Mathematical Word Problems (MWPs) are among the most challenging tasks in natural language processing because they require both linguistic understanding and multi-step numerical reasoning. While Chain-of-Thought (CoT) prompting has shown promise, its linear structure often propagates errors, limiting overall effectiveness. To address this limitation, we present the a systematic study of Tree-of-Thought (ToT) reasoning for Bengali MWPs using the SOMADHAN dataset. Owing to computational and token-cost constraints, we evaluate a curated set of 100 representative problems across multiple large language models (LLMs), including GPT-OSS and LLaMA variants, under standard prompting, CoT, and ToT strategies. Our results show that CoT improves baseline accuracy from 78% (standard prompting) to 83% on average, while ToT further increases performance by up to 5 percentage points, achieving 88% accuracy with GPT-OSS-120B. These improvements highlight that ToT is particularly effective in medium-to-large-scale models but may offer less advantage for smaller ones. Overall, our findings establish ToT as a robust framework for solving mathematical problems in low-resource languages such as Bengali. More broadly, this study shows that structured reasoning methods like ToT can provide more reliable and globally consistent outcomes than CoT, paving the way for better reasoning strategies in multilingual NLP.

Agentic workflows, where multiple AI agents collaborate to accomplish complex tasks like reasoning or planning, play a substantial role in many cutting-edge commercial applications, and continue to fascinate researchers across fields for their potential to accomplish expensive, complex tasks that, until recently, only humans have been trusted to do. These workflows depend critically on the prompts used to provide the roles models play in such workflows. Poorly designed prompts that fail even slightly to guide individual agents can lead to sub-optimal performance that may snowball within a system of agents, limiting their reliability and scalability. To address this important problem of inference-time prompt optimization, we introduce ProRefine, an innovative inference-time optimization method that uses an agentic loop of LLMs to generate and apply textual feedback. ProRefine dynamically refines prompts for multi-step reasoning tasks without additional training or ground truth labels. Evaluated on five benchmark mathematical reasoning datasets, ProRefine significantly surpasses zero-shot Chain-of-Thought baselines by 3 to 37 percentage points. This approach not only boosts accuracy but also allows smaller models to approach the performance of their larger counterparts. This highlights its potential for building more cost-effective and powerful hybrid AI systems, thereby democratizing access to high-performing AI.

Math word problem (MWP) serves as a fundamental research topic in artificial intelligence (AI) dating back to 1960s. This research aims to advance the reasoning abilities of AI by mirroring the human-like cognitive intelligence. The mainstream technological paradigm has evolved from the early rule-based methods, to deep learning models, and is rapidly advancing towards large language models. However, the field still lacks a systematic taxonomy for the MWP survey along with a discussion of current development trends. Therefore, in this paper, we aim to comprehensively review related research in MWP solving through the lens of human cognition, to demonstrate how recent AI models are advancing in simulating human cognitive abilities. Specifically, we summarize 5 crucial cognitive abilities for MWP solving, including Problem Understanding, Logical Organization, Associative Memory, Critical Thinking, and Knowledge Learning. Focused on these abilities, we review two mainstream MWP models in recent 10 years: neural network solvers, and LLM based solvers, and discuss the core human-like abilities they demonstrated in their intricate problem-solving process. Moreover, we rerun all the representative MWP solvers and supplement their performance on 5 mainstream benchmarks for a unified comparison. To the best of our knowledge, this survey first comprehensively analyzes the influential MWP research of the past decade from the perspective of human reasoning cognition and provides an integrative overall comparison across existing approaches. We hope it can inspire further research in AI reasoning. Our repository is released on https://github.com/Ljyustc/FoI-MWP.

Math word problems (MWPs) are critical K-12 educational tools, and customizing them to students' interests and ability levels can increase learning outcomes. However, teachers struggle to find time to customize MWPs for each student given large class sizes and increasing burnout. We propose that LLMs can support math education by generating MWPs customized to student interests and math education standards. To this end, we use a joint human expert-LLM judge approach to evaluate over 11,000 MWPs generated by open and closed LLMs and develop the first teacher-annotated dataset for standards-aligned educational MWP generation. We show the value of our data by using it to train a 12B open model that matches the performance of larger and more capable open models. We also use our teacher-annotated data to train a text classifier that enables a 30B open LLM to outperform existing closed baselines without any training. Next, we show our models' MWPs are more similar to human-written MWPs than those from existing models. We conclude by conducting the first study of customized LLM-generated MWPs with grade school students, finding they perform similarly on our models' MWPs relative to human-written MWPs but consistently prefer our customized MWPs.

Large language models (LLMs) have demonstrated significant capabilities in solving mathematical problems expressed in natural language. However, multilingual and culturally-grounded mathematical reasoning in low-resource languages lags behind English due to the scarcity of socio-cultural task datasets that reflect accurate native entities such as person names, organization names, and currencies. Existing multilingual benchmarks are predominantly produced via translation and typically retain English-centric entities, owing to the high cost associated with human annotater-based localization. Moreover, automated localization tools are limited, and hence, truly localized datasets remain scarce. To bridge this gap, we introduce a framework for LLM-driven cultural localization of math word problems that automatically constructs datasets with native names, organizations, and currencies from existing sources. We find that translated benchmarks can obscure true multilingual math ability under appropriate socio-cultural contexts. Through extensive experiments, we also show that our framework can help mitigate English-centric entity bias and improves robustness when native entities are introduced across various languages.

