Intuition in Mathematical Operations Research

Abstract

The object is to understand how to surmount many of the roadblocks encountered in operations research by viewing the subject against the background of science in general. After disposing of some preliminary issues of logic concerning the sufficiency of a body of knowledge to determine the truth (or the probabilities) of statements made in its terms, the scientific method is examined, as based on three processes: A, experimental observation; B, deductive—often mathematical—reasoning; C, “concept formation”—that creative act which (as noted by H. Poincaré) transcends the others. It is the special form of intuition known to the innovative mind, perceiving “order,” “unity,” “harmony,” and leading inductively to general principles. It is not to be confused with mechanical pattern recognition; nor is it just “gut feeling.” Examples are outlined from the mathematical sciences—as well as the counter-example of sterile analyses, dear to officialdom, often unable to see that the whole is greater than the sum of its parts. Finally, historical examples in operations research are given, showing how its road-blocks were overcome by the creative application of concept formation.