MKM 2001 - Call for Papers

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

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

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

Whereas the workshop is designed to provide a forum for discussion and presentation 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 the workshop and the special issue, jointly or independently.

Scope

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

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

By the workshop and the subsequent special issue on mathematical knowledge management 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 the special issue, "mathematical knowledge management" should be parsed as "(mathematical knowledge) management" and not as "mathematical (knowledge management)". In other words, the scope of the workshop and the special issue is "the management of mathematical knowledge" and not "the mathematical theory of general knowledge management"!)

Hence, in more detail, the scope of both the workshop and the special issue is defined 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 the interconnection between mathematical knowledge management and automated theorem proving systems, math assistants, and current mathematical software systems.

An important goal of the workshop and the special issue is to bring together the representatives of the research groups currently working on standards and systems 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 management is not only a technical question of improved tools but also a question of how the 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 in some well-defined collection of sources as for example a journal or a book series) and given a mathematical concept, a mathematical problem or a mathematical method find all relevant information on the concept, problem, or method in the literature considered.

This problem has many subproblems depending on how the mathematical literature is "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/or specifications of certain algorithms etc.
...

The problem has many subproblems also depending on what we ultimately want as the 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 of the problem of retrieving mathematical knowledge, the full potential of special and general computer-supported theorem proving systems and related systems will be indispensable.

Computer-supported Build-up of Mathematical Knowledge

The second main problem of mathematical knowledge management is the problem of new approaches and computer-support for structuring and building up future mathematical knowledge bases in order to bring mathematical knowledge retrieval to a new level of efficiency, reliability, and completeness 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 logical structure of knowledge rather than on the basis of key words
interaction of formal mathematical knowledge bases with computer-supported proving systems
interaction of formal mathematical knowledge bases with current mathematical software systems (algorithm libraries, etc.)
tools for restructuring the available knowledge in some mathematical area w.r.t. to a desired aspect
...

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

The construction of new tools for mathematical knowledge management for the current mathematical community will not be sufficient. Rather, we also have to address the question of how future mathematicians will have to change their working technique and how future math students will have to be trained for working (doing math research, teaching mathematics, and applying mathematics) reasonably within the frame of computer-supported global mathematical knowledge webs. It may be foreseen that the impact of computer-supported mathematical knowledge webs on the behavior and formal qualification of mathematicians will be drastic. Conversely, a new generation of formally well trained mathematicians will be necessary to make significant progress in the efficiency, reliability, and completeness of mathematical knowledge management.