# Multilingual Mathematical Reasoning: Advancing Open-Source LLMs in Hindi and English

arXiv: https://arxiv.org/abs/2412.18415 · HTML: https://mlsanity.com/paper/2412.18415/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 26 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Placed in

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

## Builds on (most cited first, 17 of 17)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations?](https://mlsanity.com/paper/2405.05904/) (2024)
- [A Careful Examination of Large Language Model Performance on Grade School Arithmetic](https://mlsanity.com/paper/2405.00332/) (2024)
- [Take a Step Back: Evoking Reasoning via Abstraction in Large Language Models](https://mlsanity.com/paper/2310.06117/) (2023)
- [IndicTrans2: Towards High-Quality and Accessible Machine Translation Models for all 22 Scheduled Indian Languages](https://mlsanity.com/paper/2305.16307/) (2023)
- [Airavata: Introducing Hindi Instruction-tuned LLM](https://mlsanity.com/paper/2401.15006/) (2024)
- [Investigating Symbolic Capabilities of Large Language Models](https://mlsanity.com/paper/2405.13209/) (2024)
- [Solving for X and Beyond: Can Large Language Models Solve Complex Math Problems with More-Than-Two Unknowns?](https://mlsanity.com/paper/2407.05134/) (2024)
- [Improving Multimodal LLMs Ability In Geometry Problem Solving, Reasoning, And Multistep Scoring](https://mlsanity.com/paper/2412.00846/) (2024)

## Built on by (most cited first, 5 of 5)

- [A Survey of Multilingual Reasoning in Language Models](https://mlsanity.com/paper/2502.09457/) (2025)
- [Reasoning Transfer for an Extremely Low-Resource and Endangered Language: Bridging Languages Through Sample-Efficient Language Understanding](https://mlsanity.com/paper/2504.02890/) (2025)
- [Long-context Non-factoid Question Answering in Indic Languages](https://mlsanity.com/paper/2504.13615/) (2025)
- [Talking to Yourself: Defying Forgetting in Large Language Models](https://mlsanity.com/paper/2602.20162/) (2026)
- [Tool-Augmented Hybrid Ensemble Reasoning with Distillation for Bilingual Mathematical Problem Solving](https://mlsanity.com/paper/2512.19093/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) excel in linguistic tasks but struggle with mathematical reasoning, particularly in non English languages like Hindi. This research aims to enhance the mathematical reasoning skills of smaller, resource efficient open-source LLMs in both Hindi and English. We evaluate models like OpenHathi 7B, LLaMA-2 7B, WizardMath 7B, Mistral 7B, LLeMMa 7B, MAmmoTH 7B, Gemini Pro, and GPT-4 using zero-shot, few-shot chain-of-thought (CoT) methods, and supervised fine-tuning. Our approach incorporates curriculum learning, progressively training models on increasingly difficult problems, a novel Decomposition Strategy to simplify complex arithmetic operations, and a Structured Solution Design that divides solutions into phases. Our experiments result in notable performance enhancements. WizardMath 7B exceeds Gemini's accuracy on English datasets by +6% and matches Gemini's performance on Hindi datasets. Adopting a bilingual approach that combines English and Hindi samples achieves results comparable to individual language models, demonstrating the capability to learn mathematical reasoning in both languages. This research highlights the potential for improving mathematical reasoning in open-source LLMs.