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
1,000page 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mathematical facts don't get superseded—they get added onto.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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