# Presentation: 285583

## Math on the Weband the DLMF Project

- Daniel W Lozier
- National Institute of Standards and Technology
- Gaithersburg, MD 20899-8910 USA
- _[lozier@nist.gov](mailto:lozier@nist.gov)_
- http://dlmf.nist.gov

- SIAM Johns Hopkins University

- Nov 9, 2005

## Outline

- Introduction
- Some *Math on the Web* issues
- The DLMF Project
- DLMF website demonstration
- DLMF search demonstration
- Concluding remarks and future work

- SIAM Johns Hopkins University

- Nov 9, 2005

## Online Access to Papers

- Author’s home pages
- Department websites
- Preprint servers
- Professional society websites
- University libraries

- Journal websites
- Commercial clearinghouses
- MathSciNet
- Zentralblatt MATH

- SIAM Johns Hopkins University

- Nov 9, 2005

## So What’s the Problem?And What’s the Solution?

- Only recently have papers begun to exist electronically. And there are too many different ways to access the electronic ones. *We need a standard way to access all papers electronically*.
- WDML (the World Digital Mathematics Library) to the rescue! (well, it’s a possibility, anyway)
- _[http://www.](http://www.wdml.org/)__[wdml](http://www.wdml.org/)__[.org/](http://www.wdml.org/)_

- SIAM Johns Hopkins University

- Nov 9, 2005

## WDML Vision

-    In light of mathematicians’ reliance on their discipline’s rich published heritage and the key role of mathematics in enabling other scientific disciplines, *the DML strives to make the entirety of past mathematics scholarship available online, at reasonable cost, in the form of an authoritative and enduring digital collection*, developed and curated by a network of institutions.
- Cornell University DML Project, 2003-2004
- Funded by NSF

- SIAM Johns Hopkins University

- Nov 9, 2005

## Selected Retrodigitization Projects

- JSTOR (US, 30 math/stat journals)
- NUMDAM (France, 10 math journals)
- GDZ (Germany, 38 math journals)
- EMANI (105 math journals from 4 libraries in China, Germany, US, France; German-Russian initiative in progress for ~70 Russian journals)

- SIAM Johns Hopkins University

- Nov 9, 2005

## For Further Information...

- Allyn Jackson*, The Digital Mathematics Library*, Notices of the AMS, Sep 2003, pp. 918-923
- John Ball, *The IMU and You*, Notices of the AMS, Nov 2005, pp. 1208-1210

- SIAM Johns Hopkins University

- Nov 9, 2005

## A (Much) Bigger View

- MK “Mathematical Knowledge”
- Not just traditional math
- Procedural as well as declarative
- Produced as much by nonmathematicians as mathematicians
- Example: software development
- Not always well communicated in journals and textbooks

- SIAM Johns Hopkins University

- Nov 9, 2005

## How Should MK Be Managed?

- We want to use computers, Internet, Web to:
- store MK (how to encode?)
- display MK (with which browser?)
- transform MK (by computer algebra?)
- locate MK (with a search engine?)
- identify MK (by URLs?)
- etc.

- SIAM Johns Hopkins University

- Nov 9, 2005

## MK Management

-    MKM is a *new interdisciplinary field* of research involving *math, computer science, library science, and scientific publishing*. Its objective is to develop new and better ways of managing MK using sophisticated software tools.
- William M. Farmer
- ACM SIGSAM Bulletin 38(2), June 2004, pp. 47-52

- SIAM Johns Hopkins University

- Nov 9, 2005

## MKM Kickoff

- Conference:  September 2001, Hagenburg, Austria
- Special Issue: Ann. Math and AI 38, May 2003
- 11 papers on, e.g., formula presentation, semantic markup, authoring systems, formal math systems, theorem provers, new knowledge libraries
- Includes 2 papers on DLMF and 1 on EMANI

- SIAM Johns Hopkins University

- Nov 9, 2005

## Major MKM Events To Date

- Hagenburg (2001)
- Bertinoro (2003)
- Bialystok (2004)
- Bremen (2005)
- England (2006)

- McMaster U (2002)
- Herriot-Watt U (2003)
- JMM Phoenix (2004)

- SIAM Johns Hopkins University

- Nov 9, 2005

## The DLMF: What is the Model?

- GPO (1964)

- Dover (1965)

- SIAM Johns Hopkins University

- Nov 9, 2005

## GPO & Dover Impacts

- Sales to Date:  >150,000 (GPO), >600,000 (Dover)

- Citing Journals:  Physics, engineering, math, stat

- Citations:

- SIAM Johns Hopkins University

- Nov 9, 2005

- SIAM Johns Hopkins University

- Nov 9, 2005

## DLMF Approach

- Math Database + Special Software Tools
- DLMF Handbook
- DLMF Web Site
- DLMF CD-ROM
- Other DLMF Documents (future)

- SIAM Johns Hopkins University

- Nov 9, 2005

## Personnel

- 4 principal editors
- 10 associate editors
- 35 authors
- 25 validators
- 15 NIST staff

- SIAM Johns Hopkins University

- Nov 9, 2005

## Web Demonstration

- Features
- Strong coverage of special functions
- References to proofs for every equation
- Links to online references, reviews, constants, software, ...
- State-of-the-art 2D and 3D graphics
- (Math-aware search)
- _[Demonstration](file:///D:/xdlmf/snapshot-2005-10-07/index.html)_

- SIAM Johns Hopkins University

- Nov 9, 2005

## Search Demonstration

- Features
- Accepts math and text queries (with “wild cards”)
- Understands DLMF, Maple, Mathematica names
- Targets are equations, figures, tables, sections
- Still very much an object of R&D
- _[Demonstration](http://localhost/dlmf/search.html)_

- SIAM Johns Hopkins University

- Nov 9, 2005

## Computer Algebra

- DLMF chapter provides basic algorithms, references to additional algorithms, links to software
- A few CA proofs have been provided for DLMF equations – an example follows

- SIAM Johns Hopkins University

- Nov 9, 2005

## Slide 21

- SIAM Johns Hopkins University

- Nov 9, 2005

## Idea of the Proof

- Construct 4th order homogeneous ODE for LHS (differentiate modified Bessel ODE, annihilate inhomogeneous term, substitute 1⁄2)
- Construct general solution of 4th order ODE
- Develop a few terms of asymptotic expansions of the LHS and the 4th order ODE
- Match the first 4 coefficients (solve 4th order linear system)

- SIAM Johns Hopkins University

- Nov 9, 2005

## Slide 23

- SIAM Johns Hopkins University

- Nov 9, 2005

## Slide 24

- SIAM Johns Hopkins University

- Nov 9, 2005

## Future Directions

- (Complete basic DLMF content)
- (Publish DLMF book, release DLMF web site)
- Conduct research in MKM
*semantic math* (XML, MathML, ...)
*math search* (Xquery, Xpath, ...)
*active math* (tables, graphs & software “on demand”)
- Use DLMF as *research laboratory* for development, application, testing and evaluation of MKM in the field of special functions

- SIAM Johns Hopkins University

- Nov 9, 2005