Large language models (LLMs) now perform strongly on many public math suites, yet frontier separation within mathematics increasingly suffers from ceiling effects. We present two complementary benchmarks: SKYLENAGE-ReasoningMATH, a 100-item, structure-aware diagnostic set with per-item metadata on length, numeric density, and symbolic complexity; and SKYLENAGE-MATH, a 150-item contest-style suite spanning four stages from high school to doctoral under a seven-subject taxonomy. We evaluate fifteen contemporary LLM variants under a single setup and analyze subject x model and grade x model performance. On the contest suite, the strongest model reaches 44% while the runner-up reaches 37%; accuracy declines from high school to doctoral, and top systems exhibit a doctoral-to-high-school retention near 79%. On the reasoning set, the best model attains 81% overall, and hardest-slice results reveal clear robustness gaps between leaders and the mid-tier. In summary, we release SKYLENAGE-ReasoningMATH and report aggregate results for SKYLENAGE-MATH; together, SKYLENAGE provides a hard, reasoning-centered and broadly covering math benchmark with calibrated difficulty and rich metadata, serving as a reference benchmark for future evaluations of mathematical reasoning.

Harnessing parallelism in seemingly sequential models is a central challenge for modern machine learning. Several approaches have been proposed for evaluating sequential processes in parallel using fixed-point methods, like Newton, Picard, and Jacobi iterations. In this work, we show that these methods can be understood within a common framework based on linear dynamical systems (LDSs), where different iteration schemes arise naturally as approximate linearizations of a nonlinear recursion. This unifying view highlights shared principles behind these techniques and clarifies when particular fixed-point methods are most likely to be effective. By bridging diverse algorithms through the language of LDSs, our framework provides a clearer theoretical foundation for parallelizing sequential models and points toward new opportunities for efficient and scalable computation.

Large Language Models (LLMs) excel at various tasks, including problem-solving and question-answering. However, LLMs often find Math Word Problems (MWPs) challenging because solving them requires a range of reasoning and mathematical abilities with which LLMs seem to struggle. Recent efforts have helped LLMs solve more complex MWPs with improved prompts. This study proposes a novel method that initially prompts an LLM to create equations from a decomposition of the question, followed by using an external symbolic equation solver to produce an answer. To ensure the accuracy of the obtained answer, inspired by an established recommendation of math teachers, the LLM is instructed to solve the MWP a second time, but this time with the objective of estimating the correct answer instead of solving it exactly. The estimation is then compared to the generated answer to verify. If verification fails, an iterative rectification process is employed to ensure the correct answer is eventually found. This approach achieves new state-of-the-art results on datasets used by prior published research on numeric and algebraic MWPs, improving the previous best results by nearly two percent on average. In addition, the approach obtains satisfactory results on trigonometric MWPs, a task not previously attempted to the authors' best knowledge. This study also introduces two new datasets, SVAMPClean and Trig300, to further advance the testing of LLMs' reasoning abilities.

Translating electronic health record (EHR) narratives from English to Spanish is a clinically important yet challenging task due to the lack of a parallel-aligned corpus and the abundant unknown words contained. To address such challenges, we propose \textbf{NOOV} (for No OOV), a new neural machine translation (NMT) system that requires little in-domain parallel-aligned corpus for training. NOOV integrates a bilingual lexicon automatically learned from parallel-aligned corpora and a phrase look-up table extracted from a large biomedical knowledge resource, to alleviate both the unknown word problem and the word-repeat challenge in NMT, enhancing better phrase generation of NMT systems. Evaluation shows that NOOV is able to generate better translation of EHR with improvement in both accuracy and fluency.

Preprint August 2025 - This version has not been peer - reviewed . Abstract The progress of Large Language Models (LLMs) like ChatGPT raises the question of how they can be integrated into education. One hope is that they can support mathematics learning, including word - problem solving. Since LLMs can handle textual input with ease, they appear well - suited for solving mathematical word problems. Yet their real competence, whether they can make sense of the real - world context, and the implications for classrooms remain unclear. We conducted a scoping review from a mathematics - education perspective, including three parts: a technical overview, a systematic review of word problems used in research, and a state - of - the - art empirical evaluation of LLMs on mathematical word problems. First, in the technical overview, we contrast the conceptualization of word problems and their solution processes between LLMs and students. In computer - science research this is typically labeled mathematical reasoning, a term that does not align with usage in mathematics education. Second, our literature review of 213 studies shows that the most popular word - problem corpora are dominated by s - problems, which do not require a consideration of realities of their real - world context. Finally, our evaluation of GPT - 3.5 - turbo, GPT - 4o - mini, GPT - 4.1, o3, and GPT - 5 on 287 word problems shows that most recent LLMs solve these s - problems with near - perfect accuracy, including a perfect score on 2 0 problems from PISA. LLMs still showed weaknesses in tackling problems where the real - world context is problematic or non - sensical. In sum, we argue based on all three aspects that LLMs have mastered a superficial solution process but do not make sense of word problems, which potentially limits their value as instructional tools in mathematics classroom s. Keywords LLM; word - problem solving; AI; mathematical reasoning; modelling 1 Introduction In the last couple of years, the rapid improvement of Large Language Models (LLMs) has led to an unprecedented interest in educational research in artificial intelligence in general, and of LLMs in particular (Kasneci et al., 2023) . However, while LLMs excel at producing, translating and reviewing text, they are not natively designed for processing numerical information, calculating, or proving (Chang et al., 2024) . C ompared to other tasks, solving mathematical problems is relatively difficult for LLMs (Testolin, 2024) . This is also true for mathematical word - problems solving.