Towards robust automated math problem solving: a survey of statistical and deep learning approaches

• Published in: Evolutionary intelligence Vol. 17; no. 5-6; pp. 3113 - 3150
• Main Authors: Saraf, Amrutesh, Kamat, Pooja, Gite, Shilpa, Kumar, Satish, Kotecha, Ketan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2024; Springer Nature B.V
• Subjects: Applications of Mathematics; Artificial Intelligence; Automation; Bioinformatics; Control; Data analysis; Datasets; Engineering; Linguistics; Mathematical and Computational Engineering; Mathematical logic; Mathematical problems; Mechatronics; Natural language processing; Problem solving; Review Article; Robotics; Statistical Physics and Dynamical Systems; Indic NLP; IndicXNLI; Tabular word problem solving; Multimodal problem solving; Geometrical word problem solving; Mathematical word problem solving
• ISSN: 1864-5909; 1864-5917
• DOI: 10.1007/s12065-024-00957-0

Automated mathematical problem-solving represents a unique intersection of natural language processing (NLP) and mathematical reasoning, posing significant challenges in semantic comprehension and logical deduction. This survey paper explores the domain of mathematical word problems (MWPs), focusing on the nuanced integration of linguistic understanding and mathematical logic required for their resolution. Despite progress, the automated solution of MWPs through NLP techniques remains challenging. We present a comprehensive review of the latest datasets and computational models, focusing on those addressing geometrical, tabular, and multimodal problem types-areas not extensively covered in prior surveys. Our review extends beyond previous surveys by analyzing the solving of MWPs in languages such as Hindi and Arabic, areas less explored in existing research. We critically review the latest datasets and computational models designed for MWPs, highlighting the scarcity of resources that cater to the complexity of problems in Hindi, Arabic, and similar languages. This gap underscores the need for comprehensive datasets that reflect the diversity of MWPs in these languages and for models capable of navigating the linguistic nuances inherent in non-English and non-Chinese contexts. Our analysis points to the limitations of current approaches, including their focus on specific data formats and limited generalizability across different mathematical contexts. Furthermore, our critical analysis identifies prevailing limitations within current methodologies, including over-reliance on specific data formats and a lack of generalizability across diverse mathematical contexts. In response, we propose a research agenda to develop sophisticated models that understand and reason across a broader spectrum of problem types and languages and create datasets that capture the real-world diversity of MWPs in Hindi, Arabic, and beyond. This paper sets a direction for future research to advance NLP-driven mathematical problem-solving toward technically adept and universally applicable models across linguistic boundaries, thereby making strides toward truly global NLP applications in education and beyond.