MKM 2001 - Call for Papers

Mathematical Knowledge Management is an exciting new field in theintersection of mathematics and computer science.

We need efficient, new techniques - based on sophisticated formal mathematicsand software technology - for taking fruit of the enormous knowledge availablein current mathematical sources and for organizing mathematical knowledge in anew way.

The Workshop and the Special Issue should bring together mathresearchers, software developers, publishing companies, math organizations,and teachers for exchanging their views and approaches and for pushing thefield.

Whereas the workshop is designed to provide a forum for discussion andpresentation of early ideas, the special issue is a forum for polished,refereed papers in the area of mathematical knowledge management.
Participation and presentation of talks and papers is possible in both theworkshop and the special issue, jointly or independently.

Scope

Mathematical knowledge management is a new and exciting topic in theintersection of mathematics and computer science:

Currently much effort/money is spent for producing new mathematicalknowledge.
Very little effort/money is spent for improving the reliability andefficiency of tools for retrieving what is already known in mathematics.
Current techniques for mathematical knowledge retrieval are verycumbersome, unreliable and shockingly unsuccessful.

By the workshop and the subsequent special issue on mathematical knowledgemanagement we want to provide a forum for math researchers, system designers,publishing companies, math professional organizations, math research managers,etc. for presenting and discussing recent work in the

computer-supported management of mathematical knowledge.

(Note that, in order to achieve maximum focus for both the workshop and thespecial issue, "mathematical knowledge management" should be parsed as"(mathematical knowledge) management" and not as "mathematical (knowledgemanagement)". In other words, the scope of the workshop and the special issueis "the management of mathematical knowledge" and not "the mathematical theoryof general knowledge management"!)

Hence, in more detail, the scope of both the workshop and the special issue isdefined to be

early ideas, philosophy, opinions, strategical goals
formal languages, logical background
standards, representations, and translation between representations
algorithms, heuristics, innovative formal methods including theorem proving
existing and future tools, systems
organizational considerations

for the two main problems of mathematical knowledge management:

computer-supported retrieval of mathematical knowledge and
computer-supported build-up of mathematical knowledge .

A particular emphasis of the workshop and the special issue will be on theinterconnection between mathematical knowledge management and automatedtheorem proving systems, math assistants, and current mathematical softwaresystems.

An important goal of the workshop and the special issue is to bring togetherthe representatives of the research groups currently working on standards andsystems for mathematical knowledge management as, for example, OpenMath,MathML, OMDoc, Mizar, THEOREMA, MathWorld, QED, TPTP, MBase, OMEGA, ILF, HELM,EULER, LIMES, etc.

Also, it should be clear that the future of mathematical knowledge managementis not only a technical question of improved tools but also a question of howthe culture of doing mathematics will and should be changed. Hence,contributions to these strategical questions are also highly welcome.

Computer-supported Retrieval of Mathematical Knowledge

Problem: Given the mathematical literature (in some area of mathematics, or insome well-defined collection of sources as for example a journal or a bookseries) and given a mathematical concept, a mathematical problem or amathematical method find all relevant information on the concept, problem, ormethod in the literature considered.

This problem has many subproblems depending on how the mathematical literatureis "given":

in the traditional way of text on paper
as natural language texts in electronic form (e.g. Latex)
as formal texts (well-formed formulae in some logic) in electronic form
as executable code, e.g. mathematical software systems and/orspecifications of certain algorithms etc.
...

The problem has many subproblems also depending on what we ultimately want asthe output of a search:

references to the literature
relevant mathematical text
relevant formal definitions, theorems, proofs
methods
executable code of algorithms
knowledge formally derivable from the stored knowledge
...

It is clear that, as soon as we want to tackle more sophisticated versions ofthe problem of retrieving mathematical knowledge, the full potential ofspecial and general computer-supported theorem proving systems and relatedsystems will be indispensable.

Computer-supported Build-up of Mathematical Knowledge

The second main problem of mathematical knowledge management is the problem ofnew approaches and computer-support for structuring and building up future mathematical knowledge bases in order to bring mathematicalknowledge retrieval to a new level of efficiency, reliability, andcompleteness that should significantly surpass the efficiency, reliability,and completeness of current retrieval tools for the current mathematical knowledge bases as represented in current libraries.

This problem, again, has many subproblems:

practical languages for the formalization of mathematics
language standards for formal mathematics
structuring of mathematical knowledge on the basis of the logicalstructure of knowledge rather than on the basis of key words
interaction of formal mathematical knowledge bases with computer-supportedproving systems
interaction of formal mathematical knowledge bases with currentmathematical software systems (algorithm libraries, etc.)
tools for restructuring the available knowledge in some mathematical areaw.r.t. to a desired aspect
...

Interaction with the Organization of Mathematical Research and Teachingand the Application of Mathematics

The construction of new tools for mathematical knowledge management for the current mathematical community will not be sufficient. Rather, we alsohave to address the question of how future mathematicians will have tochange their working technique and how future math students will haveto be trained for working (doing math research, teaching mathematics, andapplying mathematics) reasonably within the frame of computer-supported globalmathematical knowledge webs. It may be foreseen that the impact ofcomputer-supported mathematical knowledge webs on the behavior and formalqualification of mathematicians will be drastic. Conversely, a new generationof formally well trained mathematicians will be necessary to make significantprogress in the efficiency, reliability, and completeness of mathematicalknowledge management.

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