Digitisation, Representation, and Formalisation Digital Libraries of Mathematics

  • Andrew A. Adams
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2594)


One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.


Digital Library Mathematical Knowledge Theorem Prove Computer Algebra System Mathematical Text 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AA01]
    M. Athale and R. Athale. Exchange of mathematical information on the web: Present and Future. In Buchberger and Caprotti [BC01].Google Scholar
  2. [APSC+01]
    A. Asperti, L. Padovani, C. Sacerdoti Coen, G. Ferruccio,, and I. Schena. Mathematical Knowledge Management in HELM. In Buchberger and Caprotti [BC01].Google Scholar
  3. [APSCS01]
    A. Asperti, L. Padovani, C. Sacerdoti Coen, and I. Schena. HELM and the Semantic Math-Web. Springer-Verlag LNCS 2152, 2001.zbMATHGoogle Scholar
  4. [AS72]
    M. Abramowitz and I. A. Stegun. Handbook of mathematical functions with formulas, graphs and mathematical tables. Dover, 1972.Google Scholar
  5. [AZ99]
    M. Aigner and G. M. Ziegler. Proofs from THE BOOK. Springer, 1999.Google Scholar
  6. [Bab23]
    C. Babbage. On the Theoretical Principles of the Machinery for Calculating Tables. Edin Phtl Jrl, 8:122–128, 1823.Google Scholar
  7. [BB+96]
    B. Barras, S. Boutin, et al. The Coq Proof Assistant Reference Manual (Version 6.1). Technical report, INRIA, 1996. Available on-line with Coq distribution from
  8. [BB01]
    P. Baumgartner and A. Blohm. Automated Deduction Techniques for the Management of Personal Documents (Extended Abstract). In Buchberger and Caprotti [BC01]Google Scholar
  9. [BC01]
    B. Buchberger and O. Caprotti, editors. MKM 2001 (First International Workshop on Mathematical Knowledge Management)., 2001.
  10. [Bor01]
    J. M. Borwein. The International Math Union’s Electronic Initiatives (Extended Abstract). In Buchberger and Caprotti [BC01].Google Scholar
  11. [CA+86]
    R. L. Constable, S. F. Allen, et al. Implementing Mathematics with the NuPrl Proof Development System. Prentice-Hall, 1986.Google Scholar
  12. [Dav01]
    J. Davenport. Mathematical Knowledge Representation (Extended Abstract). In Buchberger and Caprotti [BC01].Google Scholar
  13. [Dew00a]
    M. Dewar. OpenMath: An Overview. ACM SIGSAM Bulletin, 34(2):2–5, June 2000.CrossRefGoogle Scholar
  14. [Dew00b]
    M. Dewar. Special Issue on OPENMATH. ACM SIGSAM Bulletin, 34(2), June 2000.Google Scholar
  15. [Fro02]
    M. Froumentin. Mathematics on the Web with MathML., 2002.
  16. [FTBM96]
    R. Fateman, T. Tokuyasu, B. P. Berman, and N. Mitchell. Optical Character Recognition and Parsing of Typeset Mathematics. Journal of Visual Communication and Image Representation, 7(1):2–15, March 1996.CrossRefGoogle Scholar
  17. [GM93]
    M. J. C. Gordon and T. F. Melham, editors. Introduction to HOL. CUP, 1993.Google Scholar
  18. [Har71]
    M. Hart. Project gutenberg, 1971.
  19. [Har00]
    J. Harrison. Formal verification of floating point trigonometric functions. Springer-Verlag LNCS 1954, 2000.Google Scholar
  20. [JB01]
    M. Jones and N. Beagrie. Preservation Management of Digital Materials (A Handbook). The British Library, 2001.Google Scholar
  21. [Kea00]
    T. Kealey. More is less. Nature, 405(279), May 2000.Google Scholar
  22. [Knu79]
    D. Knuth. TEX and METAFONT: New directions in Typesetting. AMS and Digital Press, 1979.Google Scholar
  23. [Koh01]
    M. Kohlhase. OMDoc: Towards an Internet Standard for the Administration, Distribution and Teaching of Mathematical Knowledge. In J. A. Campbell and E. Roanes-Lozano, editors, Proceedings of Artificial Intelligence and Symbolic Computation 2000, pages 32–52. Springer LNCS 1930, 2001.zbMATHGoogle Scholar
  24. [Lam94]
    L. Lamport. LATEX: A Document Preparation System, 2/E. Addison Wesley, second edition, 1994.Google Scholar
  25. [Loz01]
    D. Lozier. The NIST Digital Library of Mathematical Functions Project. In Buchberger and Caprotti [BC01].Google Scholar
  26. [McC62]
    J. et al. McCarthy. LISP 1.5 Programmer’s Manual. MIT Press, 1962.Google Scholar
  27. [Mic01]
    G. O. Michler. How to Build a Prototype for a Distributed Mathematics Archive Library. In Buchberger and Caprotti [BC01].Google Scholar
  28. [ML84]
    P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, 1984.Google Scholar
  29. [Mos97]
    P. D. Mosses. CoFI: The Common Framework Initiative for Algebraic Specification and Development. pages 115–137. Springer LNCS 1214, 1997.Google Scholar
  30. [MY01]
    B. R. Miller and A. Youssef. Technical Aspects of the Digital Library of Mathematical Functions Dreams and Realities. In Buchberger and Caprotti [BC01].Google Scholar
  31. [Pau88]
    L. C. Paulson. The Foundation of a Generic Theorem Prover. J. Automated Reasoning, 5:363–396, 1988.MathSciNetCrossRefGoogle Scholar
  32. [SOR]
    N. Shankar, S. Owre, and J. M. Rushby. The PVS Proof Checker: A Reference Manual. Computer Science Lab, SRI International.Google Scholar
  33. [Try80]
    A. Trybulec. The Mizar Logic Information Language, volume 1 of Studies in Logic, Grammar and Rhetoric. Bialystok, 1980.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Andrew A. Adams
    • 1
  1. 1.School of Systems EngineeringThe University of ReadingUK

Personalised recommendations