1. MathML and Digital Libraries
Timothy W. Cole
University of Illinois at Urbana-Champaign
Workshop on International Scientific Data, Standards & Digital JCDL 2005, Denver, CO

2. University of Illinois at UC
Digital Typography?
Typography, when considered “as the servant of mathematics,” should have as a goal “to communicate mathematics effectively by making it possible to publish mathematical papers and books of high quality, without excessive cost.”
-- Donald Knuth (inventor of TEX), 1978
Where do we go from TEX?
11 June 2005
University of Illinois at UC

3. University of Illinois at UC
MathML Antecedents
HTML Math (Dave Raggett, 1994; HTML 3.0/3.2)
Limited functionality
Community preference to keep HTML simple, generic
SGML ISO (1994) Mathematics DTD
Exclusively presentational
Not as sophisticated as MathML
W3C Math Working Group Formed 1997
MathML 1.0 released 1998
MathML 2.0 released 2001
11 June 2005
University of Illinois at UC

4. MathML – Presentation Markup
Used to describe the layout structure of mathematical notation – focus on visual constructs (about 30 elements). Includes:
Token elements – primarily PCData content models
Layout Schemata, for building expressions – element content models
Semantic hints via invisible characters are encouraged
<math xmlns=' <mrow> <msqrt> <mi>z</mi> </msqrt> <mo>=</mo> <msup> <mi>z</mi> <mfrac><mn>1</mn><mn>2</mn></mfrac> </msup> </mrow>
</math>
11 June 2005
University of Illinois at UC

5. MathML – Content (Semantic) Markup
Intended to support encoding of the underlying mathematical structure of an expression, rather than any particular rendering for the expression – about 120 elements
Limited scope, designed to express “commonplace mathematical constructs,” i.e., through about first 2 years of college (calculus)
can be extended,e.g., through the use of OpenMath
<math xmlns='
<apply><eq/>
<apply><root/>
<degree><cn type='integer'>2</cn></degree><ci>z</ci></apply>
<apply><power/> <ci>z</ci><cn type='rational'>1<sep/>2</cn></apply>
</apply>
</math>
11 June 2005
University of Illinois at UC

6. Displaying MathML in Web Browsers
Mozilla / Netscape 7.x renders MathML natively
But not all elements supported, or supported well
Internet Explorer does not render MathML natively
But plug-ins available – TechExplorer, MathPlayer
Syntax for using MathML different between browsers
W3C provides XSLT that allows a page to viewable in both
Rendering quality also depends on fonts available
Thousands of code points have been added to Unicode
STIXFonts.org is creating more than 4,000 freely available new glyphs for these Unicode points (rest were pre-existing)
11 June 2005
University of Illinois at UC

7. Other Software Support for MathML (2004)
Editors: MathType + Word, Integre MathML Editor, SciWriter, MathFlow, Scientific Workplace, MathFlow + Epic/XMetaL, OpenOffice, others
Interactive Components: Techexplorer, WebEQ
TeX Converters: TeXML, Hermes, tex4ht, others
Computation: Maple, Mathematica, REDUCE, others
11 June 2005
University of Illinois at UC

8. University of Illinois at UC
Using MathML (as of 2004)
MathML incorporated into a number of document types:
Docbook, NIH Journal Archiving & Publishing, etc.
MathML is being used in STM publications :
In production: American Institute of Physics, US Patent Office
In pilot: Springer, Wiley, Marcel Dekker, Elsevier, others
MathML behind the scenes in e-Learning software:
Blackboard, WebCT, eCollege, Diploma.EDU, MapleTA, other
BUT adoption by author community limited to date
11 June 2005
University of Illinois at UC

