Mathematicians: Real-World Applications Are Key To Increasing The Field's Appeal

Strong academic-industry links are deemed essential to the resuscitation of math's ability to attract and retain top-notch students Mathematicians are looking at the numbers, and some don't like what they see. Despite a spate of recent reports and studies urging greater support for the mathematical sciences and math education, academic funding levels and student retention rates are still far below what math practitioners believe is warranted. A follow-up study to a 1984 National Research Cou

Mar 16, 1992
Marcia Clemmitt
Strong academic-industry links are deemed essential to the resuscitation of math's ability to attract and retain top-notch students
Mathematicians are looking at the numbers, and some don't like what they see. Despite a spate of recent reports and studies urging greater support for the mathematical sciences and math education, academic funding levels and student retention rates are still far below what math practitioners believe is warranted.

A follow-up study to a 1984 National Research Council "national plan" for mathematics reports that "almost no progress" was made in increasing support for senior academic mathematics researchers in the period between 1984 and 1990.

The total number of senior researchers receiving grants from the government and other sources increased only from 1,800 in 1984 to 1,900 in 1990. The 1990 figure is far short of the 2,600 the council recommended as necessary to put math research on a par with work in other disciplines and to recognize mathematics' value in underpinning other scientific research. Meanwhile, dropout rates among math students remained high, with about half withdrawing from mathematics courses each year after the ninth grade, and up through the Ph.D. level.

A growing number of mathematicians put much of the blame for those alarming trends on the mathematics community itself. They say academic mathematicians need to look beyond math department walls and try to change the way other scientists and the public view their discipline by undertaking more collaborative research projects aimed at highlighting the usefulness of mathematics, especially projects involving industry scientists and engineers.

"We need to ask ourselves, `If we're so valuable, why are we hired in such small numbers? Why are we rewarded so little?' " says Joseph Pimbley, an assistant professor of mathematics at Rensselaer Polytechnic Institute in Troy, N.Y. "The answer isn't always, `Society's terrible.' If students aren't coming into math, if corporate decision-makers aren't recognizing our importance, we need to see what we've done that's given everybody the impression that mathematics isn't valuable or useful."

What mathematicians have done to foster that impression, say Pimbley and others, is put too much emphasis on the abstract beauty of pure mathematics and too little on its practical applications, especially in other scientific and technical disciplines. Developing research partnerships between academic mathematicians and industry can help improve that image, many who have tried collaborations say; but they also stress that successful partnerships are difficult to form.

Researchers who have participated in these joint ventures cite several things mathematical scientists need to do to make collaborations between academia and industry work. These include:

* Learning more about the scientific fields to which their work might be applied;

* Learning the language of business well enough to convince corporate managers that mathematics has something worthwhile to offer;

* Being persistent in seeking out industrial partners;

* Changing the academic incentive system to reward research that produces concrete applications;

* Approaching a problem in terms of its specific conditions instead of a set of hypothetical parameters that can be easily changed;

* Trying out different formats for collaborations to find which best suit the needs of corporate clients as well as researchers and their institutions.

The Mathematics Clinic at Harvey Mudd College in Claremont, Calif., has put undergraduate students together with mathematics faculty to solve specific industrial problems since 1973. Clinic director Stavros Busenberg says the pro-gram's success can be measured not just in the number of corporate clients who bring repeat business but in the kind of students the clinic helps Harvey Mudd College attract to its campus.

Three to five undergraduate math students, along with a faculty adviser, work on a client's problem for a semester or an academic year, presenting an analysis and proposed solution to the client at the end of that time. Projects include optimization studies of missile guidance systems and mathematical models for predicting groundwater pollution. Businesses, government agencies, and nonprofit groups each pay the school $31,500 per project. "That's the cost of funding," says Busenberg. "We do an annual review, and over 90 percent of our clients report that they got their money's worth and then some." Repeat clients include Chevron Oil Field Research Co. of La Habra, Calif.; Los Angeles-based Teledyne Microelectronics; and the U.S. Forestry Service, school officials say.

According to Busenberg, the industrial clinic is an important tool in attracting and educating gifted math students. "The chance to work on real problems, interesting problems, is a recruiting tool for us in getting bright young people," he says. "It gives them a wider view of the career track in than they would get otherwise. A significant number eventually go into industry. They don't regard it as below the dignity of exceedingly intelligent people."

Busenberg cautions mathematics department officials hoping to launch similar programs at their schools that successful collaborations require persistence, communications skills, and some rethinking of the traditional reward systems in college math departments.

Busenberg describes the long process of bringing a new client with a potentially interesting problem into the clinic. Calls and letters are necessary, he says, but they're not enough: "You must visit." A case in point Busenberg cites was that of an airline hoping to improve its scheduling system whose operations he surveyed. "I was able to describe similar problems we'd done--figuring out how to get the best customer satisfaction in a situation full of uncertainties," he says.

