Towards Systematic Reasoning with Language Models

Mathematics requires systematic reasoning, namely the step-wise application of knowledge in a sound manner to reach a conclusion. Can language models (LMs) perform this kind of systematic reasoning with knowledge provided to it? Or, even more ambitiously, can LMs reason systematically with their own internal knowledge acquired during pretraining? In this talk, I'll attempt to answer these questions, illustrated with our recent work on using LMs for logical deduction, proof generation, and multistep textual entailment problems. While progress has been made, there is still a way to go. To illustrate this, I'll conclude by posing a (currently unsolved) grand challenge - answering Fermi problems - to the math reasoning community, requiring combining systematic reasoning, mathematics, and world knowledge together.