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

arXiv: https://arxiv.org/abs/2111.05364 · HTML: https://mlsanity.com/paper/2111.05364/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 71 references that are in the map.
- First posted on arXiv 29 Oct 2021.

## Builds on (most cited first, 28 of 28)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [K-Adapter: Infusing Knowledge into Pre-Trained Models with Adapters](https://mlsanity.com/paper/2002.01808/) (2020)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [WT5?! Training Text-to-Text Models to Explain their Predictions](https://mlsanity.com/paper/2004.14546/) (2020)
- [Reinforcement Learning of Theorem Proving](https://mlsanity.com/paper/1805.07563/) (2018)
- [Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems](https://mlsanity.com/paper/2009.11506/) (2020)
- [NumNet: Machine Reading Comprehension with Numerical Reasoning](https://mlsanity.com/paper/1910.06701/) (2019)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Mapping to Declarative Knowledge for Word Problem Solving](https://mlsanity.com/paper/1712.09391/) (2017)
- [Semantically-Aligned Universal Tree-Structured Solver for Math Word Problems](https://mlsanity.com/paper/2010.06823/) (2020)
- [Semantics of the Black-Box: Can knowledge graphs help make deep learning systems more interpretable and explainable?](https://mlsanity.com/paper/2010.08660/) (2020)
- [Unit Dependency Graph and its Application to Arithmetic Word Problem Solving](https://mlsanity.com/paper/1612.00969/) (2016)
- [Learning by Fixing: Solving Math Word Problems with Weak Supervision](https://mlsanity.com/paper/2012.10582/) (2020)
- [Knowledge-intensive Language Understanding for Explainable AI](https://mlsanity.com/paper/2108.01174/) (2021)
- [SMART: A Situation Model for Algebra Story Problems via Attributed Grammar](https://mlsanity.com/paper/2012.14011/) (2020)
- [KI-BERT: Infusing Knowledge Context for Better Language and Domain Understanding](https://mlsanity.com/paper/2104.08145/) (2021)
- [A Meaning-based Statistical English Math Word Problem Solver](https://mlsanity.com/paper/1803.06064/) (2018)
- [Solving Arithmetic Word Problems with Transformers and Preprocessing of Problem Text](https://mlsanity.com/paper/2106.00893/) (2021)
- [Data-Driven Methods for Solving Algebra Word Problems](https://mlsanity.com/paper/1804.10718/) (2018)
- [A framework for predicting, interpreting, and improving Learning Outcomes](https://mlsanity.com/paper/2010.02629/) (2020)
- [A Reinforcement Learning Environment for Mathematical Reasoning via Program Synthesis](https://mlsanity.com/paper/2107.07373/) (2021)

## Built on by (most cited first, 12 of 12)

- [Teaching Algorithmic Reasoning via In-context Learning](https://mlsanity.com/paper/2211.09066/) (2022)
- [Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computing](https://mlsanity.com/paper/2210.15889/) (2022)
- [Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning models](https://mlsanity.com/paper/2303.07735/) (2023)
- [Multi-View Reasoning: Consistent Contrastive Learning for Math Word Problem](https://mlsanity.com/paper/2210.11694/) (2022)
- [Why are NLP Models Fumbling at Elementary Math? A Survey of Deep Learning based Word Problem Solvers](https://mlsanity.com/paper/2205.15683/) (2022)
- [Analogical Math Word Problems Solving with Enhanced Problem-Solution Association](https://mlsanity.com/paper/2212.00837/) (2022)
- [Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspective](https://mlsanity.com/paper/2510.21999/) (2025)
- [MMTM: Multi-Tasking Multi-Decoder Transformer for Math Word Problems](https://mlsanity.com/paper/2206.01268/) (2022)
- [Techniques to Improve Neural Math Word Problem Solvers](https://mlsanity.com/paper/2302.03145/) (2023)
- [CogNarr Ecosystem: Facilitating Group Cognition at Scale](https://mlsanity.com/paper/2407.18945/) (2024)
- [A Theoretical Review on Solving Algebra Problems](https://mlsanity.com/paper/2411.00031/) (2024)
- [SafeMath: Safe Solutions for Unsafe Math Word Problems](https://mlsanity.com/paper/2603.25201/) (2026)

## Abstract (arXiv)

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.