The reasoning ability of large language models (LLMs) can be unleashed with reinforcement learning (RL) (OpenAI, 2024; DeepSeek-AI et al., 2025a; Zeng et al., 2025). The success of existing RL attempts in LLMs usually rely on high-quality samples of large volumes. In this paper, we challenge conventional assumptions about data requirements in RL for LLMs by demonstrating the effectiveness of one-shot reinforcement learning. Specifically, we introduce polymath learning, a framework for designing one training sample that elicits multidisciplinary reasoning improvement. We present three key findings: (1) A single, strategically selected math reasoning sample can produce significant performance improvements across multiple domains, including physics, chemistry, and biology; (2) Analysis of salient mathematical skills provides insight into the characteristics associated with effective polymath samples; and (3) An engineered synthetic sample that integrates multidisciplinary elements and broader skill coverage achieves stronger performance than naturally occurring individual samples. Across various reasoning benchmarks, polymath learning achieves stronger performance than larger datasets, demonstrating that reasoning structure and skills in samples, rather than quantity, may be the key to unlock enhanced reasoning capabilities in language models. Our results suggest a shift, dubbed as sample engineering, toward precision engineering of samples that complements simply increasing data volume.

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