Mathematical Challenges from Theoretical/Computational Chemistry

The committee has examined evidence supplied to it in the form of prior reports, expert testimony at its meetings, selected studies of the scientific literature, and personal contacts in the mathematical sciences and chemistry communities. As a result of these investigations and its collective evaluation of the available information, the committee has reached the following conclusions.

• Several notable "success stories" can be identified, illustrating the value of interdisciplinary stimulation and synergistic research collaboration involving cooperation between the mathematical sciences and the theoretical/computational chemistry communities.

• Many opportunities appear to exist for further collaborations between the mathematical and chemical sciences that could result in high-quality scholarship and research progress that would advance national interests. The productivity of applied computational chemistry would likely be enhanced as a result, which could be potentially significant for industry.

• Active encouragement of further collaborations is warranted because it would likely result in an acceleration of such research progress.

• Cultural differences between the mathematics and the chemistry communities, involving language, training, aesthetics, and research style, have tended to act as barriers to collaboration, even in circumstances that might otherwise suggest the benefit of cooperation.

• Institutional structures and reward systems in the academic community have often placed significant difficulties in the way of collaborative research across traditional disciplinary boundaries, which can be especially inhibiting to those in early career stages.

• Government funding agencies have for the most part made constructive efforts to identify and fund worthy interdisciplinary and collaborative research. However, this process is still somewhat haphazard. Agencies tend to be organized along traditional disciplinary lines, and the evaluation of interdisciplinary proposals relies on personal contacts between program managers and on timely and comprehensive responses from what is typically a small pool of qualified reviewers. The time lapse involved in the proposal evaluation process thus has often been anomalously long.

• To a large extent, both mathematical scientists and theoretical/computational chemists are relatively unaware of the most exciting recent advances in each others' fields. Consequently both groups tend to be insensitive to the opportunities for interdisciplinary cross-fertilization that could produce intellectual novelty and productivity enhancements on both sides.

• The system of prizes and awards administered by the mathematical sciences and chemistry professional societies is currently not geared to recognize and reward interdisciplinary collaborative research advances.

• The national environment--including Congress, funding agencies, and the professional societies (see, e.g., Joint Policy Board for Mathematics, 1994)--has become perceptibly more conducive to encouraging and supporting interdisciplinary and collaborative research, particularly as it may concern industrial innovation and productivity. Government agencies in particular are currently in a mood to actively encourage joint industrial-academic research, even though proprietary rights barriers to free collaboration are recognized to exist.

• The overwhelming volume of specialized technical literature aggravates the communication problems between fields and occasionally leads to wasted effort, redundancy, and rediscovery. It appears that well-researched and well-written review articles spanning normally disconnected specialties in the mathematical sciences and in theoretical/computational chemistry represent a disproportionately small fraction of the technical literature, in spite of the fact that they can eliminate redundant effort.

In response to these conclusions and to the insights gained from its study, the committee makes the following recommendations:

Undergraduate Education. The best way to attract scientists to interdisciplinary work is to get them interested as undergraduates. It is recommended that universities encourage undergraduate interdisciplinary research courses, seminars, and summer programs. For example, mathematical sciences departments could institute seminars for undergraduates in which chemists (and other scientists) would be invited to discuss chemistry research areas that might benefit from interaction with mathematics. The committee recommends that chemistry departments establish seminars for undergraduates in which mathematical scientists would be invited to discuss modern mathematics. Graduate students (and interested faculty) would of course be welcome to attend these seminars.

In the experience of the committee members, one very successful vehicle for getting mathematics and chemistry undergraduates interested in research is the REU (Research Experience for Undergraduates) program sponsored by the National Science Foundation (NSF). In addition to fostering interdisciplinary undergraduate activity at research universities, there is a real educational opportunity here for four-year liberal arts institutions that traditionally encourage undergraduates to write senior honors theses and to otherwise construct, expand, and explore their own undergraduate education.

Graduate Education. Departments in the mathematical and chemical sciences should encourage graduate degrees (both M.S. and Ph.D.) that involve dual (mathematics and chemistry) mentoring. Dual mentoring activity between chemistry and physics and chemistry and biology has been successful in many universities. The committee recommends that mathematics graduate students consider a minor in chemistry instead of a minor in an area of mathematics related to their research specialty. Theoretical and computational chemistry graduate students should consider a minor in mathematics or, alternatively, take a core of mathematical courses appropriate to their interest (perhaps in the framework of a special "interdisciplinary track"). One way to encourage cross-disciplinary graduate education is to allow graduate students in one area to enroll in upper-level undergraduate courses in another area for graduate credit.

