This paper introduces MatEvolve, a novel framework for materials design that leverages a synergistic approach combining symbolic manipulation with large language models (LLMs). The core idea is to shift away from traditional enumeration-screening methods towards an insight-exploration-validation paradigm. MatEvolve employs a domain-specific language called Material Edit Language (MEL), which allows for precise, atom-level modifications of material structures. The framework is composed of three main components: MEL, a Material Edit Base (MEB) that stores expert knowledge in MEL format, and a Material Evolution Engine (MEE) that orchestrates the design process using a two-stage exploration strategy. The MEL provides a structured and interpretable way to represent and manipulate material modifications, addressing the limitations of coarse representations like SMILES or direct CIF manipulation. The MEB integrates expert knowledge, enhancing the LLM's ability to guide material design. The MEE employs a two-stage exploration strategy, balancing broad exploration with deep optimization, which is crucial for navigating the vast chemical space. The authors demonstrate the effectiveness of MatEvolve on two materials design tasks: solid-state electrolytes and electrode materials, showing significant improvements over baseline methods. The experimental validation focuses on optimizing material properties relevant to these applications, such as ionic conductivity and stability. The paper presents a compelling approach to materials design by combining the strengths of symbolic manipulation and LLMs, offering a structured and efficient way to explore the complex chemical space. The results suggest that MatEvolve can effectively discover materials with improved properties compared to traditional methods, highlighting the potential of this approach for accelerating materials discovery. The authors also provide a comparison of different LLMs, showing that MatEvolve is effective with various models, including open-source alternatives. The paper's contribution lies in its novel framework that integrates symbolic manipulation with LLMs for materials design, providing a structured and efficient approach to materials discovery. The use of MEL, MEB, and MEE, along with the two-stage exploration strategy, demonstrates a well-designed system for navigating the complex chemical space. The experimental results on solid-state electrolytes and electrode materials further validate the effectiveness of the proposed framework.