Information about the meaning of mathematical variables in text is useful in NLP/IR tasks such as symbol disambiguation, topic modeling and mathematical information retrieval (MIR). We introduce variable typing, the task of assigning one mathematical type (multi-word technical terms referring to mathematical concepts) to each variable in a sentence of mathematical text. As part of this work, we also introduce a new annotated data set composed of 33,524 data points extracted from scientific documents published on arXiv. Our intrinsic evaluation demonstrates that our data set is sufficient to successfully train and evaluate current classifiers from three different model architectures. The best performing model is evaluated on an extrinsic task: MIR, by producing a typed formula index. Our results show that the best performing MIR models make use of our typed index, compared to a formula index only containing raw symbols, thereby demonstrating the usefulness of variable typing.

We present an approach to mathematical information retrieval (MIR) that exploits a special kind of technical terminology, referred to as a mathematical type. In this paper, we present and evaluate a type detection mechanism and show its positive effect on the retrieval of research-level mathematics. Our best model, which performs query expansion with a type-aware embedding space, strongly outperforms standard IR models with state-of-the-art query expansion (vector space-based and language modelling-based), on a relatively new corpus of research-level queries.