Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems. (arXiv:2111.05364v1 [cs.CL])

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.



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