Engineering in all its sub-areas requires sophisticated mathematics and statistics to formulate, analyze, and solve today's problems. Successful mathematical models have saved billions of dollars by replacing expensive, and sometimes very risky, scaled-down or full-scale experimentation.

Effects of Technology Development on Research in the Mathematical Sciences

Dramatic technological changes, especially in computation and communications, have revolutionized mathematical research itself, even in its core and more traditional areas. The growing power of computers now often enables large-scale experimentation to verify hypotheses and provides tools for the visualization of sophisticated geometric objects and for the manipulation or analysis of algebraic expressions. The result is the expanding field of experimental mathematics. The revolution in communications has also dramatically changed the way in which mathematical research is carried out. Electronic mail and facsimile machines have drastically reduced communication turn-around time, thus facilitating collaborations between mathematical scientists who are physically located at different sites around the world. Indeed, from 1981 to 1993, the percentage of papers written by U.S. mathematicians involved in an international co-authorship almost doubled, from 13% to nearly 25% (NSF, 1998, p. 11). The development of the Internet has also made mathematical information much more accessible to the research community in the form of electronic archives of preprints, electronic journals, and so forth.

However, good communications technology and videoconferencing cannot replace the extended person-to-person experience that is of crucial importance in mathematical research. Nor can it substitute for a stimulating significant immersion in a new and different, supportive, and idea-charged research environment.

Growth and Change in the U.S. Mathematical Sciences Research Community

With the end of the Cold War, many highly qualified mathematicians, including leaders in their fields, relocated from the former Soviet Union and countries in Eastern Europe, as well as from China, to the United States. The influx of talented foreign-born graduate students to U.S. university mathematical sciences departments has increased as well. The best among these foreign students often find jobs and stay in the United States upon completing their degree programs. (For average stay rates, see Figure 7, p. 40, in COSEPUP, 1997). In 1996, non-U.S. citizens earned nearly 57% of the total doctoral degrees awarded in mathematical and computer sciences (AMS, 1996).

The size of the mathematical research community has increased substantially since the competition that resulted in the establishment of the Mathematical Sciences Research Institute and the Institute for Mathematics and Its Applications. In 1993, 22,820 PhD mathematicians were employed in the United States (NSF, 1998, p. 3), compared with about 13,000 in 1979 (COSEPUP, 1997, Figure B-7, p. 62). Of those mathematicians employed in 1993, 14,670 were employed by universities and 4-year colleges, and more than 9,500 were active in research. The number of PhDs awarded annually by U.S. mathematics departments has grown from 800 in 1986 to 1,240 in 1995 (COSEPUP, 1997, Figure 3, p. 35). A more limited job market in academia has tended to cause more PhD mathematicians to seek jobs in industry or finance, which argues for the need for more varied research opportunities for graduate students and younger mathematicians. (For data on employment trends for PhD mathematicians, see Table B-1, p. 63, in COSEPUP, 1997.)

The growth of the international mathematical community (according to the World Directory of Mathematicians, 1998, some 50,000 mathematicians in 69 countries are now involved in research activities worldwide, a figure that does not include the global community of



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