ToolMATH: A Math Tool Benchmark for Realistic Long-Horizon Multi-Tool Reasoning

We introduce \ToolMATH, a math-grounded benchmark that evaluates tool-augmented language models in realistic multi-tool environments where the output depends on calling schema-specified tools and sustaining multi-step execution. It turns math problems into a controlled, correctness-checkable benchmark with tool sets, enabling systematic evaluation of model reliability under (1) large, overlapping tool catalogs and (2) the absence of the intended capability. \ToolMATH provides actionable diagnostic evidence of failure modes in tool-augmented agents, helping identify the control mechanisms required for robustness. \ToolMATH roughly contains 8k questions and 12k tools; we provide an additional hard-set \ToolMATHHard with questions and tools. Our evaluation reveals that the key failure factor is due to the inability to reason, leading to the accumulation of intermediate results' errors and constrain later decisions. Tool-list redundancy do not simply add noise, but amplify small early deviations into irreversible execution drift. The benchmark highlights that when the intended capability is missing, distractor tools can sometimes serve as partial substitutes in solution paths, yet they can also mislead models into ungrounded tool trajectories. Finally, comparisons between tool-use protocols emphasize that improvements come less from local action selection and more from long-range plan coherence and disciplined use of observations.