Faculty Interaction. Mathematics and chemistry departments should on occasion invite a person from the other area to speak in a research seminar or a colloquium. Lists of speakers of potential interest to industry should be circulated to local industrial laboratories, and vice versa.

Interdisciplinary Research. The committee recommends that mathematics and chemistry departments encourage and value individual and collaborative research that is at the interface of the two disciplines. Such work has the potential for significant intellectual impact on computational chemistry, and hence on the future evolution of chemical research and its applications to problems of importance in our society.

Professional Societies. The American Mathematical Society (AMS) issued a policy statement in 1994 that supports interdisciplinary research. The second goal of that statement is to "connect the power of mathematics and mathematical thinking to problems in science, technology, and society." This policy statement is reinforced by specific recommendations to "enlarge the scope and extent of interdisciplinary research connecting mathematics with other fields" and to "emphasize the value of such connections during the mathematical training of both undergraduate and graduate students" (American Mathematical Society, undated).

Professional meetings in mathematics and chemistry--for instance, those of the AMS, American Chemical Society, Society for Industrial and Applied Mathematics (SIAM), and the Chemical Physics Division of the American Physical Society--would benefit from talks very much like the seminar and colloquium talks described in the recommendation for faculty interaction above, from shorter presentations in special sessions, and from panel discussions. There are already some promising moves in this direction as reflected, for example, by recent AMS sessions on mathematics and molecular biology or SIAM sessions on molecular chemistry problems and optimization. These sessions at national and regional professional society meetings could generate a mailing list of interested mathematicians and chemists, which could be the kernel of a community of people interested in interdisciplinary research. Appropriate specialized interest groups such as already exist for other fields might be established. One way to encourage these interests is by initiating small interdisciplinary workshops, perhaps incorporating tutorials for students. Examples of successful interdisciplinary meetings are the mathematics and molecular biology series in Santa Fe and the mathematical physiology series held at the Mathematical Sciences Research Institute at the University of California at Berkeley. Funding agencies have in the past funded carefully planned interdisciplinary meetings.

Prizes and Awards. The committee recommends that professional societies in the mathematical and chemical sciences examine the feasibility of establishing awards and named lectureships for work at the mathematics-chemistry interface. High-level public recognition by peers would be a major step toward breaking down interdisciplinary barriers.

Expository Articles and Books. Professional journals in mathematics and chemistry could enhance their quality, appeal, and influence by publishing expository articles on work at the mathematics-chemistry interface. There is a shortage of books written for someone who is mathematically (chemically) sophisticated and desires fairly precise but nonrigorous chemical (mathematical) explanations. The committee encourages mathematicians and chemists to write expository books aimed at this interdisciplinary area.

Interdisciplinary and Industrial Postdoctorals and Sabbaticals. Mathematics and chemistry departments should encourage postdoctoral and faculty sabbatical study at the mathematics-chemistry interface. The committee recommends that the chemical software, pharmaceutical, and chemical industries expand their use of mathematics postdoctorals and faculty on sabbatical leave, and increase their cooperation with and utilization of existing NSF programs such as the University-Industry Cooperative Research Program in the Mathematical Sciences; Industry-Based Graduate Research Assistantships and Cooperative Fellowships in the Mathematical Sciences; Mathematical Sciences University-Industry Postdoctoral Research Fellowships; and Mathematical Sciences University-Industry Senior Research Fellowships. Another opportunity in this regard exists at the Institute for Mathematics and Its Applications at the University of Minnesota, which has an active industrial postdoctoral research program with the aim of broadening the perspectives of recent doctoral recipients in the mathematical sciences and preparing them for research careers involving industrial interaction.

References

American Mathematical Society, undated, AMS National Policy Statement 94-95: Summary, American Mathematical Society, Providence, R.I.

Joint Policy Board for Mathematics, 1994, Recognition and Rewards in the Mathematical Sciences, American Mathematical Society, Providence, R.I.

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