After the visit, Busenberg says, there are follow-up letters and, later, more calls. It takes patience and a willingness to keep trying, along with "the ability to communicate with managers. Math is a vital component in our intellectually based economy. But you need to speak enough of the language of business to show how your mathematics can make their businesses more competitive."

But if universities are to cooperate with industry at all, says Busenberg, mathematics departments have to be more open-minded about the kinds of work they reward with promotions. "There's derision connected with publishing in the hyphenated [interdisciplinary] journals: Many mathematicians say mathematical physics or mathematical biology don't count," he says. "If people are worried they won't be promoted if they do collaborative work, they won't. The rewards system must be adjusted first."

Avner Friedman, director of the Institute for Mathematics and Its Applications at the University of Minnesota in Minneapolis, contends that paying more attention to real-world problems is simply bringing the field of mathematics back to its historical roots.

"Through history, mathematics has developed hand in hand with other sciences; but in the last few years, so many new theories have developed that mathematicians have forgotten where it's all coming from," he says. "It's necessary for math's survival to interface with other [scientific] disciplines.~" Friedman says that mathematicians need to reexamine some of their working assumptions if that interface is to be a smooth one, however. "You must start with the industrial context," he says. "The first goal is to have something to say about solutions--usable results--in the context of particular details. Often, mathematicians say, `If I change the problem just a little bit, I can do more interesting mathematics.'

But the first axiom is: Don't change the problem." At Rensselaer Polytechnic's Math/Industry Workshops, mathematics faculty and graduate students, plus visiting faculty from other institutions, spend a week of concentrated effort on problems brought by industry scientists. Current workshop director Pimbley says the mathematical issues that arise from industrial problems are a boon for mathematicians, who are always looking for interesting mathematical questions. But, he says, mathematics students are often unwilling to learn enough about another discipline to understand in depth the mathematical issues it contains.

"When a lot of people say, `Well, I'll collaborate,' they mean something like `I can solve differential equations. So the chemistry student will show me her equations, and I'll solve them,' " Pimbley says. "But that's just tinkering. It doesn't lead to much in the long run. The only way to find the real mathematical issues involved in the other person's field is to roll up your sleeves and learn about it. But that's not a common attitude."

Peter Castro, supervisor of applied mathematics and statistics at the Eastman Kodak Co.'s Computation Sciences Laboratory in Rochester, N.Y., says that while more cooperation with academic mathematicians would help industry mathematicians and scientists create better products, it could also help academic mathematicians showcase the importance of their work.

The trick, Castro says, is finding the right partnerships and determining the degree of involvement the mathematicians should take in these collaborations.

Says Castro: "Industrial mathematicians are struggling to communicate to management the importance of getting more mathematicians involved. We see hints of what math can do for us, but we are few. There's seldom the horsepower within a company to pull it off.

"At the same time, academic mathematicians have this tremendous output of material--new techniques and theorems. One good way to justify the funding of all that work is by pointing to its applications. But industry people have little time to scan the literature for useful things, so there's a low hit ratio. If academic mathematicians would help us--point us toward new theorems and techniques they know about that might apply to what we're doing, or choose problem areas of interest from our work--then they'd up the hit ratio of the math that actually gets used."

Like Harvey Mudd's Busen-berg, Castro points to the university incentive system, which rewards published theorems but not practical products arising from mathematical work, as a barrier to academy/industry cooperation. But Castro hopes some new types of collaboration might help surmount that barrier.

Instead of working with industry researchers to see a problem all the way through to a detailed solution, he says, academic mathematicians might serve as advisers, providing industrial researchers with fresh mathematical input that would eventually result in tangible products while generating publishable theorems for themselves.

"They could get to know the company's problems and make sure that the available and possibly applicable math is brought to our attention," Castro says.

"And if we need a set of results and the theorems aren't available, they can come up with those theorems, and we'll take it from there. The theorems are publishable work, in areas they probably wouldn't think of doing otherwise."

Creating that balance between publishable results and practical outcomes may become crucial for the mathematics community as science funding agencies grow more cautious, many mathematicians say. "There's been a gradual change towards emphasis on applications in science funding," says James G. Glimm, chairman of the department of applied mathematics at the State University of New York at Stony Brook. "I don't know how far the trend will go, but I think it's a sure bet it will continue."

Glimm, who edited a 1991 National Research Council report detailing the contributions of mathe- matics to the aircraft, semiconductor, petroleum, auto, and telecommunications industries, adds: "That approach to funding is going to challenge the math community to justify its role in the scientific and technical enterprise as a whole."