mlsanityData to 14 Oct 2026

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

arXiv 2111.05364 ↗First posted 29 Oct 2021cs.CL cs.AIcited by 12

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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.

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

28 of 71 references.

References · 28

  1. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  2. 2018GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understandingcited by 4,899
  3. 2019SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systemscited by 1,729
  4. 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 878
  5. 2019MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalismscited by 662
  6. 2017Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problemscited by 650
  7. 2019Analysing Mathematical Reasoning Abilities of Neural Modelscited by 335
  8. 2020K-Adapter: Infusing Knowledge into Pre-Trained Models with Adapterscited by 319
  9. 2021A Diverse Corpus for Evaluating and Developing English Math Word Problem Solverscited by 318
  10. 2019Deep Learning for Symbolic Mathematicscited by 270
  11. 2020WT5?! Training Text-to-Text Models to Explain their Predictionscited by 148
  12. 2018Reinforcement Learning of Theorem Provingcited by 69
16 more
  1. 2020Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problemscited by 60
  2. 2019NumNet: Machine Reading Comprehension with Numerical Reasoningcited by 59
  3. 2021Neural-Symbolic Solver for Math Word Problems with Auxiliary Taskscited by 38
  4. 2017Mapping to Declarative Knowledge for Word Problem Solvingcited by 36
  5. 2020Semantically-Aligned Universal Tree-Structured Solver for Math Word Problemscited by 35
  6. 2020Semantics of the Black-Box: Can knowledge graphs help make deep learning systems more interpretable and explainable?cited by 31
  7. 2016Unit Dependency Graph and its Application to Arithmetic Word Problem Solvingcited by 25
  8. 2020Learning by Fixing: Solving Math Word Problems with Weak Supervisioncited by 25
  9. 2021Knowledge-intensive Language Understanding for Explainable AIcited by 25
  10. 2020SMART: A Situation Model for Algebra Story Problems via Attributed Grammarcited by 14
  11. 2021KI-BERT: Infusing Knowledge Context for Better Language and Domain Understandingcited by 11
  12. 2018A Meaning-based Statistical English Math Word Problem Solvercited by 10
  13. 2021Solving Arithmetic Word Problems with Transformers and Preprocessing of Problem Textcited by 7
  14. 2018Data-Driven Methods for Solving Algebra Word Problemscited by 4
  15. 2020A framework for predicting, interpreting, and improving Learning Outcomescited by 2
  16. 2021A Reinforcement Learning Environment for Mathematical Reasoning via Program Synthesiscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 6; 2023: 2; 2024: 2; 2025: 1; 2026: 1.

12 papers.

  1. 2022Teaching Algorithmic Reasoning via In-context Learningcited by 112
  2. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 35
  3. 2023Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning modelscited by 18
  4. 2022Multi-View Reasoning: Consistent Contrastive Learning for Math Word Problemcited by 13
  5. 2022Why are NLP Models Fumbling at Elementary Math? A Survey of Deep Learning based Word Problem Solverscited by 9
  6. 2022Analogical Math Word Problems Solving with Enhanced Problem-Solution Associationcited by 4
  7. 2025Foundation of Intelligence: Review of Math Word Problems from Human Cognition Perspectivecited by 1
  8. 2022MMTM: Multi-Tasking Multi-Decoder Transformer for Math Word Problemscited by 0
  9. 2023Techniques to Improve Neural Math Word Problem Solverscited by 0
  10. 2024CogNarr Ecosystem: Facilitating Group Cognition at Scalecited by 0
  11. 2024A Theoretical Review on Solving Algebra Problemscited by 0
  12. 2026SafeMath: Safe Solutions for Unsafe Math Word Problemscited by 0