AI-rithmetic

Alex Bie, Travis Dick, Alex Kulesza, Prabhakar Raghavan, Vinod Raman, Sergei Vassilvitskii

Keywords: Large language models, arithmetic

TL;DR: Frontier LLMs fail at basic arithmetic and most of their errors can be explained

Abstract:

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.

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Submission Number: 56