "I started cycling rather late, in early 1981 or so. After my divorce I wanted to keep more contact with my son. He was at UC Davis and everyone bikes there, so..." After Herb had been invited to Oberwolfach, he decided to do a big bike tour in Germany and asked his son to join him. What should have been a fanastic vacation ended dramatically when Herb could not make the turn on a downhill slope and ended up head first in a lumber yard. "It must have been terrible for my son. His first bike tour with his dad and then I had this dreadful accident." Herb spent one week in a hospital in Villingen-Schwenningen. Sebius Doedel [Sebius is enjoying the same Chardonnay in this restaurant] remembers the event quite well, because he paid Herb a visit at the hospital. Sebius tells us how he came to the hospital and asked the nurses where he could find Herb Keller. The nurses immediately knew who he meant, because Herb was their most honored guest: "Ah, der Herr Keller! Der ist mit einem Helikopter eingeflogen!!"

Despite this bad accident, Herb has kept cycling ever since. He has also had many other bicycling accidents, but none as remarkable as this first one. "It cured my eyesight! For 30 years I had glasses, even bi-focals, but I haven't worn glasses since."

Bristol, April 2005.

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