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RICHARD E. BELLMAN 1920-1984 BY SOLOMON W. GOLOMB On Friday, May 11, 1984, "A Celebration of the Life and Accom- plishments of Professor Richard E. Bellman" was held on the Los Angeles campus of the University of Southern California. His col- leagues and friends from around the world gathered to share their memories of this remarkable man. Some of their comments were pub- lished by the university as"A Tribute to Richard Bellman." We can- not include them all in this volume, but the following excerpts pro- vi`Ze an indication of the extraordinary impact Dick Bellman had in his life and work. R~cHARD BELLMAN was a towering figure among the contrib- utors to modern control theory anct systems analysis. His in- vention of dynamic programming marked the beginning of a new era in the analysis and optimizations of large-scale sys- tems and opener! 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 speech recog- . . nltlon. Richard Bellman was born in Brooklyn, New York, on Au- gust 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 23

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24 MEMORIAL TRIBUTES 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 com- pletec! his work toward a Ph.D. in a record time of three months. In the immediate postwar years, Princeton was a center of defense-motivatec! research activity in nonlinear differential equations. As a graduate student at Princeton, Bellman be- came 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 Sta- bility 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 Depart- ment at Princeton from 1946 to 1948, Bellman left the east coast to become a member of the faculty of Stanford Univer- sity in 1948 and then joined the newly established Rancl Cor- poration in Santa Monica, California, in 1953. At Rand, he became interested in the theory of multistage decision pro- cesses, which was then emerging as an important problem area in the control of both small- ancI 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 func- tional equation techniques in a wide spectrum of fields ex- tending far beyond the problem areas that provided the ini- tial motivation for his ideas. In addition to his fundamental and far-ranging work on dynamic programming, Richard Bellman macle a number of important contributions to both pure and applier! mathe- matics. Particularly worthy of note is his work on invariant imbedcling, which by replacing two-point boundary prob- lems 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 system iclentifi-

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RICHARD E. BELLMAN 25 cation has lee! to many results of a practical nature in the study of nonlinear systems. In recent years, BelIman's research activity focused in- creasingly on the application of mathematics to medicine anc! biological sciences. His interest in these and relater! areas re- flected his strong conviction that mathematics should not be content with being a beautiful castle with no bridges to the real worIcl. There was a time when BelIman's outspoken crit- icisms of the elitist attitudes of the mathematical establish- ment were greeted with hostility and derision. Today, when pure mathematicians are experiencing ctifficulties in finding suitable jobs, many of those who disagreed with Bellman will concede that he was right. Bellman left the Ranc! Corporation in 1965 to join the fac- ulty of the University of Southern California, where he held joint appointments as professor of mathematics, electrical engineering, and medicineappointments he held until his death on March 19, 1984. A prolific writer, he authored! over six hundrecl published research papers, approximately forty books, and several monographs. Richard BelIman's fundamental contributions to science and engineering won him many honors and worIclwide rec- ognition. 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 Appliecl Mathematics; first Dick- son 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 Re- search Society of America; and the 1979 Institute of Electri- cal and Electronics Engineers' Medal of Honor in recogni- tion of the invention of (dynamic programming. His honorary degrees inclucle the doctor of science of the University of Abercleen, ScotIancl, in 1973; the doctor of laws of the University of Southern California in 1974; and the doctor of mathematics of the University of Waterloo, Can-

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26 MEMORIAL TRIBUTES acia, in 1975. He was electect a fellow of the American AcacI- emy of Arts and Sciences in 1975, a member of the National Academy of Engineering in 1977, and a member of the Na- tional Academy of Sciences in 1983. fR. E. Larson and L. A. Zadeh] 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 circum- stances that wouIcI have overwhelmed and crushed men of lesser caliber. In these superb human qualities, as in his cre- ative work, ~ firmly believe that Dick Bellman has lived on a level at least the equal of Beethoven. fRoger felli~e] Of his great contributions, ~ think that he wouict fee! that the students he inspirer! were among the most important; through them his ideas go on and will be expanded to meet the neecis of expanding technology and human need. The only function that Richarc! Bellman could not bound was his own energy ant] imagination. fFieur Mitchell The measure of a man is the number of people whose lives he has influenced anc! the contributions he has macle. Dick Bellman not only influenced the lives of many people, but he hac! the rare genius to be able to contribute to many fields. fAlan Rowe] Someone said that the Soviet Union is not just another country it's another world, another planet. Ancl it, incleecl, is. But the stars, we might say, continuing the metaphor, are the same on every planet. They shine for everyone and everywhere. Dick was, anct is, such a star. His influence in the Soviet Union is deep and profound. His works penetrated many areas of Soviet academia, inclustry, and economy in general. From the academic point of view, there is not a single university that (toes not offer courses based on Dick's works. Hun~lrecls of papers continuing Dick's ideas are pub- lishec! annually in Soviet journals. It is harclly possible to find a researcher in the quantitative sciences and engineering un- familiar with, at least, the term "Dynamic Programming."

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RICHARD E. BELLMAN 27 Dick's name is probably cited more at Soviet scientific meetings than at American ones. As an inctirect 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 ant! published in the Soviet Union. No other American scientist has been given such hon- ors 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 too} as well as an important source of mathe- matical work. His results are always practical and easily ap- plicable. Probably, this is why his mathematical discoveries have important engineering implications in such areas as sys- . . . . . ~ tem science, contro , communications, ~~oeng~neer~ng, etc. The depth anti importance of problems consiclered, the practical applicability, and the timeliness of his works, this is what, in my view, macle the largest impact and definect Dick's influence on Soviet science. Dick gave all of us, his students and friends in every coun- try throughout the worIct, an ultimate example of scientific creativity and success, personal courage and strength, friendly devotion and support. tSemyon Meerkov] He was contemptuous of the established orcler and intol- erant of mediocrity. He was strikingly handsome, brilliant, ant] 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 ~ couIct see was that behinc! the fa- cacle of arrogance and bravado was a man who was capable of great kincIness, a man who was decent, straightforward and generous in the extreme. He diec! 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. tLofti Zadeh]

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28 MEMORIAL TRIBUTES At the time of his cleath at age sixty-three, Richard Bell- man had just completed his autobiography, The Eye of the Hurricane, World Scientific Publications, Singapore, ~ 984. He is survived by his wife, Nina; his son, Eric; and his ciaugh- ter, Kirstie.

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