Lecture to the
                    Washington-Baltimore Section of the
              Society for Industrial and Applied Mathematics
     
                  Wednesday, November 9, 2005, 8:30 p.m.
           Johns Hopkins University, Homewood Campus, Baltimore
     
                           Dr. Daniel W. Lozier
             Mathematical and Computational Sciences Division
              National Institute of Standards and Technology
                        Gaithersburg, MD 20899-8910
     
                   MATH ON THE WEB AND THE DLMF PROJECT
     
     The Web has had a tremendous impact in many areas of modern life.
     An example is the ability to search for very detailed
     information, such as a place to buy parts for a home appliance
     and instructions for installing them. A corresponding impact in
     science is the ability to locate and print published papers as
     well as ephemera such as unpublished manuscripts, working papers,
     and supporting data. In mathematics we can look forward to a
     future in which specific formulas and theorems are located
     quickly and easily, and in which effective tools exist for
     incorporating them accurately and conveniently into papers and
     computer algebra systems. This talk will begin by surveying
     representative impacts that are beginning to emerge in
     mathematics, such as the World Digital Mathematics Library, and
     will continue by describing an ongoing series of conferences on
     Mathematical Knowledge Management. The work reported in these
     conferences is dedicated to developing the future outlined above.
     
     Then the talk will turn to a description of a large and complex
     project that is constructing a Digital Library of Mathematical
     Functions. The DLMF will include a free public Web site,
     maintained and disseminated by the National Institute of
     Standards and Technology. It will provide selected and validated
     properties of special functions together with advanced graphics
     and a search engine. The capabilities of the current Web site
     will be demonstrated.
     
     In addition to the Web site, a 1000-page printed handbook will be
     published and marketed commercially. The mathematical content and
     presentational style of the Web site and handbook is patterned
     after the widely used Handbook of Mathematical Functions, edited
     by Abramowitz and Stegun. The Web site is not just a copy of the
     handbook; it is a laboratory for research into the dynamic
     delivery of serious mathematics to advanced users. The goal is to
     provide unrestricted electronic access to an important body of
     mathematical knowledge, together with effective tools for
     utilizing the knowledge.
     
     The DLMF is being constructed under the leadership and with the
     financial support of the National Institute of Standards and
     Technology. External funding has been supplied by the National
     Science Foundation. Currently it is in the final stages of
     preparation for public release in 2006.