Atomic Thinking of LLMs: Decoupling and Exploring Mathematical Reasoning Abilities

Large Language Models (LLMs) have demonstrated outstanding performance in mathematical reasoning capabilities. However, we argue that current largescale reasoning models primarily rely on scaling up training datasets with diverse mathematical problems and long thinking chains, which raises questions about whether LLMs genuinely acquire mathematical concepts and reasoning principles or merely remember the training data. In contrast, humans tend to break down complex problems into multiple fundamental atomic capabilities. Inspired by this, we propose a new paradigm for evaluating mathematical atomic capabilities.