Abstract. In this paper, we present an ontology of mathematical knowledge concepts that covers a wide range of the fields of mathematics and introduces a balanced representation between comprehensive and sensible models. We demonstrate the applications of this representation in information extraction, semantic search, and education. We argue that the ontology can be a core of future integration of math-aware data sets in the Web of Data and, therefore, provide mappings onto relevant datasets, such as DBpedia and ScienceWISE.

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.2000 Mathematical Subject Classification. 68T30, 68P20. Key words and phrases. Ontology engineering, mathematical knowledge, metadata extraction, information retrieval, math formula search.This work was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (project 3056).

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