Session I: Foundations -- A Proof-Theoretic Approach to Hierarchical Math Library Organization -- An Exploration in the Space of Mathematical Knowledge -- Session II: Authoring -- Authoring Presentation for openmath -- Translating Mathematical Vernacular into Knowledge Repositories -- Assisted Proof Document Authoring -- Session III: Representations -- A Tough Nut for Mathematical Knowledge Management -- Textbook Proofs Meet Formal Logic – The Problem of Underspecification and Granularity -- Processing Textbook-Style Matrices -- Session IV: Proving -- A Generic Modular Data Structure for Proof Attempts Alternating on Ideas and Granularity -- Impasse-Driven Reasoning in Proof Planning -- Literate Proving: Presenting and Documenting Formal Proofs -- Session V: MKManagement Tools -- Semantic Matching for Mathematical Services -- Mathematical Knowledge Browser with Automatic Hyperlink Detection -- A Database of Glyphs for OCR of Mathematical Documents -- Session VI: Documents -- Toward an Object-Oriented Structure for Mathematical Text -- Explanation in Natural Language of ?????-Terms -- Engineering Mathematical Knowledge -- Session VII: MKM Case Studies -- Computational Origami of a Morley’s Triangle -- Designing Diagrammatic Catalogues of Types of Basic Interval Equation: A Case Study -- Gröbner Bases — Theory Refinement in the Mizar System -- Session VIII: Course Materials -- An Interactive Algebra Course with Formalised Proofs and Definitions -- Interactive Learning and Mathematical Calculus -- Session IX: Migration -- XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy -- Determining Empirical Characteristics of Mathematical Expression Use -- Transformations of MML Database’s Elements -- Translating a Fragment of Weak Type Theory into Type Theory with Open Terms.

This volume contains the proceedings of the Fourth International Conference on Mathematical Knowledge Management MKM 2005 held July 15–17, 2005 at - ternational University Bremen, Germany. Previous conferences have been at the Research Institute for Symbolic Computation (RISC) Linz, Austria (September 2001), at Bertinoro, Italy (March 2003), and Bialowiecze, Poland (September 2004). Mathematical knowledge management (MKM) is a ?eld in the intersection of mathematics and computer science, providing new techniques for managing the enormous volume of mathematical knowledge available in current mathematical sources and making it available through the new developments in information technology. The annual MKM Conference brings together mathematicians, software - velopers, publishing companies, math organizations, math users, and educators to exchange their views and approaches, current activities and new initiatives. For the ?rst time, MKM 2005 chose to have post-conference proceedings, as otherwise the submission deadline would have collided with other conferences and crimped time since MKM 2004 in September 2004. The decision also faci- tatedkeepingtheconferenceopentonewideasaswellaskeepingupthematurity of the papers necessary for inclusion into archival proceedings. With a May 15 deadline, MKM 2005 received 38 submissions. Each submission was reviewed by at least three programme committee members. The committee decided to - cept 27 papers for presentation at the conference. Out of these, 26 papers were accepted for publication in the conference proceedings after re-evaluation by the Programme Committee since they included signi?cant improvements triggered by the referee reports and the discussions at the conference.