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Statements of Interest

April 26-27, 2004

**Jonathan
M. Borwein **(Computer
Science Faculty, Dalhousie University) http://www.cs.dal.ca/~jborwein/

I have two major areas of interest.

First, my previous (www.colab.sfu.ca, www.cecm.sfu.ca) and present (www.cs.dal.ca/ddrive) research Labs rely heavily on internet based tools and resources.

Second, as chair of the IMU committee on electronic matters (www.ceic.math.ca), I am tasked with advising and assisting the international mathematical community on such matters. In particular, I am concerned in federated searching and in digital mathematics libraries.

**Drew
Burton** (Mathematical Reviews Office, American
Mathematical Society.) drb@ams.org

I am a long-term manager of the computing group at the Mathematical Reviews office of the American Mathematical Society. I am essentially the product manager for MathSciNet.

MathSciNet is widely used to search the mathematical literature. The AMS is constantly looking for ways to better serve the mathematical community.

Much of the power of the MathSciNet interface is based on our decades-old devotion to carefully maintained and well structured data. We hold great hope that developments in XML and related technologies will provide tools that will improve MathSciNet.

**Su-Shing
Chen** (Department of Computer & Information Science
& Engineering, University of Florida) suchen@cise.ufl.edu

I am interested in searching mathematics in two aspects: to improve the understanding and research on mathematics as a mathematician and to develop novel search algorithms/protocols/architectures for mathematics as a computer scientist.

My recent research has been bioinformatics, applied mathematics to science and engineering. So I am also interested in novel reasoning/searching to enhance interdisciplinary research.

**Thomas
Fischer** (Metadata and Databases, Lower Saxony
State and University Library and Niedersächsische Staats- und
Universitätsbibliothek, Historisches Gebäude)

I
am working at the State and University Library Göttingen, the
central German library for pure mathematics. Apart from books
we collect mathematics in digital form:

- as retrodigitized images of printed books and articles (over
1 million pages),

- as born digital material, e.g. electronic theses and other
publications,

- as links to websites in our subject gateways (e.g. www.MathGuide.de).

We rely on metadata to organize this material, and obviously for all this searching in different forms is relevant. For the digitized printed versions, recognition of characters, structure and formulas will be useful, for digital material extraction of metadata, classification and probably formula processing could make access much more efficient. Finally, these techniques could be used for harvesting mathematics from the Web. The ultimate goal of a World Digital Mathematics Library will require advanced methods of searching in all these directions to make the material readily available.

**Gerry
Grenier** (Staff Director, Publishing Technologies,
IEEE, Inc.) g.grenier@ieee.org

I direct the creation and operation of IEEEXplore, the IEEE digital library (http://ieeexplore.ieee.org). Over one million peer reviewed journal and conference papers in electrical engineering and computer science are available via subscription through IEEE Xplore.

I am interested in understanding the technical and social challenges of searching math on the web. Questions that I have include: a. What will authors need to provide? Will I need to educate the authoring community? Will I need to develop/provide authoring tools for authors to provide a more search-friendly math syntax? Currently the author community is TeX centric. b. What changes will I need to make in my search engine indexing? I currently use Verity K2 to provide search functionality and would like to discuss how an end user can construct and submit effective queries. c.What value will math searching have to an end-user? A naive question perhaps but one that we should answer nevertheless. We should set clear, understandable expectations.

I hope that this meeting will serve to create a community of interest that will influence W3C and the search engine community. Toward that end we should discuss a sustainability plan for the group.

**Patrick Ion** (Mathematical
Reviews, American Mathematical Society.) ion@ams.org

As an Associate Editor of Math Reviews (MR), I've selected, classified and edited reviews of many mathematical papers. Since starting at MR I've been wondering about how to find the mathematics there, as opposed to just scanning text for substrings. Though in the early days when the glib answer was "use Prolog", there's actually been no progress in this, as far as I can see.

- With facilitation provided by the new XML markup styles, can one prepare new documents where the math is easier to find, and can one expose new views of older material by retrofitting such markup?
- Is the statistical text searching provided by, say, Google, all we need to help navigate the literature, when combined with the domain expertise of specialist users?
- Is the traditional text searching and attractive Web interface to an expanded form of the MR database provided by MathSciNet all mathematics and science can use?
- Do the variations of notation and notational styles over mathematics and science pose real obstacles to wide applications of particular techniques?
- Are there essential human limitations at work here?

I chaired or co-chaired the W3C Math Working Group 1998-2003. The WG disbanded in 2003 having fulfilled its charter, to be succeeded by the new W3C Math Interest Group. The Math WG's primary product, the MathML specification, of which I was also an author and an editor, is an XML markup language precisely intended to bring the documents of science within the purview of tools developed in more general contexts: business, publishing, computer algebra. There may be special techniques needed to provide searching of mathematical formalism, but there should also be the chance to avoid treating mathematical (or scientific) material as penalty copy.

- What are the algorithmic opportunites provided by the new mathematical notation explicitly based on decorated rooted planar trees?
- How applicable are the XML searching tools being developed in the wider commercial environment to scientific text?
- Can more effective communication of mathematical semantics be realized with the new markup and internet protocols?

Mathematical knowledge management is a general rubric that can be thought to include the capture and encoding of mathematical knowledge, consideration of its presentation, communication and dissemination, and concern over its authentication and justification, discovery and application. Everything just mentioned is undergoing changes as a result of the use of computers and the Web. I've been involved with an early prototype portal to mathematics in the AMS Math on the Web pages.

