Richard Ernest Bellman (1920-1984) was an American applied mathematician who, while working at the RAND Corporation in the 1950s, developed dynamic programming: a systematic method for solving complex decision problems by breaking them into a sequence of smaller, overlapping subproblems and reusing their solutions. His book “Dynamic Programming,” first published by Princeton University Press in 1957, set out the theory and gave the field its name.
Dynamic programming applies to problems that have an optimal substructure, meaning an optimal solution to the whole is built from optimal solutions to its parts. Bellman’s “principle of optimality,” stated in the book, captures this idea: an optimal sequence of decisions has the property that, whatever the first decision, the remaining decisions must themselves be optimal with respect to the state that results. This principle underlies the recursive equations now known as Bellman equations.
In studying problems where the number of variables grows large, Bellman coined the phrase “the curse of dimensionality” to describe how the amount of computation and data needed explodes as the number of dimensions increases. The term remains in common use across optimization, control theory, and machine learning.
Bellman’s name is attached to several enduring results. The Bellman equation is central to dynamic programming and reinforcement learning, and the Bellman-Ford algorithm computes shortest paths in a graph that may contain edges with negative weights. His 1957 book remains a primary reference for the method he created.