Speaker:

Daniel W Lozier
Applied and Computational Mathematics Division
National Institute of Standards and Technology
Gaithersburg, MD 20899-8910

Title:

MKM and the NIST Digital Library of Mathematical Functions

Abstract:

Universal access to highly specialized subject matter has been made
possible, in principle, by the Internet and World Wide Web. For
example, scientific articles and books are no longer published only in
hardcopy, and older material is in the process of being digitized and
collected into "digital" libraries. But the concept of a digital
library extends far beyond the traditional role of a research library
providing access to published literature. In mathematics, a digital
library can be envisioned that acts like an online handbook, providing
a resource for locating mathematical facts together with the means to
adapt the facts for use in other computerized settings, such as
software packages or theorem-proving systems.

Many issues need to be considered to realize the full potential of
mathematical digital libraries. These include issues related to
encoding, representing, manipulating, transforming, searching,
visualizing, displaying and printing mathematical data. But what is
mathematical data? What form should the data take? How can we validate
data, and after we have transformed it, how can we be sure it remains
valid? These questions push MKM research in the direction of formal
mathematics.

As a practical example of a mathematical digital library, a major new
mathematics repository is being constructed to meet 21st century needs
for reliable reference information about elementary and special
functions. It will cover the basic properties of many functions
commonly used in engineering, physics and statistics. Drawing on the
mathematical knowledge that is being encoded in the repository,
automated procedures for generating a Web interface are being
developed. The interface will have facilities to search for text and
equations, download formulas into word processors and computer algebra
systems, display 3D still graphics and animations, manipulate (zoom
and rotate) 3D surfaces of functions, link to available Math Reviews
and full texts of references, and link to sources of relevant
mathematical software.

The Digital Library of Mathematical Functions (DLMF) consists of this
repository and associated software tools. Within the next 12 to 18
months NIST will release two products for the general scientific
public.  The first is a free Web site, to be disseminated from a NIST
server as part of its program to provide standard scientific reference
information. The second is a 1000-page handbook, to be printed and
marketed under license to NIST by a qualified mathematics publisher.

In this talk the DLMF project will be described and the Web site
demonstrated. The current implementation is based on current standards
and software, such as AMS-LaTeX and VRML, but procedures are being
developed to employ emerging standards. For example, instead of
pasting in images of equations we can now generate presentation
MathML.  Experiments with encoding limited equation semantics, using
content MathML, have been encouraging. Furthermore, with a view toward
future mathematical digital library activities at NIST, we are
tracking current research in mathematical knowledge management.