# Richard E. Bellman

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**Richard Ernest Bellman**, (August 26, 1920 – March 19, 1984)

was an American applied mathematician and inventor of dynamic programming in 1953 while affiliated with RAND Corporation. Dynamic programming defines a mathematical theory devoted to the study of multistage processes. These processes are composed of sequences of operations in which the outcome of those preceding may be used to guide the course of future ones ^{[2]}, an application in computer chess and games is the use of transposition tables inside an iterative deepening framework ^{[3]}. He worked and published on Markov decision processes, and in 1958, he published his first paper on stochastic control processes ^{[4]}, where he introduced what is today called the Bellman equation, also known as dynamic programming equation.

During World War II, Bellman worked in Los Alamos on the Manhattan project. He received his Ph.D. at Princeton under the supervision of Solomon Lefschetz in 1947, and since 1949 he worked for many years at RAND, and was professor at University of Southern California since 1965. In the 50s he was persecuted by McCarthy ^{[5]} ^{[6]}.

## Contents

# Retrograde Analysis

The dynamic programming methodology which defined the field of retrograde endgame analysis was discovered by Bellman in 1965 ^{[7]}. Bellman had considered game theory from a classical perspective as well ^{[8]} ^{[9]}, but his work came to fruition in his 1965 paper, where he observed that the entire state-space could be stored and that dynamic programming techniques could then be used to compute whether either side could win any position ^{[10]}.

# Selected Publications

^{[11]} ^{[12]}

## 1947

- Richard E. Bellman (
**1947**).*On the Boundedness of Solutions of Non-Linear Differential and Difference Equations*. Ph.D. thesis, pdf

## 1950 ...

- Richard E. Bellman (
**1953**).*An Introduction to the Theory of Dynamic Programming*. R-245, RAND Corporation - Richard E. Bellman (
**1954**).*The Theory of Dynamic Programming*. P-550, RAND Corporation, pdf - Richard E. Bellman (
**1954**).*On a new Iterative Algorithm for Finding the Solutions of Games and Linear Programming Problems*. Technical Report P-473, RAND Corporation, Santa Monica, CA - Richard E. Bellman (
**1957**).*Dynamic Programming*. Princeton University Press - Richard E. Bellman (
**1957**).*The Theory of Games*. Technical Report P-1062, RAND Corporation, Santa Monica, CA - Richard E. Bellman (
**1957**).*Markovian decision processes*. Journal of Mathematics and Mechanics 38, 716–719 - Richard E. Bellman (
**1958**).*Dynamic Programming and Stochastic Control Processes*. RAND Corporation, Santa Monica, CA, Information and Control 1, pp. 228–239

## 1960 ...

- Richard E. Bellman (
**1960**).*Sequential Machines, Ambiguity, and Dynamic Programming*. Journal of the ACM, Vol. 7, No. 1 - Richard E. Bellman, Stuart E. Dreyfus (
**1962**).*Applied Dynamic Programming*. RAND Corporation, Princeton University Press, pdf - Richard E. Bellman (
**1962**).*Dynamic Programming Treatment of the Travelling Salesman Problem*. Journal of the ACM, Vol. 9, No. 1, 1961 pdf preprint - Richard E. Bellman (
**1965**).*On the Application of Dynamic Programming to the Determination of Optimal Play in Chess and Checkers.*PNAS - Richard E. Bellman (
**1969**).*Information science: A function is a mapping-plus a class of algorithms*. Information Sciences, Vol. 1, No. 3

## 1970 ...

- Richard E. Bellman, Magnus Giertz (
**1973**).*On the Analytic Formalism of the Theory of Fuzzy Sets*. Information Sciences, Vol. 5^{[13]}

## 1980 ...

## 2000 ...

- Stuart E. Dreyfus (
**2002**).*Richard Bellman on the Birth of Dynamic Programming*. Operations Research, Vol. 50, No. 1, pdf - Richard E. Bellman (
**2003**).*Dynamic Programming*. Dover Publications

## 2010 ...

- Richard E. Bellman (
**2010**).*Dynamic Programming*. With a new introduction by Stuart E. Dreyfus, Princeton University Press - Richard E. Bellman, Stuart E. Dreyfus (
**2015**).*Applied Dynamic Programming*. Princeton University Press

# External Links

- Richard E. Bellman from Wikipedia
- Bellman biography by John J. O'Connor and Edmund F. Robertson
- Richard Bellman - GHN: IEEE Global History Network
- The Mathematics Genealogy Project - Richard Bellman
- Bellman equation from Wikipedia
- Hamilton–Jacobi–Bellman equation from Wikipedia
- Bellman–Ford algorithm from Wikipedia
- Bellman pseudospectral method from Wikipedia
- The Bellman Equation, Richard Bellman, The Movie by Gabriel Leif Bellman

- Bellman Equation Documentary Preview, YouTube Video

# References

- ↑ The Bellman Equation, Richard Bellman, The Movie by Gabriel Leif Bellman
- ↑ Richard E. Bellman (
**1953**).*An Introduction to the Theory of Dynamic Programming*. R-245, RAND Corporation - ↑ Algorithms that use dynamic programming from Wikipedia
- ↑ Richard E. Bellman (
**1958**).*Dynamic Programming and Stochastic Control Processes*. RAND Corporation, Santa Monica, CA, Information and Control 1, pp. 228–239 - ↑ The Bellman Equation, Richard Bellman, The Movie by Gabriel Leif Bellman
- ↑ McCarthyism from Wikipedia
- ↑ Richard E. Bellman (
**1965**).*On the Application of Dynamic Programming to the Determination of Optimal Play in Chess and Checkers.*Proceedings of the National Academy of Sciences of the United States of America - ↑ Richard E. Bellman (
**1954**).*On a new Iterative Algorithm for Finding the Solutions of Games and Linear Programming Problems*. Technical Report P-473, RAND Corporation, U. S. Air Force Project RAND, Santa Monica, CA - ↑ Richard E. Bellman (
**1957**).*The Theory of Games*. Technical Report P-1062, RAND Corporation, Santa Monica, CA - ↑ Lewis Stiller (
**1996**).*Multilinear Algebra and Chess Endgames*. Games of No Chance edited by Richard J. Nowakowski, pdf - ↑ List of Publications: Richard Bellman
- ↑ DBLP: Richard Bellman
- ↑ Fuzzy set from Wikipedia