IFIP WG 2.5 Project 78 Mathematical Knowledge Management Modern computing and communication facilities have transformed the way in which knowledge is produced, managed, exchanged, and consumed. Nevertheless, some of these processes remain challenging when the information is highly mathematical in nature. New opportunities and demands in science and engineering are resulting in pressures to improve our ability to represent complex mathematical information on computers, to efficiently find it, to preserve its semantics during interchange, and to exploit it to efficiently generate yet new knowledge. A growing research community is emerging around these issues. The topics considered include * Computer representations of mathematical data * Presentation of math on the Web * MathML, OpenMath, and related standards * Mathematical digital libraries and repositories * Authoring languages and tools * Search and retrieval of highly mathematical content * Data mining and discovery in mathematical databases * Integration with computer algebra systems and automated theorem proving * Collaboration tools for mathematics * Tools for mathematical workflows Leuven 2010: ============ Ron Boisvert made a live presentation of the in May 2010 released "NIST Digital Library of Mathematical Functions". http://dlmf.nist.gov/ Boulder 2011: ============= Ron Boisvert presented a "LaTeX to XML converter" found in http://dlmf.nist.gov/LaTeXML Santander 2012: =============== NIST is still very active in this area. Boisvert presented the project description above. Shanghai 2013: ============== Ron Boisvert briefed the group on current developments in the representation and display of mathematics on the web. An important positive development is the inclusion of MathML, W3C's XML-based standard for math markup as part of HTML5, the current proposed next version of the HTML standard. The adoption of this standard by browsers would greatly improve upon the current state, in which only a few browsers provide native support for MathML. For example, Internet Explorer does not support MathML, although a plugin is available. Firefox indicates that they intend to support this standard. In spite of this development, universal support for math on the web remains in jeopardy. Browser developers are far from universal in their committment to actually implement the MathML part of the standard. In particular, Microsoft is not expected to do so. Ironically, one of the reasons for the reluctance by developers to invest the effort to implement MathML is the success of MathJax. MathJax is a javascript engine for displaying mathematics (expressed as TeX or MathML) that works in all browsers. MathJax is a project of the MathJax Consortium, a joint venture of the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM). As such, it is not a standards-based solution, relying on community support for its development, which will need to be active and continuous as browsers proliferate. Vienna 2014: ============ Ford will provide a report on recent developments related to this project including a discussion of how browsers such as Firefox and InternetExplorer are supporting this effort. Halifax 2015: ============= Report by Boisvert: In June 2015 MathML 3.0 was approved as an ISO standard. See http://www.w3.org/2015/06/mathmlpas.html.en This is good news, as it becomes an actual "standard" as opposed to merely a "recommendation," which gives the effort more legitimacy, and could result in more pressure to implement it as part of various accessibility efforts or regulations. Browser developers may not feel so susceptible to that pressure, however. The situation there is pretty much the same as last year: Firefox and MathJax continue their development and improvements; Chrome (Google)and Safari (Apple) continue to ignore MathML; they may feel that MathJax solves the problem. The W3C Math WG recently initiated an effort to get a conversation going with browser vendors. The idea was to understand the hurdles in implementation, with the aim of explaining, or even evolving the specification to ease implementation. Firefox and the IE have indicated interest, though Google (Chrome) and Apple (Safari) will probably not participate. Sydney, 2018: ============= Reported by Boisvert About six years ago, the International Mathematical Union spawned a project to create what has become known as the Global Digital Mathematics Library (GDML) [1,2,3]. With a very grand vision of free digital access to all mathematical literature, the project has a very lofty goal. This goal was echoed in a study sponsored by the US National Academies [4]. Current members of that working group are: Thierry Bouche, Institut Fourier & Cellule MathDoc, Grenoble, France Bruno Buchberger, RISC, Hagenberg/Linz, Austria Patrick Ion, Mathematical Reviews/AMS, Ann Arbor, MI, US Michael Kohlhase, Jacobs University, Bremen, Germany Jim Pitman, University of California, Berkeley, CA, US Olaf Teschke, zbMATH/FIZ, Berlin, Germany Stephen Watt, University of Western Ontario, London, ON, Canada Eric Weisstein, Wolfram Research, McAllen, TX, US We at NIST have interacted with Ion, Kohlhase, Pitman and Watt on the Digital Library of Mathematical Functions (DLMF) project [5]. One of the issues that has arisen is the interoperability of digital systems for special functions. Among these are: the DLMF, the Wolfram Functions site [6], Mathematica, Maple, Matlab and NAG. It is observed that the definitions (including specific scalings) used for special functions can differ among these systems. To try to understand the extent of this problem, the GDML has begun a project called the Special Functions Concordance. It's goal will be to document, in detail the differences in the definitions/implementations used by these systems. Ultimately, a formal machine-readable dictionary of special functions could be developed (the DLMF has been suggested as the source/repository), which could assist in the automated interchange of information between such systems. NIST is participating. [1] https://www.mathunion.org/ceic [2] https://blog.wias-berlin.de/imu-icm-panel-wdml/ [3] https://en.wikipedia.org/wiki/Global_Digital_Mathematics_Library [4] https://www.nap.edu/catalog/18619/developing-a-21st-century-global-library-for-mathematics-research [5] http://dlmf.nist.gov/ [6] http://functions.wolfram.com/ Amsterdam, 2023: ================ Reported by Boisvert NIST remains involved with the mathematical knowledge management (MKM) community. An important contribution is the LaTeXML system created by Bruce Miller for converting LaTeX into various web-based formats. https://math.nist.gov/~BMiller/LaTeXML/ LaTeXML emulates TeX as far as possible (in Perl), converting the TEX or (LATEX) document into LATExml’s XML format. That format is modelled on the typical document structure found in LATEX, and inspired by HTML, MathML, OpenMath and others. That abstract document is then further transformed into HTML of various flavors, with MathML and SVG, or into JATS or ePub. While originally created for use in the NIST Digital Library of Mathematical Functions project, https://dlmf.nist.gov/, LaTeXML is freely distributed, and has found a good deal of use within the MKM community. Of great need are corpora of well-marked-up technical documents to allow researchers to experiment with tools (e.g., machine-learning-based) to find, understand and reuse information with significant mathematical content.To that end, Miller and colleagues has been applying LaTeXML tool convert the massive corpus at arXiv.org. Such conversion is not easy, since LaTeX (and TeX) contain only the bare minimum of semantic-preserving markup. Nevertheless, to date, LaTeXML has converted the entire current 1.97M-document arXiv.org corpus into HTML+MathML with over 75% success rate (documents producing, at worst, warnings). A collection of data derived from these for use by the MKM community has been made publically available, https://corpora.mathweb.org/. The NIST Digital Library of Mathematical Functions, https://dlmf.nist.gov/ continues to be maintained and updated by NIST. Quarterly updates are regularly applied to fix errors, make clarifications, and to add new material to existing chapters. A major new chapter on Orthogonal Polynomials of Several Variables should be released during 2023.