# PyraMathBench: Evaluating and Improving Mathematical Capability in Large Language Models

arXiv: https://arxiv.org/abs/2606.03858 · HTML: https://mlsanity.com/paper/2606.03858/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 47 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

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

## Builds on (most cited first, 25 of 25)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [ToolLLM: Facilitating Large Language Models to Master 16000+ Real-world APIs](https://mlsanity.com/paper/2307.16789/) (2023)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Gorilla: Large Language Model Connected with Massive APIs](https://mlsanity.com/paper/2305.15334/) (2023)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [TAT-QA: A Question Answering Benchmark on a Hybrid of Tabular and Textual Content in Finance](https://mlsanity.com/paper/2105.07624/) (2021)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [ToolkenGPT: Augmenting Frozen Language Models with Massive Tools via Tool Embeddings](https://mlsanity.com/paper/2305.11554/) (2023)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [EASYTOOL: Enhancing LLM-based Agents with Concise Tool Instruction](https://mlsanity.com/paper/2401.06201/) (2024)
- [RestGPT: Connecting Large Language Models with Real-World RESTful APIs](https://mlsanity.com/paper/2306.06624/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [Goat: Fine-tuned LLaMA Outperforms GPT-4 on Arithmetic Tasks](https://mlsanity.com/paper/2305.14201/) (2023)
- [Ape210K: A Large-Scale and Template-Rich Dataset of Math Word Problems](https://mlsanity.com/paper/2009.11506/) (2020)
- [PURR: Efficiently Editing Language Model Hallucinations by Denoising Language Model Corruptions](https://mlsanity.com/paper/2305.14908/) (2023)
- [Synthetic Data Generation & Multi-Step RL for Reasoning & Tool Use](https://mlsanity.com/paper/2504.04736/) (2025)
- [Numeracy for Language Models: Evaluating and Improving their Ability to Predict Numbers](https://mlsanity.com/paper/1805.08154/) (2018)
- [MathBERT: A Pre-trained Language Model for General NLP Tasks in Mathematics Education](https://mlsanity.com/paper/2106.07340/) (2021)
- [Exploring the Numerical Reasoning Capabilities of Language Models: A Comprehensive Analysis on Tabular Data](https://mlsanity.com/paper/2311.02216/) (2023)
- [Learning Numeral Embeddings](https://mlsanity.com/paper/2001.00003/) (2019)
- [Towards Robust Numerical Question Answering: Diagnosing Numerical Capabilities of NLP Systems](https://mlsanity.com/paper/2211.07455/) (2022)

## Abstract (arXiv)

Despite the pivotal role of numerical reasoning as the cornerstone of mathematical capabilities in large language models (LLMs) across applications, few benchmarks evaluate LLMs by integrating numerical processing and mathematical reasoning, hindering the interpretability of failures in math tasks. We introduce PyraMathBench, a comprehensive hierarchical benchmark with 32,505 questions derived from 7,404 math word problems, spanning 4 key cognitive aspects, 14 subcategories, and 2 modalities. Experiments reveal that LLMs' performance is severely compromised by inadequate numerical computation and weak handling of abstract numerical questions. To address this, we propose the Smart Optimization & Learning-based VErsatile module (SOLVE) and Interactive Relative Policy Optimization (IRPO), which enhance LLMs' numerical-mathematical synergy via efficient tool calls (fuzzy matching and low-quality call rejection). Comparative experiments show Qwen-2.5 achieves a 5.0 score improvement with SOLVE and IRPO training.