# LLMs for Mathematical Modeling: Towards Bridging the Gap between Natural and Mathematical Languages

arXiv: https://arxiv.org/abs/2405.13144 · HTML: https://mlsanity.com/paper/2405.13144/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 15 of its 36 references that are in the map.
- First posted on arXiv 21 May 2024.

## Placed in

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

## Builds on (most cited first, 15 of 15)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [How well do Large Language Models perform in Arithmetic tasks?](https://mlsanity.com/paper/2304.02015/) (2023)
- [Solving Math Word Problems by Combining Language Models With Symbolic Solvers](https://mlsanity.com/paper/2304.09102/) (2023)
- [MathBench: Evaluating the Theory and Application Proficiency of LLMs with a Hierarchical Mathematics Benchmark](https://mlsanity.com/paper/2405.12209/) (2024)
- [Evaluating and Improving Tool-Augmented Computation-Intensive Math Reasoning](https://mlsanity.com/paper/2306.02408/) (2023)
- [Language Models can be Logical Solvers](https://mlsanity.com/paper/2311.06158/) (2023)

## Built on by (most cited first, 30 of 49)

- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [ErrorRadar: Benchmarking Complex Mathematical Reasoning of Multimodal Large Language Models Via Error Detection](https://mlsanity.com/paper/2410.04509/) (2024)
- [BPP-Search: Enhancing Tree of Thought Reasoning for Mathematical Modeling Problem Solving](https://mlsanity.com/paper/2411.17404/) (2024)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [Constructing Industrial-Scale Optimization Modeling Benchmark](https://mlsanity.com/paper/2602.10450/) (2026)
- [A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solving](https://mlsanity.com/paper/2509.08269/) (2025)
- [SAC-Opt: Semantic Anchors for Iterative Correction in Optimization Modeling](https://mlsanity.com/paper/2510.05115/) (2025)
- [VeriEquivBench: An Equivalence Score for Ground-Truth-Free Evaluation of Formally Verifiable Code](https://mlsanity.com/paper/2510.06296/) (2025)
- [ConstraintBench: Benchmarking LLM Constraint Reasoning on Direct Optimization](https://mlsanity.com/paper/2602.22465/) (2026)
- [Large Language Models in Operations Research: Methods, Applications, and Challenges](https://mlsanity.com/paper/2509.18180/) (2025)
- [FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization](https://mlsanity.com/paper/2605.25246/) (2026)
- [ModelingAgent: Bridging LLMs and Mathematical Modeling for Real-World Challenges](https://mlsanity.com/paper/2505.15068/) (2025)
- [OPT-Engine: Benchmarking the Limits of LLMs in Optimization Modeling via Complexity Scaling](https://mlsanity.com/paper/2601.19924/) (2026)
- [NEMO: Execution-Aware Optimization Modeling via Autonomous Coding Agents](https://mlsanity.com/paper/2601.21372/) (2026)
- [CALM Before the STORM: Unlocking Native Reasoning for Optimization Modeling](https://mlsanity.com/paper/2510.04204/) (2025)
- [OptiVerse: A Comprehensive Benchmark towards Optimization Problem Solving](https://mlsanity.com/paper/2604.21510/) (2026)
- [Execution-Verified Reinforcement Learning for Optimization Modeling](https://mlsanity.com/paper/2604.00442/) (2026)
- [MM-OptBench: A Solver-Grounded Benchmark for Multimodal Optimization Modeling](https://mlsanity.com/paper/2605.12154/) (2026)
- [TriVAL: A Tri-Validation Framework for Faithful Automatic Optimization Modeling](https://mlsanity.com/paper/2605.23966/) (2026)
- [OR-Space: A Full-Lifecycle Workspace Benchmark for Industrial Optimization Agents](https://mlsanity.com/paper/2605.28158/) (2026)
- [OptSkills: Learning Generalizable Optimization Skills from Problem Archetypes via Cluster-Based Distillation](https://mlsanity.com/paper/2605.29829/) (2026)
- [Beyond Objective Equivalence: Constraint Injection for LLM-Based Optimization Modeling on Vehicle Routing Problems](https://mlsanity.com/paper/2606.04816/) (2026)
- [Teaching LLMs to Think Mathematically: A Critical Study of Decision-Making via Optimization](https://mlsanity.com/paper/2508.18091/) (2025)
- [Can Large Language Models Autoformalize Kinematics?](https://mlsanity.com/paper/2509.21840/) (2025)
- [SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations](https://mlsanity.com/paper/2511.00685/) (2025)
- [Large Language Model-Assisted Planning of Electric Vehicle Charging Infrastructure with Real-World Case Study](https://mlsanity.com/paper/2511.19055/) (2025)
- [Models Can Model, But Can't Bind: Structured Grounding in Text-to-Optimization](https://mlsanity.com/paper/2605.21751/) (2026)
- [ORAgentBench: Can LLM Agents Solve Challenging Operations Research Tasks End to End?](https://mlsanity.com/paper/2606.19787/) (2026)
- [MiniOpt: Reasoning to Model and Solve General Optimization Problems with Limited Resources](https://mlsanity.com/paper/2606.25832/) (2026)
- [SLAI T-Rex: Full-Parameter Post-training of the DeepSeek-V4 Family on Ascend SuperPOD](https://mlsanity.com/paper/2607.20145/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have demonstrated strong performance across various natural language processing tasks, yet their proficiency in mathematical reasoning remains a key challenge. Addressing the gap between natural and mathematical language requires advanced reasoning capabilities, approaching those of Artificial General Intelligence (AGI). However, the evaluation remains challenging, as perfectly representing reality is inherently elusive, and traditional methods like manual or direct comparison of mathematical statements (Ramamonjison et al., 2023) are insufficient for assessing true modeling ability. We propose a process-oriented framework to evaluate LLMs' ability to construct mathematical models, using solvers to compare outputs with ground truth. Introducing Mamo, a benchmark with 1,209 questions covering ordinary differential equations, linear programming, and mixed-integer linear programming, we enable automatic evaluation of modeling accuracy. The results show that existing LLMs struggle with complex mathematical modeling tasks, with larger models demonstrating superior performance, while open-source models remain competitive in simpler cases but still fall short of proprietary models in more challenging problems.