This research paper explores autocurriculum, a training strategy that allows language models to autonomously identify and focus on the most challenging problems to improve their reasoning capabilities. By using an outcome verifier to prioritize prompts the model fails to solve, the authors prove that supervised fine-tuning requires exponentially fewer expert demonstrations than traditional non-adaptive methods. In the context of reinforcement learning, this approach decouples the computational cost of training from the quality of the initial reference model, significantly reducing the total number of reasoning traces needed. These theoretical improvements are achieved without making assumptions about problem difficulty or data distribution, relying instead on adaptive data selection inspired by classical boosting. Ultimately, the study provides a formal framework for understanding how self-designed curricula can make the development of high-performance reasoning models more statistically and computationally efficient.