From Chains to Atoms: A Unified Math Agent with Atomic Capability-Grounded Reasoning

Mathematical reasoning serves as a critical testbed for LLMs, offering both ob- jectively verifiable outcomes and a wide spectrum of complexity. Despite recent progress, existing approaches remain fundamentally limited: (1) linear Chain-of-Thought scales by extending reasoning, often leading to overthinking and local optimality; (2) agent systems usually lack effective alignment of mathematical atomic capabilities between planning, execution, and feedback, preventing the specialized action of agent reasoning. We introduce AtomMath-Agent, a Unified Math Agent based on atomic capability-grounded reasoning unit, which comprises one mathematical atom-goal paired with an atomic capability. Agent's planner forms these units a dependency graph shared by planning, execution, and memory. The Planner specifies what mathematical capability is required, while Executor determines a capability-conditioned atom skill for how to realize it. The atomic unit also defines a verification protocol based on it mathematical atomic capability, which is used for feedback of results and dynamic planning of subsequent steps. This shared representation turns atomic reasoning into the organizing principle of the agent. Across seven backbones, AtomMath-Agent improves text-only and multimodal accuracy by 5.0 and 4.4 points on average. Tool-matched comparisons and controlled ablations further show gains and support the roles of atomic units and replanning. We further apply AtomMath-Agent to data synthesis and improve agentic mid-training, with the clearest transfer from math to other agent tasks. These results provide insights and demonstrate atomic capability-grounded reasoning as a unified thought for LLM-based agent community.