# AI-rithmetic

arXiv: https://arxiv.org/abs/2602.10416 · HTML: https://mlsanity.com/paper/2602.10416/

## Key facts

- Cited by 1 papers 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 (most cited first, 30 of 31)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [Thinking Like Transformers](https://mlsanity.com/paper/2106.06981/) (2021)
- [Investigating the Limitations of Transformers with Simple Arithmetic Tasks](https://mlsanity.com/paper/2102.13019/) (2021)
- [Teaching Arithmetic to Small Transformers](https://mlsanity.com/paper/2307.03381/) (2023)
- [Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs](https://mlsanity.com/paper/2402.14903/) (2024)
- [Arithmetic Without Algorithms: Language Models Solve Math With a Bag of Heuristics](https://mlsanity.com/paper/2410.21272/) (2024)
- [A Mechanistic Interpretation of Arithmetic Reasoning in Language Models using Causal Mediation Analysis](https://mlsanity.com/paper/2305.15054/) (2023)
- [Transformers Can Achieve Length Generalization But Not Robustly](https://mlsanity.com/paper/2402.09371/) (2024)
- [Transformers Can Do Arithmetic with the Right Embeddings](https://mlsanity.com/paper/2405.17399/) (2024)
- [Limitations of Language Models in Arithmetic and Symbolic Induction](https://mlsanity.com/paper/2208.05051/) (2022)
- [Language Models Use Trigonometry to Do Addition](https://mlsanity.com/paper/2502.00873/) (2025)
- [GPT Can Solve Mathematical Problems Without a Calculator](https://mlsanity.com/paper/2309.03241/) (2023)
- [Positional Description Matters for Transformers Arithmetic](https://mlsanity.com/paper/2311.14737/) (2023)
- [Interpreting and Improving Large Language Models in Arithmetic Calculation](https://mlsanity.com/paper/2409.01659/) (2024)
- [Language Models Encode Numbers Using Digit Representations in Base 10](https://mlsanity.com/paper/2410.11781/) (2024)
- [Language Models Do Hard Arithmetic Tasks Easily and Hardly Do Easy Arithmetic Tasks](https://mlsanity.com/paper/2406.02356/) (2024)
- [How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs](https://mlsanity.com/paper/2410.13857/) (2024)
- [Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning models](https://mlsanity.com/paper/2303.07735/) (2023)
- [Arithmetic Reasoning with LLM: Prolog Generation & Permutation](https://mlsanity.com/paper/2405.17893/) (2024)
- [The Lookahead Limitation: Why Multi-Operand Addition is Hard for LLMs](https://mlsanity.com/paper/2502.19981/) (2025)
- [Arithmetic with Language Models: from Memorization to Computation](https://mlsanity.com/paper/2308.01154/) (2023)
- [Language Models are Symbolic Learners in Arithmetic](https://mlsanity.com/paper/2410.15580/) (2024)
- [Lost in Transmission: When and Why LLMs Fail to Reason Globally](https://mlsanity.com/paper/2505.08140/) (2025)
- [Do Large Language Models Truly Grasp Addition? A Rule-Focused Diagnostic Using Two-Integer Arithmetic](https://mlsanity.com/paper/2504.05262/) (2025)
- [OccamLLM: Fast and Exact Language Model Arithmetic in a Single Step](https://mlsanity.com/paper/2406.06576/) (2024)
- [Modular Arithmetic: Language Models Solve Math Digit by Digit](https://mlsanity.com/paper/2508.02513/) (2025)

## Built on by (most cited first, 1 of 1)

- [Scaling of Capability and Efficiency at Inference Time in Large Reasoning Models](https://mlsanity.com/paper/2609.27166/) (2026)

## 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.