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Digital Library of Mathematical Functions (DLMF)

Building a Networked Mathematical Knowledge Base

Back in 1964, the U.S. Department of Commerce published a handbook of mathematical functions that soon became a bestseller. The 1,000-page handbook rapidly found its way to the desks of hundreds of thousands of mathematicians, physicists, engineers, and others who use specialized mathematical functions in their work.

Nearly four decades later, the department's National Institute of Standards and Technology (NIST) is preparing to publish a substantially updated version of the printed handbook—and, more important, to provide the reference information through a freely available interactive site on the World Wide Web.

Pulling together and editing material for the Digital Library of Mathematical Functions (DLMF) has required the efforts of about 50 experts, most of them at universities, under the direction of Daniel W. Lozier, a research mathematician at NIST. The work was funded by a grant under the National Science Foundation's KDI program.

Lozier observes that "one of the things that is typical of mathematics, perhaps setting it apart from a lot of other disciplines, is that mathematical facts don't get superseded—they get added onto. So virtually everything that's in the old handbook is still relevant and still being used. That's why it's found on the desk of every working scientist today. But mathematics also does not stand still. … So in the time that has passed since this book was put together, there have been lots of developments in theory and computation and methods of applications of various functions … that need to be brought to the working public."

The goal of the DLMF Web site, according to Lozier, is "to make available to the working scientist or to the general public a place where they can get authoritative, validated information about these functions, in a form that allows them to immediately make use of it in all settings. For example, you might be writing a paper, in which you're using some of these functions. You may want to actually download from the Web site the representation of these functions that is encoded in the Web site—because the encoding that's in the Web site can also be used in word processors, especially specialized word processors that are used in science. Or they can be imported into computing systems, like Maple and Mathematica, which are technical computing systems that are used by engineers and scientists to do calculations, symbolically or numerically."

Both Lozier and Ronald F. Boisvert, director of the Mathematical and Computational Sciences Division at NIST's Information Technology Laboratory, say that NSF support through the KDI grant had been crucial to carrying out the DLMF project. "It would have been impossible to do without the KDI grant, because what in fact the KDI grant actually paid for is the work of people outside of NIST, to produce the technical material that's the substance of the DLMF," Boisvert says. "NIST staff are contributing by actually organizing the effort and producing the Web site—doing editing and that sort of thing. NIST itself just doesn't have the expertise in all of these wide varieties of functions."

Boisvert adds that "for several years we were working on selling this project. And it had good support inside [NIST]. But we really needed the funding from the KDI program to make it happen."

Lozier says he believes that the involvement of NIST and NSF in developing the new digital library is fully justified because the project will provide crucial support for scientists and engineers throughout the country. "It's really like infrastructure development—it's like building roads or ports or communications systems. This is providing information that's needed for the general commerce of the nation, but that can't be provided by anyone other than the government."

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