Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems

TL;DR

This paper reviews current methods for solving math word problems, emphasizing neural approaches, their strategies, challenges, and future opportunities for improving mathematical reasoning in AI.

Contribution

It provides a comprehensive survey of neural and non-neural methods for MWPs, highlighting strategies, design choices, and identifying key gaps and opportunities for future research.

Findings

Neural methods dominate current MWP solutions.

Three main strategies: direct answer, expression tree, template retrieval.

Identified gaps include need for external knowledge and interpretability.

Abstract

Mathematical reasoning would be one of the next frontiers for artificial intelligence to make significant progress. The ongoing surge to solve math word problems (MWPs) and hence achieve better mathematical reasoning ability would continue to be a key line of research in the coming time. We inspect non-neural and neural methods to solve math word problems narrated in a natural language. We also highlight the ability of these methods to be generalizable, mathematically reasonable, interpretable, and explainable. Neural approaches dominate the current state of the art, and we survey them highlighting three strategies to MWP solving: (1) direct answer generation, (2) expression tree generation for inferring answers, and (3) template retrieval for answer computation. Moreover, we discuss technological approaches, review the evolution of intuitive design choices to solve MWPs, and examine them for mathematical reasoning ability. We finally identify several gaps that warrant the need for external knowledge and knowledge-infused learning, among several other opportunities in solving MWPs.