George Dantzig: Quotes about mathematics

“If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming.”

George Dantzig

Source: Linear programming and extensions (1963), p. 2

Mathematics

“One of the first applications of the simplex algorithm was to the determination of an adequate diet that was of least cost. In the fall of 1947, Jack Laderman of the Mathematical Tables Project of the National Bureau of Standards undertook, as a test of the newly proposed simplex method, the first large-scale computation in this field. It was a system with nine equations in seventy-seven unknowns. Using hand-operated desk calculators, approximately 120 man-days were required to obtain a solution. … The particular problem solved was one which had been studied earlier by George Stigler (who later became a Nobel Laureate) who proposed a solution based on the substitution of certain foods by others which gave more nutrition per dollar. He then examined a "handful" of the possible 510 ways to combine the selected foods. He did not claim the solution to be the cheapest but gave his reasons for believing that the cost per annum could not be reduced by more than a few dollars. Indeed, it turned out that Stigler's solution (expressed in 1945 dollars) was only 24 cents higher than the true minimum per year $39.69.”

George Dantzig

cited in: John J. O'Connor & Edmund F.; Robertson (2003) " George Dantzig http://www-history.mcs.st-and.ac.uk/Biographies/Dantzig_George.html". in: MacTutor History of Mathematics archive, University of St Andrews.
Linear programming and extensions (1963)

Food , Way , Mathematics , Problem

“All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it.”

George Dantzig

Source: Linear programming and extensions (1963), p. vii.

Mathematics , Nature , Problem