AI-rithmetic
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Abstract (arXiv)
Modern AI systems have been successfully deployed to win medals at international math competitions, assist with research workflows, and prove novel technical lemmas. However, despite their progress at advanced levels of mathematics, they remain stubbornly bad at basic arithmetic, consistently failing on the simple task of adding two numbers. We present a systematic investigation of this phenomenon. We demonstrate empirically that all frontier models suffer significantly degraded accuracy for integer addition as the number of digits increases. Furthermore, we show that most errors made by these models are highly interpretable and can be attributed to either operand misalignment or a failure to correctly carry; these two error classes explain 87.9%, 62.9%, and 92.4% of Claude Opus 4.1, GPT-5, and Gemini 2.5 Pro errors, respectively. Finally, we show that misalignment errors are frequently related to tokenization, and that carrying errors appear largely as independent random failures.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 31 of its 38 references that are in the map. First posted on arXiv 11 Feb 2026.
Builds on
31 of 38 references.
References · 31
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- 2021Investigating the Limitations of Transformers with Simple Arithmetic Taskscited by 139
- 2023Teaching Arithmetic to Small Transformerscited by 123
- 2024Tokenization counts: the impact of tokenization on arithmetic in frontier LLMscited by 115
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- 2024Transformers Can Achieve Length Generalization But Not Robustlycited by 86
19 more
- 2024Transformers Can Do Arithmetic with the Right Embeddingscited by 78
- 2022Limitations of Language Models in Arithmetic and Symbolic Inductioncited by 71
- 2025Language Models Use Trigonometry to Do Additioncited by 70
- 2023GPT Can Solve Mathematical Problems Without a Calculatorcited by 68
- 2023Positional Description Matters for Transformers Arithmeticcited by 56
- 2024Interpreting and Improving Large Language Models in Arithmetic Calculationcited by 45
- 2024Language Models Encode Numbers Using Digit Representations in Base 10cited by 32
- 2024Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Taskscited by 24
- 2024How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMscited by 24
- 2023Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning modelscited by 18
- 2024Arithmetic Reasoning with LLM: Prolog Generation & Permutationcited by 17
- 2025The Lookahead Limitation: Why Multi-Operand Addition is Hard for LLMscited by 15
- 2023Arithmetic with Language Models: from Memorization to Computationcited by 12
- 2024Language Models are Symbolic Learners in Arithmeticcited by 11
- 2025Lost in Transmission: When and Why LLMs Fail to Reason Globallycited by 9
- 2025Do Large Language Models Truly Grasp Addition? A Rule-Focused Diagnostic Using Two-Integer Arithmeticcited by 8
- 2024OccamLLM: Fast and Exact Language Model Arithmetic in a Single Stepcited by 7
- 2025Modular Arithmetic: Language Models Solve Math Digit by Digitcited by 6
- 2025On Learning-Curve Monotonicity for Maximum Likelihood Estimatorscited by 3
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Citing papers per year: 2026: 1.
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