- Do the changes mean a shift in the nature of mathematical knowledge?
- Will this change the way mathematics is to be deployed in science and technology?
- Does this have significant impact on the institutions of science now, in particular on scientific publishing?
- Or will the realities of the business of publishing determine the available answers for mathematics?

All these questions seem to me relevant to the meaning and implementation of "the searching of mathematics".

**Nigel
Kerr** (JSTOR) nigelk@jstor.org

I am interested most in what needs for math searching (and display, additionally) JSTOR (http://www.jstor.org/) could be providing for what benefits. Mathematical expressions in JSTOR are presently somewhat less than accessible by our present search facility (sub-optimal TeX fed to a search engine we are increasingly unhappy). What could JSTOR be doing differently, how could JSTOR measure success and impact of the different options, how would these strategies for math help or affect our other need for search and display of other markup for other communities (chemistry and biology, largely)?

**Greg
Langmead** (Research and Development, Design Science,
Inc.) gregl@dessci.com

As a creator of mathematical authoring tools at Design Science, I am interested in how the preparation of documents can be enhanced to meet the needs of publishers and digital librarians, especially in the area of searching. I am also interested in controlled vocabularies and metadata as carriers of information that cannot be recovered from raw text and MathML.

As a mathematician, I am interested in learning about the strides being made in storing and finding scientific literature.

**Lori
Lorigo** (Department of Computer Science, Cornell
University) lolorigo@cs.cornell.edu

My interest in search for mathematics is focused on enabling users to find and organize relevant mathematical content in online collections of mathematics. My background includes formal methods and automated theorem prover development, leading to the development of a digital library of formal mathematics. I am interested primarily in the field of information science, and am looking at parallels and differences between more general information retrieval techniques, and the challenges, or benefits imposed by such tasks in the mathematics domain, keeping at the forefront the interactions that users will have. I am also very interested in MathML.

**Robert
Miner** (W3C Math Interest Group Co-Chair, Design
Science, Inc. "How Science Communicates") RobertM@dessci.com
www.dessci.com

Slides:
html

My interest in searching mathematics has three sources. First, I believe that MathML has the potential to make math searching more technically feasible. I am the principal investigator for a National Science Digital Library grant to explore MathML-based algorithms to enhance math searching. This workshop is being funded as part of that project.

Second, searching, knowledge management and the semantic Web are active areas of research and development, and I believe that work being done in these areas can be profitably applied to mathematics. In my role as co-chair of the W3C Math Interest Group and an editor of the MathML Recommendation, I am interested in learning if there is a facilitating role the Math Interest Group can play, by acting as liason with other W3C efforts, or by providing a neutral forum for standards activity.

Thirdly, I think that broad business trends toward XML and cross-media publishing have created a window of opportunity during which organizations are establishing workflows and devising best practices, including those that might enhance math searching. In my role as Director of New Product Development for Design Science, I am interested in learning about emerging software and information management needs, and sustainable business models for meeting them.

**Elizabeth
B. Porter** (Mathsoft Engineering & Education,
Inc.) bporter@mathsoft.com
http://education.mathsoft.com

My interest in coming to this conference is to learn the state of knowledge and development in searching math on the Web, and to contribute to the community's understanding of the constraints and challenges associated with representing math for this purpose. Though my background is in education and, in particular, development of math curriculum using technology, my recent work involves contributing to the team of developers and managers at Mathsoft developing XML representations of Mathcad's math and units architecture. Through this conference I hope to understand what others in this small community of researchers, academic and corporate, are looking for in math searching technology, and to share what my colleagues and I have discovered in coming up with our own searchable format for math.

**Masakazu
Suzuki **(Faculty of Mathematics, Kyushu University)
suzuki@math.kyushu-u.ac.jp
http://www.math.kyushu-u.ac.jp/~suzuki/

Slides: pdf

The main subject of my resarch interest is currently the development of practicaly usable software to read printed mathematical documents and to convert the results into digitized formats treatable by machine. I am also interested in knowing if there is any possibility for (near) future computer to judge, for example, the equivalence or some similarity of two theorems formulated differently?

**Paul
Topping** (Design Science, Inc.) pault@dessci.com

As president of Design Science, makers of math and MathML tools to authors, publishers, and readers, my interest is mostly in learning more about what other participants desire in applications of math searching technology within education, research, and industry.

As a computer scientist, I also have interest in the algorithms and techniques that are used in math metadata, searching, and categorization.

My company's NSF grant is funding this meeting.

**Michael
Trott** (Wolfram Research, Inc.) mtrott@wolfram.com

My interest in searching of mathematics arises from my work on the Wolfram Functions site http://functions.wolfram.com. This collection currently contains 80,000 mathematical formulas and will increase to more than one million formulas over the next few years. Despite the strict hierarchical ordering used on the site, a search capability based on the mathematical content of the identities is needed for advanced human calculations and and mechanized computer mathematics.

**Stephen
Watt** (University of Western Ontario) watt@scl.csd.uwo.ca
http://www.csd.uwo.ca/~watt

My interests related to this meeting lie in the areas of computer algebra systems and digital mathematical documents. I have been involved as one of the principals in the creation of the Maple and Axiom computer algebra systems, and as one of the authors of the MathML specification.

I am interested in searching of mathematics for several reasons, including document retrieval, mathematical software documentation and databases for mathematical handwriting recognition.