The Mathematical Sciences: A Report (1968) / Chapter Skim
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14 Tasks and Needs
14 Tasks and Needs
Pages 197-210
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From page 197... ...
This involves not only the availability of financial support but also a broad understanding of and appreciation for intellectual endeavor, a willingness to support theoretical work, and an uncompromising commitment to intellectual freedom. THE CORE Research within the core is primarily concerned with identifying, extending, and refining the critical concepts that serve to organize mathematical thought and with the precise analysis of the interrelations of these concepts.
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From page 198... ...
Many leaders in the new applied areas of mathematical sciences received their training in the rigorous atmosphere of established pure mathematics. Many future leaders in these fields, as well as leaders in fields not yet initiated, may also develop in this way.
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From page 199... ...
in two issues acknowledged federal support. These figures show that federal money has been involved in a truly significant portion of the mathematical research being done in this country.
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From page 200... ...
If funding does not show an increase commensurate with the net growth of the nation's mathematical activity, we must expect that the forces that have linked the expansion of core research to the general expansion of mathematical competence will work in reverse. Needless to say, at a time when the demand for mathematically trained personnel is expanding in every facet of our society, such a reversal would be regrettable.
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From page 201... ...
(The recent rating by the American Council of Education,32 which lists nine "distinguished" and 16 "strong" departments of mathematics reflects well the general feeling within the mathematical community.) The strongest mathematical centers play a triple role.
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From page 202... ...
One may expect that mathematization of new areas in science and technology will result, and that new problems within mathematics itself will be uncovered as well. Thus, the contribution of the physical mathematician to society extends from the very practical aspects of engineering to engineering science, to basic science, and to the stimulation of pure mathematics itself.
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From page 203... ...
As a consequence, research training is more widely needed than it might seem to be at first sight. There are demands for new and better formulations of what users of statistics are trying to do, for better and more detailed mathematical treatments of many problems, for the re-examination and modification of many results and techniques to make them more closely matched to the situations in which they are in fact used, for innovation in the form of new techniques, some for wholly new purposes, and [or innovation in how modern computing systems are to be put to work (as well as in how their results are to be presented to humans)
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From page 204... ...
Most teaching in statistics is "service" teaching, in which the guidelines of the Pierce report,3 once followed, should provide the needed financing of computer time. Courses predominantly taken by statistics majors, or by potential graduate students in statistics, are likely to require considerably greater contact with modern computing systems, involving correspondingly increased costs.
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From page 205... ...
It has been recognized for several years that the design of efficient programs is even more important than the design of machines. Third, the computerization of many applications involves large sums of money, so that an increase in effectiveness of even, say, five percent can mean a big saving in just two or three years an unusually rapid payoff for research given that the current annual cost of the federal government's acquisition and operation of computers is in the neighborhood of $?
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From page 206... ...
The shortage of trained research and teaching staff for academic computer sciences, however it may be structured within the university, is acute. New, badly needed research people must come from varied backgrounds, aIld the opportunities for sponsored research should include particularly support for young persons of imaginative and experimental bent.
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From page 207... ...
OPERATIONS RESEARCH AND MANAGEMENT SCIENCE With the aid of the computer, mathematical methods have been penetrating into every form of human activity. Those that concern the science of decision-making and its application comprise opera lions research or management science.
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From page 208... ...
This has stimulated such mathemn~i~1 air ~;~1 :~ ~ _ ~ 1~ ~ clpllnes as linear, nonlinear, and integer programming; network. graph, and matroid theory; queueing, stochastic processes reliability theory; dynamic programming and control theory Graduate programs have expanded rapidly.
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From page 209... ...
The converse problem arises when either the mathematics applied or the problem to which it is applied appears too simple, although real gain can come from the application. We are fortunate that this was not the case, for example, in the recent application of mathematical thinking to the description of all possible kinship systems satisfying certain axioms, recently carried out independently by both anthropologically and more mathematically oriented workers.
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From page 210... ...
210 Conc/~3foni vldua1 departments in any of the frontier mathematica1 herds me encouraged to spread ~ little outside their nominal boundaries not only cooperating with Workers concerned in various special arena but becoming involved in loins research or serving as inida1 homes, Folly or in park for mathematically oriented faculty not as well housed in their disciplinary departments
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