OntoMath Digital Ecosystem: Ontologies, Mathematical Knowledge Analytics and Management

In this article we consider the basic ideas, approaches and results of developing of mathematical knowledge management technologies based on ontologies. These solutions form the basis of a specialized digital ecosystem OntoMath which consists of the ontology of the logical structure of mathematical documents Mocassin and ontology of mathematical knowledge OntoMathPRO, tools of text analysis, recommender system and other applications to manage mathematical knowledge. The studies are in according to the ideas of creating a distributed system of interconnected repositories of digitized versions of mathematical documents and project to create a World Digital Mathematical Library.

Mathematical Knowledge Representation: Semantic Models and Formalisms

The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range of fields of mathematics. We demonstrate applications of this representation in mathematical formula search, and learning.