Characterizing Searches for Mathematical Concepts

Although there has been considerable interest in recent years in the development of specialized mathematical digital libraries that can index and search for mathematical documents, little is yet known about how people will search for mathematical concepts. To begin to gain some insight into that question, this paper examines the nature of queries for mathematical concepts that were created by users of a search engine. A total of 392,586 queries that contained at least one distinctive mathematical term (e.g., "Taylor Series") were identified in a two-year query log from the Parsijoo search engine; these queries were each issued in one of 69,014 search sessions. Descriptive and comparative analysis indicates that math search sessions are typically longer and less successful than general search sessions. Queries for mathematical concepts exhibit greater diversity than do queries in general - essentially the query distribution is nearly all "tail." The use of well-formed questions as queries (e.g., "How can I prove that ...") is also surprisingly common, as is the creation of queries by copying text from a document. Among the implications of this study for the design of search engines with specialized functions for handling mathematical notation are that robust support for query refinement and reformulation could prove beneficial.