9. Current Status & Open Issues
MathML 2.0 is stable, available, & in increasing use
Proving useful for many publication & educational applications
Tailored for use on the Web; interactivity demostrated
Commitment to stay open & maintain backward compatibility
Limitations, Issues, & Needs
Utility for research mathematics?
Use in / cross-walks with other Sci-Tech MLs
Low-level: fonts / glyphs, character entity definitions, …
Semantic utility not yet proven (being investigated): - Comparing MathML expressions for degree of equivalence - Searching by MathML expressions
11 June 2005
University of Illinois at UC

10. An Example: Wolfram Functions Website

11. MathML in Functions Site

12. University of Illinois at UC
But…
Rendering of MathML typically not exactly the same application to application
For most complex functions, MathML not enough – must augment with annotations meaningful to Mathematica
Applications still rely on something other than MathML for complex, behind the scenes functionality
No canonical forms – no accepted normalization rules
11 June 2005
University of Illinois at UC

13. Experiment: Using MathML to Link Literature
Hypotheses:
Readers of a journal article may want to know more about mathematical functions used in article … And vice-versa
Functions site keywords/phrases & MathML found in body of articles may be useful for linking, search & discovery
Approach:
Examine journal article testbed for presence of Functions site keywords; add links & terminology to article metadata
Extract selected MathML occurrences from article body; “normalize”; add to article metadata
11 June 2005
University of Illinois at UC

14. Article Testbed: Illinois DLI-I / D-Lib Test Suite
Funded under DLI-I (NSF, DARPA, & NASA) Continued under CNRI’s D-Lib Test Suite
Featured:
Multi-publisher, Markup-Based Full-Text Journal Testbed.
Studies of Processing, Indexing, Normalization, Retrieval, Rendering, Linking & End-User Searching Needs.
Testbed contains 75,000+ Articles from 60 Journal Titles
Received as SGML (various DTDs); converted to XML
Content from AIP, APS, ASCE, IEE, ASM, ACM, Elsevier
Additional support from IEEE, NRL, NTT Learning Systems
11 June 2005
University of Illinois at UC

15. University of Illinois at UC
Searching for Occurrences of Functions Site Metadata Terms in Article Testbed
Functions Site: 83,000 pages containing keywords in HTML <meta> elements
Approximately 7,500 unique keywords
Not all keywords useful for full-text search
Eliminated numerals, Mathematica expressions, single word phrases, phrases containing selected words
About 1,000 keywords left after automated filtering
367 of these keywords appear in journal article testbed
44,000 articles contain at least one keyword
On average each of those 44,000 contain 2 keywords
11 June 2005
University of Illinois at UC

16. Issues in Using Functions Keywords/phrases for Characterizing Articles
Vocabulary switching
Keywords in mathematics, not necessarily terms used in physics, electrical engineering, & computer science
Meaning of words in full-text less precise
Synonyms, less specific use, etc.
Context – same descriptive keywords may map to many different branches of Functions site
E.g., 300 occurrences of “q-series” in Functions site; which are relevant to 18 articles containing this keyword?
Use hierarchical tree of Functions Site to place user in reasonable proximity
11 June 2005
University of Illinois at UC

17. Using MathML Found in Article Body
2.5 million occurrences of MathML in testbed, but most not useful for searching & linking
MathML used for greek characters in text
Many instances short, inline fragments
Quality – many instances can’t be parsed by Mathematica
Criteria
Explicitly equations (block display format)
Minimum length, 200 bytes
Accepted by Mathematica kernel
About 3% of occurrences meet criteria
11 June 2005
University of Illinois at UC

18. Observations from this early experiment
Currently, text cues in articles seem more effective for linking than mathematical cues
Mathematics embedded in articles needs lots of processing to begin to be useful for discovery, linking, …
We need to understand mathematical equivalents of language grammar, noun-phrases, …
11 June 2005
University of Illinois at UC

19. Searching Mathematics Directly

20. Search Results

21. More Like This One

22. University of Illinois at UC
Links
Wolfram Functions Website
W3C Math Working Group
Design Science
Enhancing the Searching of Mathematics (IMA Hot Topic)
11 June 2005
University of Illinois at UC