Math Society Copes with Change at 100

BOSTON—For the 20,000 members of the American Mathematical Society, this year’s centennial is an occasion for both celebration and concern. American mathematics in many ways is at its zenith in terms of prestige and scope. Yet federal support for the “pure” mathematics represented by the AMS has failed to keep up with inflation, and there is little hope for a turnabout until the federal deficit is brought under control. There is turmoil as well inside the AMS. After a year of sometimes heated debate, AMS members are now voting on whether the society should oppose research funding from the Defense Department, especially money tied to the Strategic Defense Initiative. The results are due out this spring. Amid this ferment, AMS officials have been searching for an executive director to replace William LeVeque, who is stepping down in the fall after 11 years. Last month they selected William Jaco, formerly of Oklahoma State University who is now working in Australia (see accompanying interview). The turmoil does not detract from the remarkable progress American mathematics has made in the last 100 years, especially in the last two decades, AMS officials have noted. U.S. mathematicians, who had little influence in the 19th century, have moved into the fore-front of highly advanced pure mathematics. Evidence of that progress, said AMS President G. Daniel Mostow of Yale, can be found in the Fields Medals, the highest award in mathematics. “Before 1962, only one of eight Fields Medal winners was an American,” Mostow said. Since 1962, he noted, nine of 22 medals have gone to Americans and two more have gone to mathematicians trained in the United States. That achievement has been reflected in the success of the AMS itself. Founded in 1888 by three members who hoped to foster comradeship in a field that was largely ignored by the rest of the American scientific community, the AMS has grown into an organization with more than 20,000 members, a large publishing house and an annual budget of about $13 million. The non-profit society traditionally has served as a publishing house for “core” mathematicians. Its output is prolific: While the number fluctuates, LeVeque said, the AMS typically publishes about 18 journals and 50 to 60 books each year. Its most important journal is Mathematical Reviews, which generates about a third of its budget. Publications have accounted for much of the society’s financial growth, LeVeque said. During his tenure as director, he noted, membership remained fairly constant but the budget has tripled. Thanks to its publishing activities, the AMS is virtually self-supporting, LeVeque said. “We get a few hundred thousand dollars a year from the NSF [National Science Foundation], principally to run conferences of one sort or another. That is all pass-through money.” Annual dues of $88 for regular members account for another 10 percent of the budget, he said, “and the remainder of it is produced by things that we sell—that is, books and journals and registration fees at conferences and meetings.” Its publishing activities continue to grow. An online service allows members to search an electronic version of Mathematical Reviews, and the AMS is expanding its ef- forts to translate major foreign mathematical publications into English. While publishing will remain the society’s primary focus, AMS officials realized during the past few years that academic pursuits are not enough. They have joined the Mathematical Association of America and the Society for Industrial and Applied Mathematics in a variety of other activities to foster the health of the field. The AMS, the first mathematical society in the United States, is concerned primarily with mathematicians who do “pure” mathematics. The MAA, which has 26,000 members, is concerned primarily with mathematics education and college-level mathematics. SIAM, with about 6,500 members, caters to applied mathematicians and those working in industry MAA and SIAM were spun off from the AMS years ago; they retain a large overlap in membership. In 1981, citing a serious imbalance in federal funding of mathematics compared with other sciences, mathematicians working under the auspices of the National Research Council formed a study panel. Their report, issued in 1984 and known by the name of its chairman, Edward David. called for a doubling of funding for basic mathematics research within five years. Now, almost four years later, federal funding for basic mathematics has increased about 70 percent, from about $68 million to $115 million annually. But Fred Hoffman, an MIT mathematics professor who is the Washington representative for the three societies, noted that the increase in real terms is only about 40 percent. The immediate outlook is not encouraging, Hoffman said. Congress gave NSF only 3.3 percent more for basic research this year, an increase that falls behind inflation. Hoffman does not expect mathematics to gain a disproportionate share of that small raise. In addition, because NSF provides “97 percent of the pure mathematics research money,” he said, there is little hope that the shortfall can be made up somewhere else. Mostow shares Hoffman's pessimism. “There is some concern that American mathematics may have reached its.. . high-water mark