Electronic Proceedings of the First International Workshop


Mathematical Knowledge Management: MKM'2001


Much time, effort, and money is being spent on inventing and proving new mathematical results. This effort is well spent for a discipline that forms the core of our current technology-based society. In fact, impressive progress has been made over the past decades in expanding the depth and breadth of our mathematical knowledge.

However, a decent part of our time, effort, and money is spent inefficiently because the knowledge added is hard to retrieve and, in fact, very little time, effort, and money is currently spent for improving the management of mathematical knowledge.

Of course, the advancements of computer technology, in particular the global web, promise to give us new tools of unprecedented power for making knowledge retrieval much more efficient and, of course, we already feel the practical and pleasant implications of this in our daily work when, by doing a few clicks, we get access to a huge amount of relevant information whose retrieval would have taken us many hours in libraries etc. just a couple of years ago.

However, I think that the urgently necessary improvement of mathematical knowledge management is essentially not a technological question but rather a deeply mathematical question and, in fact, a question of improving our abilities to do formal mathematics. I believe that mathematical knowledge management will turn out to be one of the most exciting future topics of mathematics and will lead to a new understanding of the fundamentals of mathematics in the same way as the foundational problems of mathematics in the early 20th century lead to a new, and much deeper, understanding of mathematics and to a whole wave of new directions, techniques and results. The impacts of advances in mathematical knowledge management on all of science and technology will be dramatic both because of the role of mathematics as the universal "thinking technology" of all science and technology and because techniques to be worked out for mathematical knowledge management will be applicable also for other, less structured, disciplines.

I also think that significant improvement in mathematical knowledge management will only be possible if the next generation of mathematicians reaches a much higher level in mastering the formal aspects of our field. Thus mathematical knowledge management is neither only a question of computer technology nor only a mathematical question but also a question of the sociology of the mathematical community. I am deeply convinced that ample time must be reserved for a thorough practical training of students in the formal and methodological aspects of mathematics in future math and computer science curricula. Only by combining the best tools of computer technology with a new and deep understanding and mastering of the structural formal fabrics of mathematics and the improved formal training of mathematicians will it be possible to reach a new level of accessibility and, hence, usefulness of mathematics.

Because of the high topicality of the emerging field of mathematical knowledge management, I decided to guest-edit a special issue on this topic for the Annals of Mathematics and Artificial Intelligence and, in preparation of this special issue but organizationally independently, to organize an international workshop at RISC. I think that, as far as I know, this workshop is the first international event explicitly devoted to the topic of mathematical knowledge management in general and I am very happy that so many researchers representing so many different approaches are following our invitation. I am looking forward to presentations and discussions that will produce new interactions, ideas, projects and joint political activities for fast advancements in the next few years. In fact, some participants already proposed to host the future second and further editions of the MKM workshop. I think this is great and shows how timely and topical the workshop is.

Let me also take the opportunity to thank those who contributed to making the workshop possible, most prominently to Olga Caprotti, Christian Vogt, and Betina Curtis who basically structured, supervised and did all the preparatory work for this workshop so that I just could enjoy the excitement of the mathematical aspect of the field.

Bruno Buchberger