# Stepwise Self-Consistent Mathematical Reasoning with Large Language Models

arXiv: https://arxiv.org/abs/2402.17786 · HTML: https://mlsanity.com/paper/2402.17786/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 24 Feb 2024.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 23 of 23)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [ART: Automatic multi-step reasoning and tool-use for large language models](https://mlsanity.com/paper/2303.09014/) (2023)
- [LEGO-Prover: Neural Theorem Proving with Growing Libraries](https://mlsanity.com/paper/2310.00656/) (2023)
- [Retrieval-augmented Generation to Improve Math Question-Answering: Trade-offs Between Groundedness and Human Preference](https://mlsanity.com/paper/2310.03184/) (2023)
- [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)
- [Retrieval Augmentation for Commonsense Reasoning: A Unified Approach](https://mlsanity.com/paper/2210.12887/) (2022)

## Built on by (most cited first, 8 of 8)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning](https://mlsanity.com/paper/2410.17885/) (2024)
- [AdaptiveStep: Automatically Dividing Reasoning Step through Model Confidence](https://mlsanity.com/paper/2502.13943/) (2025)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics](https://mlsanity.com/paper/2502.14333/) (2025)
- [Graph-Augmented Reasoning: Evolving Step-by-Step Knowledge Graph Retrieval for LLM Reasoning](https://mlsanity.com/paper/2503.01642/) (2025)
- [Formula-R1: Incentivizing LLM Reasoning over Complex Tables with Numerical Computation via Formula-Driven Reinforcement Learning](https://mlsanity.com/paper/2505.23667/) (2025)
- [RAISE: Enhancing Scientific Reasoning in LLMs via Step-by-Step Retrieval](https://mlsanity.com/paper/2506.08625/) (2025)

## Abstract (arXiv)

Using Large Language Models for complex mathematical reasoning is difficult, primarily due to the complexity of multi-step reasoning. The main challenges of this process include (1) selecting critical intermediate results to advance the procedure, and (2) limited exploration of potential solutions. To address these issues, we introduce a novel algorithm, namely Stepwise Self-Consistent Chain-of-Thought (SSC-CoT). SSC-CoT employs a strategy of selecting intermediate steps based on the intersection of various reasoning chains. Additionally, SSC-CoT enables the model to discover critical intermediate steps by querying a knowledge graph comprising relevant domain knowledge. To validate SSC-CoT, we present a new dataset, TriMaster100, tailored for complex trigonometry problems. This dataset contains 100 questions, with each solution broken down into scored intermediate steps, facilitating a comprehensive evaluation of the mathematical reasoning process. On TriMaster100, SSC-CoT triples the effectiveness of the state-of-the-art methods. Furthermore, we benchmark SSC-CoT on the widely recognized complex mathematical question dataset, MATH level 5, and it surpasses the second-best method by 7.2% in accuracy. Code and the TriMaster100 dataset can be found at: https://github.com/zhao-zilong/ssc-cot.