The Mathematical Sciences: A Report (1968) / Chapter Skim
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1 Mathematics and Society
1 Mathematics and Society
Pages 3-12
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From page 3... ...
Yet this statement hardly begins to convey or account for the current explosive penetration of mathematical methods into other disciplines, amounting to a virtual "mathematization of culture." Mathematics can be described as the art of symbolic reasoning. Mathematics is present wherever chains of manipulations of abstract symbols are used; such chains may occur in the mind of a human being, as marks on paper, or in an electronic computer.
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From page 4... ...
The twentieth-century penetration of mathematical methods into the biological sciences has come about in several ways, perhaps most importantly through the increasing study of biological phenomena by the methods of chemical physics. The development of statistics, which the needs of the biological sciences helped to stimulate, has led to the extensive field of biostatistics.
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From page 5... ...
Computer science, which deals with manifold problems of building and utilizing computers, contains, among other things, very important mathematical components. THE NEED FOR MATHEMATICALLY TRAINED PEOPLE The mathematization of our society brings with it an increasing need for people able to understand and use mathematics.
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From page 6... ...
APPLIED MATHEMATICAL SCIENCES There are now four major areas in the mathematical sciences that have particularly direct and important relationships with other sciences and technologies: computer science, operations research, statistics, and physical mathematics (classical applied mathematics)
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From page 7... ...
The field sometimes labeled operations research is now growing rapidly, though not so explosively as computer science. Its emphasis today is on solving problems of allocation (routing problems and scheduling problems are two major types)
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From page 8... ...
In the central core, mathematical ideas and techniques, no matter what their origin, are analyzed, generalized, codified, and transformed into tools of wide applicability. In assessing the importance of the core, one should keep in mind that there is always an interplay and exchange of ideas between so-called "pure" mathematics, that is, mathematics pursued primarily for intrinsic intellectual and aesthetic reasons, and so-called "applied" mathematics, that is, mathematics consciously used as a tool for understanding various aspects of nature.
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From page 9... ...
A puzzle about the seven bridges in Kcinigsberg led to the theory of graphs, a basic mathematical tool of computer science, and indirectly influenced the development of topology. A question raised by a professional gambler led Pascal and Fermat to the theory of probability.
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From page 10... ...
In the interval between World Wars I and II, mathematics in the United States became somewhat more important relative to world mathe matics. Political developments in Europe in the 1930's led many European mathematicians to seek refuge in the United States and to become active members of the American mathematical community.
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From page 11... ...
Beginning with the Oslo congress of 1936, two Fields Medals have been awarded at each international congress of mathematicians, except that most recently at the Moscow congress of 1966 four were awarded. In all, 14 Fields Medals have been awarded, with the distribution of medalists by country as follows: France, four; the United States, four; England, two; Finland, Japan, Norway, and Sweden, one each.
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From page 12... ...
Four or five others have been and are frequent visitors to the United States, each having spent at least one academic year here. Some of these are active collaborators with various American mathematicians.
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