  Large-scale pre-trained models like BERT, have obtained a great success in
various Natural Language Processing (NLP) tasks, while it is still a challenge
to adapt them to the math-related tasks. Current pre-trained models neglect the
structural features and the semantic correspondence between formula and its
context. To address these issues, we propose a novel pre-trained model, namely
\textbf{MathBERT}, which is jointly trained with mathematical formulas and
their corresponding contexts. In addition, in order to further capture the
semantic-level structural features of formulas, a new pre-training task is
designed to predict the masked formula substructures extracted from the
Operator Tree (OPT), which is the semantic structural representation of
formulas. We conduct various experiments on three downstream tasks to evaluate
the performance of MathBERT, including mathematical information retrieval,
formula topic classification and formula headline generation. Experimental
results demonstrate that MathBERT significantly outperforms existing methods on
all those three tasks. Moreover, we qualitatively show that this pre-trained
model effectively captures the semantic-level structural information of
formulas. To the best of our knowledge, MathBERT is the first pre-trained model
for mathematical formula understanding.
