Stam’s Identities Collection: A Case Study for Math Knowledge Bases

In the frame of the work of the Working Group “Global Digital Mathematical Library”, Jim Pitman proposed Aart Stam’s collection of combinatorial identities as a benchmark for “digitizing” mathematical knowledge. This collection seems to be a challenge for “digitization” because of its size (1300 pages in a .pdf file) and because of the fact that, for the most part, it is hand-written. However, after an in-depth analysis, it turns out that the real challenges are of mathematical and logical nature. In this talk we discuss what digitization of such a piece of mathematics means and report on various tools that may help in this endeavor. The tools range from technical tools for typing formulae all the way to sophisticated algebraic and reasoning algorithms. The experiments for applying these tools to Stam’s collection are currently carried out by two of the working groups at RISC.

The work described in this talk is carried out in a team at RISC consisting of B. Buchberger, C. Koutschan, A. Maletzky, P. Paule, C. Raab, S. Radu, C. Schneider, and W. Windsteiger.

Authors and Affiliations

1. Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Linz, Austria

   Bruno Buchberger

Corresponding author

Correspondence to Bruno Buchberger .

Editors and Affiliations

1. Universität Kaiserslautern , Kaiserslautern, Germany

   Gert-Martin Greuel

2. Zuse Institute Berlin , Berlin, Germany

   Thorsten Koch

3. Johannes Kepler University Linz , Hagenberg, Austria

   Peter Paule

4. University of Notre Dame , Notre Dame, Indiana, USA

   Andrew Sommese

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