"Computers do not decrease the need for mathematical analysis, but rather greatly increase this need. They actually extend the use of analysis into the fields of computers and computation, the former area being almost unknown until recently, the latter never having been as intensively investigated as its importance warrants. Finally, it is up to the user of computational equipment to define his needs in terms of his problems, In any case, computers can never eliminate the need for problem-solving through human ingenuity and intelligence." (Richard E Bellman & Paul Brock, "On the Concepts of a Problem and Problem-Solving", American Mathematical Monthly 67, 1960)
"There is the very real danger that a number of problems which could profitably be subjected to analysis, and so treated by simpler and more revealing techniques. will instead be routinely shunted to the computing machines [...] The role of computing machines as a mathematical tool is not that of a panacea for all computational ills." (Richard E Bellman & Paul Brock, "On the Concepts of a Problem and Problem-Solving", American Mathematical Monthly 67, 1960)
"The theory of elliptic functions is the fairyland of mathematics. The mathematician who once gazes upon this enchanting and wondrous domain crowded with the most beautiful relations and concepts is forever captivated." (Richard E Bellman, "A Brief Introduction to Theta Functions", 1961)
"A final goal of any scientific theory must be the derivation of numbers. Theories stand or fall, ultimately, upon numbers." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"Another direction of research is fuzzy systems. This will greatly increase the use of mathematics from the inanimate to the animate. In the past, mathematics has been used for the analysis of physical systems. With fuzzy systems and computer simulation we can study many processes in the social sciences." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"Conversely, once it was realized that the concept of policy was fundamental in control theory, the mathematicization of the basic engineering concept of 'feedback control', then the emphasis upon a state variable formulation became natural. We see then a very interesting interaction between dynamic programming and control theory. This reinforces the point that when working in the field of analysis it is exceedingly helpful to have some underlying physical processes clearly in mind." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"Mathematical model making is an art. If the model is too small, a great deal of analysis and numerical solution can be done, but the results, in general, can be meaningless. If the model is too large, neither analysis nor numerical solution can be carried out, the interpretation of the results is in any case very difficult, and there is great difficulty in obtaining the numerical values of the parameters needed for numerical results." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"If there are paradoxes in mathematics, think of how many paradoxes there must be in ordinary speech. The existence of paradoxes involves logic. This led naturally to the question of local logics. It seems to me that it is no more natural to expect that a universal logic will hold than that a universal geometry holds." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"In the real world, none of these assumptions are uniformly valid. Often people want to know why mathematics and computers cannot be used to handle the meaningful problems of society, as opposed, let us say, to the moon boondoggle and high energy-high cost physics. The answer lies in the fact that we don't know how to describe the complex systems of society involving people, we don't understand cause and effect, which is to say the consequences of decisions, and we don't even know how to make our objectives reasonably precise. None of the requirements of classical science are met. Gradually, a new methodology for dealing with these 'fuzzy' problems is being developed, but the path is not easy." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"Stability theory is the study of systems under various perturbing influences. Since there are many systems, many types of influences, and many equations describing systems, this is an open-ended problem. A system is designed so that it will be stable under external influences. However, one cannot predict all external influences, nor predict the magnitude of those that occur. Consequently, we need control theory. If one is interested in stability theory, a natural result is a theory of control." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"The trouble with an analog computer is that one begins to construct mathematical models which can be treated using an analog computer. In many cases this is not realistic." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"There are many difficulties in application of [the games] theory to the real world. [...] In general, competitors are not in complete opposition. As a matter of fact often they don't even have the same objectives. This difficulty can often be circumvented by using a different objective, 'games of survival'. Secondly, a decision is seldom made once. This motivated the study of multistage games [...]. Finally, decisions are not usually made simultaneously. Recognition of this fact leads to 'games of protocol' [...]. Games of protocol can also be used to handle processes involving three or more people." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
"Mathematicians makes natural questions precise." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)
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