in relation to other countries... ,“ he said. While other countries are getting better at math, he noted, federal support for U.S. mathematicians is being trimmed. Inadequate funding not only affects the ability of math researchers to do their work, Hoffman said, but also discourages bright young people from pursuing math careers. “There is a shortage of people going into fundamental mathematical research,” he said, “and if young people looking around [for career options] see that there is no money in mathematics, and they see these people in mathematics living in poverty, then they are going to choose other fields.” Mathematicians across the board are alarmed about the declining level of math education in U.S. high schools and colleges. Hoffman said part of the response is the National Research Council’s Project MS 2000, a comprehensive review of the state of college mathematics. The goal is to develop a national plan for upgrading math education and attracting more students. A $250,000 annual budget and an office in Washington are evidence of the growing willingness of the AMS and other math societies to try to persuade politicians that math is important. The reason mathematicians have been slow to organize while other scientists and engineers have used their professional societies to build strong Washington offices has something to do with the individualistic nature of mathematicians, several AMS officials said. "Very often people go into mathematics partly because they enjoy the intellectual feeling of it, but also, they feel more comfortable in a field where they don’t have to relate the same way with a large group of people,” Mostow said. “There are not so many skillful politicians who are mathematicians.” The reverse, many mathematicians agree, is also true. William Browder, a math professor at Princeton University and president-elect of the AMS, said one of his goals when he takes office in 1989 will be “to get the society to be more activist and to try to influence science policy. I think our field has suffered from the fact that there have been very few activist mathematicians.” He said he hopes that mathematicians will look at the efforts of other scientists for inspiration. The past year has seen the greatest political activism within the AMS since an occasionally bitter internal dehate about the society’s role during the Vietnam War. In January 1987 William Thurston, a Princeton mathematician, proposed two resolutions that would affect the society’s involvement with SDI and Pentagon funding. His suggestion triggered a running debate among mathematicians in Notices, a monthly AMS publication. The SDI resolution calls for the AMS to “lend no support to the Star Wars program” and states that “persons representing the AMS shall make no efforts to obtain funding for Star Wars research... The second resolution introduced by Thurston notes that military funding for mathematical research is distributed through “narrowly focused programs” and circumvents peer review. It calls for AMS officials to “direct their ef- forts towards increasing the fraction of non-military funding for mathematics research.” Thurston said he and a small group of colleagues were concerned that, by taking SDI money, mathematicians were giving legitimacy to a flawed program. On the issue of military money, he said, “it doesn’t make sense to have the military mixed up in the university system [through funding of mathematical research].” LeVeque summed up the feelings of opponents to the referendum: “Some people think their membership in the AMS is for one purpose . . and they don’t want to do politics in the AMS any more than they want to do mathematics in the ACLU. They feel that paying dues should not necessitate that they be political animals at the same time.” Three other referendum items were added to the ballot mailed out to members in January. Two urge the federal government to fund more research in mathematics; the third calls for federal agencies to use a more open process when soliciting proposals from scientists. Thurston said the latter three items were added by the AMS establishment “so that when people saw the ballot they would say, ‘Here are two questions [SDI and military funding] written m an irrational way and here are three questions on the right issues,’ and everybody will vote for those three.” Thurston said that, despite the year of maneuvering on the form of the ballot and the disagreements over the issues, the discussions within the AMS have been much friendlier than those during the Vietnam War era. “On the whole, it’s been working well,” he said of the referendum process. “We’ve been working together with the establishment.., and everybody has welcomed an opening up of Notices to more discussion.” The ballots are due March 18, and Thurston predicted passage of his two resolutions. The uncertainty has not prevented mathematicians from standing up for themselves, Hoffman believes. The mathematics community has been “getting its act together” to fight for funding, he said. “We want to get these societies working together,” he said. “We’re in it for the long haul.” Dawson is a Knight science fellow at MIT on leave from The Minneapolis Tribune.

Math Society Copes with Change at 100

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