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RICHARD E. BELLMAN 22
RICHARD E. BELLMAN 23
Richard E. Bellman
RICHARD E. BELLMAN 22
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Richard E. Bellman
By Solomon W. Golomb
On Friday, May 11, 1984, ''A Celebration of the Life and Accomplishments
of Professor Richard E. Bellman'' was held on the Los Angeles campus of the
University of Southern California. His colleagues and friends from around the
world gathered to share their memories of this remarkable man. Some of their
comments were published by the university as "A Tribute to Richard Bellman."
We cannot include them all in this volume, but the following excerpts provide an
indication of the extraordinary impact Dick Bellman had in his life and work.
Richard Bellman was a towering figure among the contributors to modern
control theory and systems analysis. His invention of dynamic programming
marked the beginning of a new era in the analysis and optimizations of large-
scale systems and opened a way for the application of sophisticated computer-
oriented techniques in a wide variety of problem areas, ranging from the design
of guidance systems for space vehicles to pest control, network routing, and
Richard Bellman was born in Brooklyn, New York, on August 26, 1920. He
received a B.A. from Brooklyn College in 1941 and an M.A. in mathematics from
the University of Wisconsin in 1943.
As part of his service in the U.S. Army, he spent two years
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at Los Alamos, where he was a member of a group in the Theoretical Physics
Division headed by Dr. R. Marshak. Leaving Los Alamos in 1946, he entered
Princeton and completed his work toward a Ph.D. in a record time of three
In the immediate postwar years, Princeton was a center of defense-motivated
research activity in nonlinear differential equations. As a graduate student at
Princeton, Bellman became a member of an inner circle of young mathematicians
led by Professor Solomon Lefschetz. His doctoral research under Lefschetz
resulted in his first major work, entitled Stability Theory of Differential
Equations, in 1946. This work was subsequently published as a book by
McGraw-Hill in 1953 and is regarded as a classic in its field.
After staying on the faculty of the Mathematics Department at Princeton
from 1946 to 1948, Bellman left the east coast to become a member of the faculty
of Stanford University in 1948 and then joined the newly established Rand
Corporation in Santa Monica, California, in 1953. At Rand, he became interested
in the theory of multistage decision processes, which was then emerging as an
important problem area in the control of both small-and large-scale systems. His
invention of dynamic programming in 1953 was a major breakthrough in the
theory of multistage decision processes. This breakthrough set the stage for the
application of functional equation techniques in a wide spectrum of fields
extending far beyond the problem areas that provided the initial motivation for
In addition to his fundamental and far-ranging work on dynamic
programming, Richard Bellman made a number of important contributions to
both pure and applied mathematics. Particularly worthy of note is his work on
invariant imbedding, which by replacing two-point boundary problems with
initial value problems makes the calculation of the solution more direct as well as
much more efficient. His work on quasi-linearization and its applications to
RICHARD E. BELLMAN 25
has led to many results of a practical nature in the study of nonlinear systems.
In recent years, Bellman's research activity focused increasingly on the
application of mathematics to medicine and biological sciences. His interest in
these and related areas reflected his strong conviction that mathematics should
not be content with being a beautiful castle with no bridges to the real world.
There was a time when Bellman's outspoken criticisms of the elitist attitudes of
the mathematical establishment were greeted with hostility and derision. Today,
when pure mathematicians are experiencing difficulties in finding suitable jobs,
many of those who disagreed with Bellman will concede that he was right.
Bellman left the Rand Corporation in 1965 to join the faculty of the
University of Southern California, where he held joint appointments as professor
of mathematics, electrical engineering, and medicine—appointments he held
until his death on March 19, 1984. A prolific writer, he authored over six hundred
published research papers, approximately forty books, and several monographs.
