Nov 9, 2005 SIAM Johns Hopkins University 1

Math on the Weband the DLMF Project

Daniel W LozierNational Institute of Standards and

TechnologyGaithersburg, MD 20899-8910 USA

lozier@nist.govhttp://dlmf.nist.gov

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Outline

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

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Online Access to Papers

• Author’s home pages• Department websites• Preprint servers• Professional society

websites• University libraries

• Journal websites • Commercial

clearinghouses• MathSciNet• Zentralblatt MATH

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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.wdml.org/

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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, 2003-2004Funded by NSF

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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)

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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

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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

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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.

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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. FarmerACM SIGSAM Bulletin 38(2), June 2004, pp. 47-52

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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

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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)

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The DLMF: What is the Model?GPO (1964) Dover (1965)

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GPO & Dover Impacts

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

Citing Journals: Physics, engineering, math, stat

Citations:

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DLMF Approach

Math Database + Special Software Tools

DLMF HandbookDLMF Web Site

DLMF CD-ROMOther DLMF Documents (future)

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Personnel

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

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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

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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

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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

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Idea of the Proof

• Construct 4th order homogeneous ODE for LHS (differentiate modified Bessel ODE, annihilate inhomogeneous term, substitute ½)

• 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)

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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