Adding Up a Solution to Competitiveness

Look at any of the so-called critical technologies you want--biotechnology, new materials, software, etc.--and the fact remains that the cheapest, most cost-effective and influential investment America could make in industrial competitiveness is in mathematics. Few things are as powerful--or as profitable--as an equation whose time has come.

The Black-Scholes options pricing formula--which lets financial engineers craft new securities and sniff out arbitrage opportunities between old ones--has transformed the flow of trillions of dollars in global capital markets. The Reed-Solomon algorithm determines the fidelity of both music and data in millions of computers and compact disc players. The emerging non-linear equations of Chaos Theory provide practical insights into the physics of the heart and the future of the environment.

As much as the cost of capital or any presidential directive, obscure equations now shape the effectiveness and competitiveness of U.S. industry. While America has tremendous mathematical talent and resources, you wouldn’t know it from the way they have been applied.

“We lead the world in this area,” asserts Louis Auslander, who recently directed mathematical research for the Pentagon’s Defense Advanced Research Projects Agency. “It’s a great advantage for us but we’re not using it.”


We should be taking that advantage and using it to create new technologies and new market opportunities. In the same way that new mathematics redefined finance, mathematics should be redefining our competitiveness in engineering and molecular biology. Universities should be creating departments of “mathematical engineering” to give people tools to manage the complexity of assembly lines. More companies should be teaming mathematicians with their engineers and innovators.

Unfortunately, most companies simply can’t figure out what to do with mathematics--or they believe that mathematics is statistics for quality control. They think of mathematics as a set of cold equations that freezes observations into unambiguous numbers rather than as a rich language that gives people new ways to describe reality.

The mathematicians themselves have made things worse. Mathematics in America has been stripped down from “the queen of the sciences” to a Sibyl-like creature of multiple factions and narcissistic indulgences. Too many brilliant mathematicians with Ph.Ds take unhealthy pride in the notion that their work has no relevance at all to the real world. Of course, Newton’s Calculus, Einstein’s Relativity and the swirl of mathematical breakthroughs generated by Chaos Theory were all inspired by real world problems.

“Mathematicians have forgotten where their problems came from,” says Avner Friedman, who directs the University of Minnesota’s Institute for Mathematics and its Applications, one of the few academic institutions explicitly looking at how to link mathematics with real-world problems.


Unfortunately, Friedman observes, “the dominant attitude” in mathematics today is that relevance is more nice than necessary. Mathematics has become less of a culture that wants to communicate than a collection of cults that talk to themselves.

“Most mathematics departments are very narrow,” Friedman says. “Only a small percentage of people are seeking collaboration with the outside world. Integration has not yet taken root.”

That’s not to say that pure mathematics--that is, mathematics based on mathematics itself, rather than on real world problems--is irrelevant or wasteful. On the contrary, many of these intellectually challenging and obscure mathematical branches can offer practical insights into real-world problems. For example, work in topological “knot theory"--the computational geometry of knots--has given a new context for biologists to consider the design of proteins, the building blocks of life.

Indeed, in a tasty irony, it turns out that the great Victorian mathematician G. H. Hardy--who reveled in the irrelevance of his elegant mathematics--in fact created equations that have had enormous impact on the development of control theory--the complex branch of mathematics that yields the software enabling ultra-sophisticated planes to fly. No matter how beautiful or elegant, it seems that mathematics can’t escape relevance.


“One has to wonder whether the mathematical thoughts that our brains are thinking reflect a certain underlying natural order or pattern that leads to virtually all our mathematics becoming applicable at some time or another,” observes Howard L. Resnikoff, a former mathematics department chairman at UC Irvine who now runs Aware, a mathematics company in Cambridge, Mass.

However, it’s clear that there is now a gross imbalance between mathematics for the sake of mathematics and mathematics driven by problems posed by complex realities. The National Science Foundation and the various branches of the Pentagon collectively spend about $150 million on “mathematics research"--but most of that is focused on excruciatingly narrow classes of problems.

What’s worse, very little of the funding promotes interdisciplinary efforts between mathematics and other fields. We don’t “leverage” mathematics well. A recent National Research Council report calls for more “technology transfer” in mathematics, but that doesn’t nearly go far enough.

“I don’t think there’s anything preventing a Caltech, a Berkeley, a Stanford or an MIT from starting a department of mathematical engineering,” Aware’s Resnikoff says. Indeed, Auslander asserts, for as little as $5 million, you can launch a new area of research in multidisciplinary mathematics. You can lure people into examining the interesting classes of problems that the reality of a complex assembly line or a intracellular transport mechanism can offer.


“We don’t need more mathematicians,” says Auslander, a distinguished mathematics professor at City University of New York. “We need more mathematicians with a different attitude.”

But we also need more policy-makers and corporate managers who understand that the numbers that can really make a difference to industrial innovation and competitiveness aren’t just found in the accounting books. The real power and beauty of mathematics isn’t in the way it can describe reality--it’s in the way it can be used to improve reality.