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“The new uses of the abstract,” called John Nash brilliant and eager to tackle math’s most difficult problems.
Last week, John Nash, the Nobel Laureate in Economics and subject of the movie A Beautiful Mind was killed in a car crash. Back in 1958, Fortune science writer George A. W. Boehm was one of the first journalists to write about game theory and other developments in “new math.” His article, “The new uses of the abstract,” featured a brief bio of Nash, which was widely cited last week as one of the first articles to mention the then rising mathematician, long before the world knew of his struggles with mental illness.
Never before have so many people applied such abstract mathematics to so great a variety of problems. To meet the demands of industry, technology, and other sciences, mathematicians have had to invent new branches of mathematics and expand old ones.
They have built a superstructure of fresh ideas that people trained in the classical branches of the subject would hardly recognize as mathematics at all.
Applied mathematicians have been grappling successfully with the world’s problems at a time, curiously enough, when pure mathematicians seem almost to have lost touch with the real world. Mathematics has always been abstract, but as Fortune reported last month, pure mathematicians are pushing abstraction to new limits. To them mathematics is an art they pursue for art’s sake, and they don’t much care whether it will ever have any practical use.
Yet the very abstractness of mathematics makes it useful. By applying its concepts to worldly problems the mathematician can often brush away the obscuring details and reveal simple patterns. Celestial mechanics, for example, enables astronomers to calculate the positions of the planets at any time in the past or future and to predict the comings and goings of comets. Now this ancient and abstruse branch of mathematics has suddenly become impressively practical for calculating orbits of earth satellites.
Even mathematical puzzles may have important applications. Mathematicians are still trying to find a general rule for calculating the number of ways a particle can travel from one corner of a rectangular net to another corner without crossing its own path. When they solve this seemingly simple problem, they will be able to tell chemists something about the buildup of the long-chain molecules of polymers.
Mathematicians who are interested in down-to-earth problems have learned to solve many that were beyond the scope of mathematics only a decade or two ago. They have developed new statistical methods for controlling quality in high-speed industrial mass production. They have laid foundations for Operations Research techniques that businessmen use to schedule production and distribution. They have created an elaborate theory of “information” that enables communications engineers to evaluate precisely telephone, radio, and television circuits. They have grappled with the complexities of human behavior through game theory, which applies to military and business strategy alike. They have analyzed the design of automatic controls for such complicated systems as factory production lines and supersonic aircraft. Now they are ready to solve many problems of space travel, from guidance and navigation to flight dynamics of missiles beyond the earth’s atmosphere.
Mathematicians have barely begun to turn their attention to the biological and social sciences, yet these once purely descriptive sciences are already taking on a new flavor of mathematical precision. Biologists are starting to apply information theory to inheritance. Sociologists are using sophisticated modern statistics to control their sampling. The bond between mathematics and the life sciences has been strengthened by the emergence of a whole group of applied mathematics specialties, such as biometrics, psychometrics, and econometrics.