## From Mathematical Result to New Technology: How Can We Reinforce the Connection?

**March 15, 2000**

**James Crowley**

As applied mathematicians, we all know that mathematics and computing are pervasive in scientific research and essential to much of today's technology. The general public, and even many scientists, however, do not think of the mathematical sciences as central to scientific progress. Too often, mathematics lurks behind the science, receiving little fanfare or recognition.

Reading a recent issue of *Science* magazine (Vol. 287, No. 5451, January 14, 2000), I was struck by the ways in which mathematics was, and wasn't, covered. This one issue of a widely read publication seems to reveal a lot about the difficulties we face in convincing non-mathematicians of the importance and usefulness of mathematics.

**Mathematics: Conspicuous For its Absence**

The issue of *Science *contained an article on the budget for the National Science Foundation for the year 2001. The article described important initiatives in nanotechnology, information technology, and biocomplexity, a mobile seismic network, field stations for ecologists---but made no mention of mathematics. This despite recent public statements by NSF director Rita Colwell on the importance of mathematics and promises of major increases in funding for the mathematical sciences.

Mathematics was also conspicuously absent from the introduction to a forthcoming series of articles, called "Pathways of Discovery." The series, readers are told, will explore "exciting areas of investigation." The introduction includes a graphical timeline of "major past events and agents of discovery." The most recent mathematician on the timeline is Isaac Newton (unless you count Albert Einstein).

The topics to be covered in the series are the planetary sciences, genomics, infectious diseases, materials science, cloning/stem cells, communication, quantum physics, the cell cycle, atmospheric sciences, neuroscience, and astrophysics/cosmology. Of course, those who work in applied mathematics or in interdisciplinary areas involving those disciplines will recognize that mathematical discoveries and computational results underlie many of the topics. But because mathematics is not explicitly mentioned, a general reader has no way of knowing that it is fundamental to the discovery process.

**A Curious Application**

The same issue of *Science* did cover one application of mathematics and computation, one that also received recent attention elsewhere (*The New York Times*, January 11, 2000)---computational modeling of bubbles in beer. The piece describes the use of CFD software (from Fluent Technologies) to model the motion of bubbles in a glass of Guinness stout. This CFD code has many applications, such as void formation in the processing of materials, that are far more practical and important than bubbles in beer. But that was the application that caught the attention of *The New York Times* and *Science*. Why?

The media seek stories that are either immediately relevant or appealing for their quirkiness. A similarly offbeat example is a paper from a recent issue of *SIAM Journal on Applied Mathematics* that caught the attention of the media; the paper describes the application of dynamical systems to the modeling of Petrarch's emotional cycles (*SIAM Journal on Applied Mathematics*, Vol. 58, August 1998, and *Dallas Morning News*, August 3, 1998).

This is not to suggest that these two applications are unworthy or uninteresting; on the contrary, in both cases the news articles were based on sound research in exciting areas and made for interesting reading. The problem is that the quirky applications tend to be the only ones the public hears about; the end result is that mathematics receives less serious coverage than other areas of science.

**Conclusion**We all know that advances in mathematics and computing have led to significant improvments in the quality of life and have had considerable economic impact. This point was driven home very strongly in, for example,

*The*

*Mathematical and Computational Sciences in Emerging Manufacturing Technologies and Management Practices*, a report published by SIAM (Avner Friedman, James Glimm, and John Lavery; 1992).

It is clear that the applied mathematics and CS&E community (and SIAM!) must work harder to reinforce the connection between new results in the discipline and new advances in technology that, in turn, drive modern economies.

I would like to offer a suggestion. Looking forward to SIAM's 50th anniversary, in 2002, we invite readers to send us their thoughts on specific contributions of applied mathematics and computing, and their impact on industry and other areas of science and engineering.