rStar-Math is a study aimed at demonstrating that small language models (SLMs) can match or even surpass the mathematical reasoning capabilities of OpenAI's o1 model without relying on more advanced models. This research employs Monte Carlo Tree Search (MCTS) to achieve 'deep thinking', allowing mathematical strategy SLMs to search based on a reward model guided by SLM. rStar-Math introduces three innovative approaches to address the challenge of training two SLMs, enhancing their mathematical reasoning abilities to a state-of-the-art level through four rounds of self-evolution and millions of synthetic solutions. The model significantly improved performance in the MATH benchmark tests and excelled in the AIME competition.