Automating discovery in mathematics and science will require sophisticated methods of information extraction and abstract reasoning, including models that can convincingly process relationships between mathematical elements and natural language, to produce problem solutions of real-world value. We analyze mathematical language processing methods across five strategic sub-areas (identifier-definition extraction, formula retrieval, natural language premise selection, math word problem solving, and informal theorem proving) from recent years, highlighting prevailing methodologies, existing limitations, overarching trends, and promising avenues for future research.

In order for language models to aid physics research, they must first encode representations of mathematical and natural language discourse which lead to coherent explanations, with correct ordering and relevance of statements. We present a collection of datasets developed to evaluate the performance of language models in this regard, which measure capabilities with respect to sentence ordering, position, section prediction, and discourse coherence. Analysis of the data reveals the classes of arguments and sub-disciplines which are most common in physics discourse, as well as the sentence-level frequency of equations and expressions. We present baselines that demonstrate how contemporary language models are challenged by coherence related tasks in physics, even when trained on mathematical natural language objectives.