
An AMS panel on "Establishing Priorities for Mathematics Research" was held at the 1996 Joint Mathematical Meetings in Orlando, Florida. The speakers were John Bahcall, an astronomer at the Institute of Advanced Studies, and AMS members Lance Small and John Polking. Astronomers have had considerable success in establishing research priorities; Bahcall said their motivation for doing so was to garner more resources for their profession, and to set their own priorities rather than let others set them. Astronomy now has a very good name on The Hill and is protected. Agencies believe astronomers have their house in order, and they are well regarded.The astronomers were able to set priorities by consensus in a period of 14 months. The task was nontrivial, but in addition to achieving the above goals, some new projects were facilitated and thinking was stimulated and organized. Bahcall described their process in useful detail.
A comment from the audience noted that all of mathematics research amounts in funds to about two mediumsized astronomy projects. Bahcall acknowledged this, but pointed out that we have roughly the same support at NSF; the major astronomy funder is NASA and "dollars weigh much less in space."
Lance Small, the next speaker, stated that it's difficult to convince mathematicians that there is a problem. At their meetings astronomers set public policy discussions without conflicts with other activities and at auspicious times of the day. (This reporter later noted that the AMS panel conflicted with 25 assorted special sessions, general sessions, minicourses, contributed paper sessions, poster sessions, invited addresses, workshops, and a retiring MAA presidential address.)
Small continued that the research mathematician's first question on setting priorities is "what will happen to summer support?" Most show little concern for the big issues. What should be done? The AMS should do more to build consensus, undertake more outreach to the mathematics community, and try to convince the membership that there are problems. We also need better efforts toward educating the public about the various uses of mathematics.
John Polking, the final speaker, was also disappointed with the turnout. (It was later noted that many fewer than 1/25th of the meeting attendees were there). What's wrong with the research community? Priorities are always set, nowadays most frequently by the Program Officers at NSF, who do a very good job. Polking has a great deal of respect for these people, and they are too little appreciated. They would like more input from the community.
Research priorities have been set at the policy level for some time. The David Report of 1984 was successful in obtaining more money for young mathematicians; it contained only one research priority: computational mathematics. The NSF went forward with this and transformed it into "computational science and engineering," even removing mathematics from the name.
A bit later, when Polking was at NSF, he attempted with little success to get the community to proceed further. Other sciences were much more successful  astronomy was the best even then. Polking gave a report with a priority on geometry, which apparently had some very beneficial effects.
Is it possible to set funding priorities in mathematics? Polking was not sure, but stated that we have to. He suggested that we look at Bahcall's model, keeping in mind the special features of mathematics: it's the most basic science, applies to all the others, and is very diverse, as is evident from its various applications. We need to make clear that in developing the theory of elliptic curves, mathematicians come up with tools and techniques that can have important applications. One important reason for proceeding to attempt to set research priorities is that in the process more members of the community would become involved in the policy issues that so strongly affect their lives.
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