mlsanityData to 14 Oct 2026

GPT Can Solve Mathematical Problems Without a Calculator

arXiv 2309.03241 ↗First posted 6 Sep 2023cs.LG cs.AI cs.CLcited by 68

Not on the map. Why?

Cited by 32 in LLM reasoning, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Previous studies have typically assumed that large language models are unable to accurately perform arithmetic operations, particularly multiplication of >8 digits, and operations involving decimals and fractions, without the use of calculator tools. This paper aims to challenge this misconception. With sufficient training data, a 2 billion-parameter language model can accurately perform multi-digit arithmetic operations with almost 100% accuracy without data leakage, significantly surpassing GPT-4 (whose multi-digit multiplication accuracy is only 4.3%). We also demonstrate that our MathGLM, fine-tuned from GLM-10B on a dataset with additional multi-step arithmetic operations and math problems described in text, achieves similar performance to GPT-4 on a 5,000-samples Chinese math problem test set. Our code and data are public at https://github.com/THUDM/MathGLM.

Key facts. Cited by 68 papers in the map (data through 14 Oct 2026). Builds on 40 of its 45 references that are in the map. First posted on arXiv 6 Sep 2023.

Builds on

40 of 45 references.

References · 40

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 40; 2025: 16; 2026: 6.

68 papers.

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  1. 2023MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuningcited by 487
  2. 2024Large Language Models for Mathematical Reasoning: Progresses and Challengescited by 284
  3. 2024From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Stepcited by 235
  4. 2024InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoningcited by 119
  5. 2024MARIO: MAth Reasoning with code Interpreter Output -- A Reproducible Pipelinecited by 81
  6. 2024Transformers Can Do Arithmetic with the Right Embeddingscited by 78
  7. 2024GraphInstruct: Empowering Large Language Models with Graph Understanding and Reasoning Capabilitycited by 58
  8. 2023Positional Description Matters for Transformers Arithmeticcited by 56
  9. 2024A Survey of Mathematical Reasoning in the Era of Multimodal Large Language Model: Benchmark, Method & Challengescited by 55
  10. 2025MathCoder-VL: Bridging Vision and Code for Enhanced Multimodal Mathematical Reasoningcited by 45
  11. 2024MathCoder2: Better Math Reasoning from Continued Pretraining on Model-translated Mathematical Codecited by 39
  12. 2024Step-Controlled DPO: Leveraging Stepwise Error for Enhanced Mathematical Reasoningcited by 35
38 more
  1. 2025Position: Multimodal Large Language Models Can Significantly Advance Scientific Reasoningcited by 33
  2. 2024AutoGeo: Automating Geometric Image Dataset Creation for Enhanced Geometry Understandingcited by 29
  3. 2025Lower Bounds for Chain-of-Thought Reasoning in Hard-Attention Transformerscited by 28
  4. 2023How Far Have We Gone in Vulnerability Detection Using Large Language Modelscited by 27
  5. 2023Mathematical Language Models: A Surveycited by 24
  6. 2024Materials science in the era of large language models: a perspectivecited by 24
  7. 2025Mathematical Reasoning in Large Language Models: Assessing Logical and Arithmetic Errors across Wide Numerical Rangescited by 24
  8. 2024MathGLM-Vision: Solving Mathematical Problems with Multi-Modal Large Language Modelcited by 21
  9. 2026Large Language Model Reasoning Failurescited by 21
  10. 2024An overview of domain-specific foundation model: key technologies, applications and challengescited by 19
  11. 2025M2-omni: Advancing Omni-MLLM for Comprehensive Modality Support with Competitive Performancecited by 19
  12. 2024BAM! Just Like That: Simple and Efficient Parameter Upcycling for Mixture of Expertscited by 16
  13. 2024Regression-aware Inference with LLMscited by 14
  14. 2023Adapting Large Language Models for Education: Foundational Capabilities, Potentials, and Challengescited by 13
  15. 2024Tele-FLM Technical Reportcited by 12
  16. 2025A Survey on Mathematical Reasoning and Optimization with Large Language Modelscited by 12
  17. 2024Explicitly Encoding Structural Symmetry is Key to Length Generalization in Arithmetic Taskscited by 11
  18. 2024Language Models are Symbolic Learners in Arithmeticcited by 11
  19. 2023Language Models as a Service: Overview of a New Paradigm and its Challengescited by 10
  20. 2024FineMath: A Fine-Grained Mathematical Evaluation Benchmark for Chinese Large Language Modelscited by 10
  21. 2024Reverse That Number! Decoding Order Matters in Arithmetic Learningcited by 9
  22. 2024Seq-VCR: Preventing Collapse in Intermediate Transformer Representations for Enhanced Reasoningcited by 9
  23. 2025Can External Validation Tools Improve Annotation Quality for LLM-as-a-Judge?cited by 9
  24. 2024Understanding Addition and Subtraction in Transformerscited by 8
  25. 2024Mastering Text, Code and Math Simultaneously via Fusing Highly Specialized Language Modelscited by 7
  26. 2024OccamLLM: Fast and Exact Language Model Arithmetic in a Single Stepcited by 7
  27. 2024Dissecting Multiplication in Transformers: Insights into LLMscited by 7
  28. 2024SciDFM: A Large Language Model with Mixture-of-Experts for Sciencecited by 7
  29. 2024PersonaMath: Boosting Mathematical Reasoning via Persona-Driven Data Augmentationcited by 7
  30. 2025Why Can't Transformers Learn Multiplication? Reverse-Engineering Reveals Long-Range Dependency Pitfallscited by 7
  31. 2024COMET: "Cone of experience" enhanced large multimodal model for mathematical problem generationcited by 6
  32. 2025Knowledge Augmented Complex Problem Solving with Large Language Models: A Surveycited by 6
  33. 2024Reasoning in Conversation: Solving Subjective Tasks through Dialogue Simulation for Large Language Modelscited by 5
  34. 2024TaskGen: A Task-Based, Memory-Infused Agentic Framework using StrictJSONcited by 5
  35. 2024CreDes: Causal Reasoning Enhancement and Dual-End Searching for Solving Long-Range Reasoning Problems using LLMscited by 5
  36. 2024RevOrder: A Novel Method for Enhanced Arithmetic in Language Modelscited by 3
  37. 2024Mars-PO: Multi-Agent Reasoning System Preference Optimizationcited by 3
  38. 2025Perspective Transition of Large Language Models for Solving Subjective Taskscited by 3

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