Humans distill experience into reusable abstractions, e.g., strategies and cautionary reminders, and apply them to gradually solve problems more effectively. We study whether Large Language Models (LLMs) can similarly benefit from such experiential abstractions. From LLMs' solution traces on the MATH training set, a stronger teacher or the LLMs themselves extract natural-language abstractions into a retrievable library. We explore two usage modes: (1) inference-time retrieval and (2) reinforcement learning (RL) with abstraction-augmented training prompts. Experiential abstractions improve LLM performance on mathematical and logical reasoning benchmarks. Self-extracted abstractions match teacher-extracted ones, and our abstraction usage framework can transfer to other datasets and models. These findings suggest LLMs can extract and apply experiential abstractions much as humans leverage distilled experience.