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The Mathematics Research Institute was established within the Mathematics Department at Ohio State University in 1990. Ohio State University funds the MRI for the purpose of inviting research visitors to the Department and supporting conferences, regular seminars, and targeted research organized by Department members. MRI has functioned effectively over the years.

New directions and objectives. This year, with substantial financial resources from Ohio State and NSF funding began a program to expand MRI from a resource, to one which, while retaining this original mission, makes the MRI an effective regional and even national resource in specific areas of mathematical research. The means would be a program of `mathematical years,' each focused in a specific area of research, each connected to an independently funded national conference or regional Focused Research Group (FRG) in that specific area, and each constructed around a theme of cross-pollination mentioned earlier.

Cross-pollination. Major advances in mathematical understanding can occur when new relationships are discovered between parts of mathematics which were thought to be unrelated. A new relationship of this type is a significant event, often quickly causing each area to be reexamined in light of results associated with the other. A longer term effect of this kind of breakthrough is that methods and techniques from one of the areas are imported to the other. This process of transfer often takes many years and requires the efforts of many mathematicians, but the result is usually the same: namely basic ideas in each area are understood at a deeper level, the ideas are seen to apply to other mathematical situations, and new methods are created which can extend far beyond the original breakthrough. For lack of a better term, we'll call this phenomenon cross-pollination of fields.

In fact most mathematicians aspire to discover relationships of this type. However, professional pressures on the individual mathematician and the explosive growth of mathematical knowledge and technique militate in the opposite direction, namely toward increased specialization. Rarely does an individual researcher have the opportunity, or time, to seriously engage in work done outside his own area of mathematics, even though he/she recognizes the value of doing so. This narrowness also extends to the organization of meetings and interactions between mathematicians: conferences have become more and more focused on sub-fields of mathematics, research institutes around the world organize semesters devoted to very specialized topics, and so on.

There exist already very valuable, ongoing initiatives within the community designed to counter-balance this increasing narrowness. The Mathematics Research Institute will address some limitations theses initiatives have. It will reach out to groups which are not necessarily already working together, and there will always be an expert residing permanently at the Institute, who could carry on the cross-pollination after the special activities are over, in the form of graduate courses, lecture notes, and the like.

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