Richard Bellman's fundamental contributions to science and engineering
won him many honors and worldwide recognition. Prominent among these are
the following: first Norbert Wiener Prize in Applied Mathematics, awarded in
1970 jointly by the American Mathematical Society and the Society for Industrial
and Applied Mathematics; first Dickson Prize from Carnegie Mellon University
in 1970; the John von Neumann Theory Award bestowed in 1976 jointly by the
Institute of Management Sciences and the Operations Research Society of
America; and the 1979 Institute of Electrical and Electronics Engineers' Medal of
Honor in recognition of the invention of dynamic programming.
His honorary degrees include the doctor of science of the University of
Aberdeen, Scotland, in 1973; the doctor of laws of the University of Southern
California in 1974; and the doctor of mathematics of the University of Waterloo,
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in 1975. He was elected a fellow of the American Academy of Arts and Sciences
in 1975, a member of the National Academy of Engineering in 1977, and a
member of the National Academy of Sciences in 1983. [R. E. Larson and L. A.
In celebrating his life here today, let us also celebrate his good humor and
his steadfast determination to produce, to achieve, to give, and to give joyfully, in
the face of circumstances that would have overwhelmed and crushed men of
lesser caliber. In these superb human qualities, as in his creative work, I firmly
believe that Dick Bellman has lived on a level at least the equal of Beethoven.
Of his great contributions, I think that he would feel that the students he
inspired were among the most important; through them his ideas go on and will
be expanded to meet the needs of expanding technology and human need. The
only function that Richard Bellman could not bound was his own energy and
imagination. [Fleur Mitchell]
The measure of a man is the number of people whose lives he has influenced
and the contributions he has made. Dick Bellman not only influenced the lives of
many people, but he had the rare genius to be able to contribute to many fields.
Someone said that the Soviet Union is not just another country—it's another
world, another planet. And it, indeed, is. But the stars, we might say, continuing
the metaphor, are the same on every planet. They shine for everyone and
everywhere. Dick was, and is, such a star. His influence in the Soviet Union is
deep and profound. His works penetrated many areas of Soviet academia,
industry, and economy in general. From the academic point of view, there is not a
single university that does not offer courses based on Dick's works. Hundreds of
papers continuing Dick's ideas are published annually in Soviet journals. It is
hardly possible to find a researcher in the quantitative sciences and engineering
unfamiliar with, at least, the term "Dynamic Programming."
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Dick's name is probably cited more at Soviet scientific meetings than at
American ones. As an indirect proof of this, let me just mention that Dick was
invited to be the main speaker at the first, and only, International Congress of
Mathematicians held in Russia, in 1966. More than ten of his books have been
translated and published in the Soviet Union. No other American scientist has
been given such honors in the USSR.
This is one of the trademarks of Dick's creative work: Truly a mathematician
of the twentieth century, he viewed a computer as a tool as well as an important
source of mathematical work. His results are always practical and easily
applicable. Probably, this is why his mathematical discoveries have important
engineering implications in such areas as system science, control,
communications, bioengineering, etc. The depth and importance of problems
considered, the practical applicability, and the timeliness of his works, this is
what, in my view, made the largest impact and defined Dick's influence on Soviet
Dick gave all of us, his students and friends in every country throughout the
world, an ultimate example of scientific creativity and success, personal courage
and strength, friendly devotion and support. [Semyon Meerkov]
He was contemptuous of the established order and intolerant of mediocrity.
He was strikingly handsome, brilliant, and a master of both the spoken and the
written word. Clearly, he was a man of towering intellect and almost equally
towering ego. But what I could see was that behind the facade of arrogance and
bravado was a man who was capable of great kindness, a man who was decent,
straightforward and generous in the extreme.
He died at peace with himself. But his ideas will continue to live, and so
will the fond memories of all of us who knew him not only as a brilliant thinker
and arrogant personality, but, more importantly, as a man of great nobility of
character and a warm, thoughtful, caring human being. [Lofti Zadeh]
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At the time of his death at age sixty-three, Richard Bellman had just
completed his autobiography, The Eye of the Hurricane, World Scientific
Publications, Singapore, 1984. He is survived by his wife, Nina; his son, Eric; and
his daughter, Kirstie.
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