THEORETICAL mathematicians, who have always lived in a lofty and arcane region half way between philosophy and science, are being dragged en masse into the contentious world of sticky moral decisions, military funding, and space age weaponry. Those who are members of the American Mathematical Society (AMS), the main professional organization in their field, may soon receive in the mail the chance to vote on two resolutions. One will express concern that federally financed research should be spent on ``traditional basic research'' instead of research directed toward specific goals such as weapons development. The other puts AMS on record as neither ``encouraging nor facilitating participation by mathematicians'' in President Reagan's Strategic Defense Initiative (SDI). Those motions are somewhat watered-down versions of proposals by a vocal minority of AMS members who strongly oppose the influence of the sudden explosion of Department of Defense (DOD) money for mathematics in general, SDI in particular. An AMS meeting last month in San Antonio voted to put the resolutions before the AMS convention this summer, but those who object to the motions are asking that the general membership, some 20,000, be polled directly.
How widespread the opposition to the funding is cannot be determined. ``I think it's just a small minority,'' says Isidore Singer, a mathematician at the Massachusetts Institute of Technology who is against the motions. ``They are just 1960s people trying to relive their childhood,'' says a researcher at the University of California at Los Angeles, who has accepted such funds and asked that his name not be used.
Nonetheless, many mathematicians, including some of America's best, have refused to take SDI funds, even when courted by the Pentagon. They include William Thurston of Princeton University, winner of the Field Medal, the mathematicians's equivalent of the Nobel Prize, and a leader in drafting the original resolutions. The question of authorizing grant proposals for SDI is a matter of controversy in the mathematics department at Harvard University.
Although political opposition to Reagan administration policies probably plays a factor in the issue, critics of DOD funding and SDI point out two concerns: that vast amounts of DOD money could radically influence the kinds of research being performed, and that large amounts are being given out without conventional peer review.
James Ionson, director of SDI's Innovative Science and Technology Program, says SDI has almost $3 million to spend for research (all unclassified) in mathematics this year, far more than has ever been spent for math. That troubles many mathematicians. They point to their colleagues in computer sciences, who now find themselves almost dependent on DOD funds.
``Military agencies are increasingly mission-oriented in their research programs,'' says Morris Hirsch of the University of California at Berkeley, an opponent of DOD funding. ``Mathematicians and their graduate students will unavoidably feel pressure - both internally and from their departments - to design their research projects to increase the likelihood of grants.''
Funding without peer review could mean that research might be aimed toward work with potentially practical uses and of possibly dubious quality, draining talent from pure research, some mathematicians fear.
The issue is more acute now because the mathematics community is the convergence of two forces. First, mathematicians have recently dicovered a need for computers and larger amounts of research monies to buy them. At the same time, the complexity of modern warfare, particularly of the envisioned antiballistic missile defense system, makes some of what theoretical mathematicians do relevant, particularly in spatial statistics, optimization, and dynamical system research.
The National Science Foundation provides very little for capital expenditures such as computers. Several mathematicians now find that the only way they can get such funds is from DOD, according to Dr. Thurston.
A few mathematicians changed jobs to avoid the conflict. Michael Shub left the City University of New York for IBM after the school accepted a DOD grant and he could not get one for his research from other sources. He says he knows of mathematicians who have been offered grants of six figures to buy computers, offers they could not refuse.
Dr. Singer, however, thinks the motions will be voted down by the general membership. He agrees that federal funding is a mixed blessing, that the government has sometimes interfered with the proper flow of research, but those instances should be handled on an individual basis.
``If it comes to pass that the government tries to strong-arm us, we should fight it when it takes place'' says Singer. But any support for mathematics would be an improvement, he believes.
Thurston, however, says he is satisfied that the issue is now before the AMS membership. ``The most significant thing is that the issues are now out in the open, that people are discussing them, and that the discussions are not fractious and contentious,'' he says. ``There are still many voices waiting to be heard.''