AI-rithmetic
It addresses a fundamental weakness in AI systems for basic arithmetic, which is incremental as it focuses on error analysis rather than solving the problem.
The paper investigates why frontier AI models perform poorly at basic integer addition despite excelling at advanced mathematics, finding that accuracy degrades with more digits and that most errors are due to operand misalignment or failure to carry, with specific error rates for models like Claude Opus 4.1, GPT-5, and Gemini 2.5 Pro.
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.