unifying force, reveal underlying structure, offer an avenue for knowledge transfer among disciplines, and serve as the vehicle for computational modeling of the processes and phenomena. Both the mathematical and materials sciences have much to gain from each other. Modern mathematical methods can aid in solving significant problems in materials science, while problems in materials science can suggest fruitful areas for mathematical research. In the larger perspective, however (National Research Council, 1989), it is clear that the scientific vigor, technological strength, and economic health of the nation all argue in favor of universities, government, industry, and professional societies stimulating and facilitating new collaborations between mathematical scientists and materials scientists.

The committee's task was to prepare a broad survey that (1) identifies and describes areas where the mathematical sciences have significantly aided materials research, (2) identifies areas of mathematical research in which increased progress would accelerate materials research, (3) identifies obstacles, if any, to increased collaborative research, and (4) makes recommendations for facilitating this type of cross-disciplinary work, including how to attract students and young researchers to this area. Chapters 2 through 8 of this report address items (1) and (2). This chapter and Chapter 9 address item (3), and Chapter 9 addresses item (4). This report is written for both mathematical and materials science researchers with an interest in advancing research at this interface, for federal and state agency representatives interested in encouraging such collaborations, and for any persons wanting information on how such cross-disciplinary, collaborative efforts can be successfully accomplished.

Concerning obstacles, it should first be noted that despite existing impediments to interdisciplinary work in these areas, there are nonetheless many successful interactions and collaborations between materials scientists and mathematical scientists (some are referred to in the technical Chapters 2 through 8 that follow). However, those impediments do need to be recognized and addressed.

One obstacle to increased collaborative research between the mathematical sciences and materials science concerns the differences in education of researchers in the two disciplines. The education of materials scientists exposes them to varying amounts of mathematics, but it mainly involves classical mathematics and therefore little knowledge of modern mathematics, especially tools that might be beneficial for exploring problems in materials science. In their education, mathematical scientists rarely take physical science courses beyond the elementary undergraduate classical courses, and therefore they generally have little feeling for current research areas and the applications of their expertise to materials sciences. Another impediment is a large jargon barrier that exists between the two disciplines. Similar jargon barriers exist even among different subdisciplines of materials science (and subdisciplines of the mathematical sciences); continual efforts are needed to eliminate jargon as a barrier to interdisciplinary research. Some negative attitudes constitute another barrier and are perhaps best summarized by the comments of, on the one hand, the great mathematician G. H. Hardy, who expressed his pleasure that none of his work had practical applications and, on the other hand, the materials scientist who cautions his students that "too much rigor leads to rigor mortis." University departmental structures that often discourage mathematical research by materials scientists and materials-oriented research by mathematical scientists present another obstacle, as this (and other) cross-



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