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l Inclustrial and Government Laboratories 1 ~ A significant number of industrial and government laboratories support research and educational activity in the mathematical sci- ences. Accurate and comprehensive data on the extent and character of this support are, however, almost completely lacking. In order to garner preliminary information on the basis of which a rough assessment could be made and more systematic surveys might be undertaken in the future, COSRIMS and the CBMS Survey Committee jointly sponsored a Panel on the Mathematical Sciences in Industry and Government. This Panel invited statements regarding their mathematical re- search and educational activities from a sample of industrial and government laboratories where such activities were known infor- mally to be substantial. Those from which responses were received included the following: Argonne National Laboratory Bell Telephone Laboratories Bettis Atomic Power Laboratory (Westinghouse Corporation) Boeing Scientific Research Laboratories David Taylor Model Basin International Business Machines Corporation Lockheed Palo Alto Research Laboratory Los Alamos Scientific Laboratory MITRE Corporation Mobil Oil Corporation National Bureau of Standards 190

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Industrial and Government Laboratories Pacific Northwest Laboratory (Battelle Memorial Institute) RAND Corporation Sandia Corporation Laboratory 191 The strength and variety of mathematical activities exhibited in the responses of these selected laboratories is no doubt considerably greater than in industrial and government laboratories generally. ACTIVITIES AT SOME MA TOR LABORATORIES Activities at the above-listed laboratories in support of mathemati- cal research and higher education are quite varied and in some instances surprisingly extensive. Industrial laboratories have some- times made developmental grants in the sciences to institutions of higher education and, occasionally, grants-in-aid directly to depart- ments of mathematics. They have also on occasion endowed dis- tinguished chairs of mathematics in universities. Activities of these kinds are certainly valuable and deserve to be applauded and en- couraged. The main contribution of industrial and government laboratories to the mathematical sciences lies, however, in their own in-house research and education efforts, and in the interplay of these with work in universities. The proportion of PhD's to total staff in the mathematical sciences at such laboratories is generally much lower than in a university. Naturally an attempt is made to appoint PhD's whose research interests will fit in with those of the laboratory, but, once appointed, such a PhD will normally be given very considerable freedom in his research activities. Direct consult- ing on company problems typically plays a relatively minor role, and sell-initiated basic research may play a very considerable one. In this way there is direct support of mathematical research on the part of industrial and government laboratories, and top mathe- maticians from these laboratories are among frequent contributors of mathematical research articles and monographs. At their best, the physical facilities and general conditions of work in these laboratories can be quite attractive. Technical libraries and library services tend to be good, and there are usually active in-house seminars and colloquia in various branches of the mathematical sciences. Provision is frequently made for bringing in distinguished university mathematicians as consultants and research collaborators, for periods varying from a day or two to several weeks

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192 Level and Forms of Support or a full summer or year. In the other direction, the laboratory may give a year's leave of absence to a distinguished mathematician on its staff when he is invited to serve as a visiting professor at a uni- versity. In such a case, the laboratory may supplement his uni- versity salary. The laboratory may also provide released time to its mathematical scientists for teaching individual graduate courses at nearby universities. Several industrial and government laboratories have attractive fellowship programs under which selected employees may study part time for PhD degrees in the mathematical sciences at neighbor- ing universities. These programs will often provide for a year's leave of absence, at three-fourths to full pay, to work on a disserta- tion. The over-all magnitude of such programs is modest but not negligible. Thus the CBMS survey found that, for academic year 1965-1966, out of some 1,570 federal and private fellowships for full-time graduate study in the mathematical sciences, approxi- mately 55 were sponsored by industry, through not all of these were fellowships for employees. There are also laboratory-supported programs of graduate mathe- matical education for employees at somewhat lower levels. In one strongly research-oriented industrial laboratory it is standard prac- tice for incoming bachelors in engineering and in mathematics to take, as part of their work for the company, a two- to three-year half-time educational program. Some of the courses are taught in extension programs at the laboratory itself, but part of the work is conducted at nearby universities and normally leads to a master's degree. The program for engineering bachelors is heavily weighted in the direction of mathematics, while the program for mathe- matics bachelors generally includes intensive work with com- puters. THE GENERAL SITUATION AND ITS PROBLEMS The above paragraphs have depicted qualitatively, at their present best, an enlightened attitude toward mathematical-research activ- ities among a few major industrial and government laboratories and a healthy interaction between these activities and those of the mathematical-science departments of universities. It would be quite misleading, however, not to emphasize that this enlightened attitude and healthy interaction appear to be far from the norm.

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Industrial and Government Laboratories 193 Many applied mathematicians feel that industrial and govern- ment laboratories have generally failed to use mathematicians effec- tively and, what is worse, are unable to imagine or evaluate the mathematician's contribution. Informal interviews with numerous mathematicians in technologically sophisticated industries suggest that the majority of these mathematicians are in a kind of limbo in their companies. Some industrial mathematicians are vigorous in asserting that management does not use, or know how to use, their services. Too many industrial mathematicians are regarded as "mathematical repairmen," people kept around to "fix mathe- matics that is breaking down" but in activities of a rather routine nature. Partly, the problem is one of communicating effectively, so that the mathematical talent within an industrial organization can be brought to bear on its mathematical problems. Many "applied mathematics sections" in industry have failed because this problem was not solved. On the other hand, when a company tries to "sprinkle" its mathematicians throughout the organization, com- munication lines tend to be very localized, and each mathematician is unrealistically expected to be a jack of all trades. Continued fail- ure to solve such extremely difficult problems threatens to impede the effective use of mathematicians in industry for years to come. There is also a problem of lack of communication and cooper- ation between the academic world and industrial and government laboratories. Quite a few industrial and applied mathematicians feel that the academic world is content with this situation, and that by and large universities are making little effort to prepare mathe- maticians for positions outside universities. This is a principal reason for our recommendation below for increased exchanges be- tween laboratories and universities. COMMENTS We feel that more young mathematicians could be profitably drawn toward the work of industrial and government laboratories; thus we recommend that a special effort be made to increase the oppor- tunities for postdoctoral research appointments in such laboratories. Specifically, a group of cooperating industries might undertake to support postdoctorals and to evaluate applications for postdoctoral appointments to industrial laboratories on a national basis through

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194 Level and Forms of Support a committee of the National Research Council. At the same time we recommend an increased reverse flow of more senior mathe- maticians from industrial and government laboratories to univer- sities on a temporary basis; we feel that such laboratories should be encouraged to send personnel to universities for a year or two after several years of work in the laboratory. In this connection, we call attention to the desirability of extending more senior postdoctoral opportunities to industrial personnel. The advantages of using more industrial personnel in graduate teaching and research direction should also be recognized. This should be encouraged, either as a form of industrial support of the universities or as a program sup- ported by a combination of government and university resources. We point out the desirability of studies leading to more accurate and comprehensive information on work in the mathematical sci- ences in industry and government, including present and projected manpower estimates at various levels of mathematical training. The qualitative picture drawn in the discussion of Activities at Some Major Laboratories (page 191) has emerged from case studies of a few of the country's major industrial and government laboratories. A more comprehensive study should include all these laboratories and the changing picture of mathematical work in industry and government generally. In particular, it should take account of the smaller mathematical consulting firms now springing up, firms that contract with a variety of industrial and commercial customers to do computer programming and systems analyses and mathematical operations-and-management studies.