Large Language Models (LLMs) demonstrate potential in the field of scientific idea generation. However, the generated results often lack controllable academic context and traceable inspiration pathways. To bridge this gap, this paper proposes a scientific idea generation system called GYWI, which combines author knowledge graphs with retrieval-augmented generation (RAG) to form an external knowledge base to provide controllable context and trace of inspiration path for LLMs to generate new scientific ideas. We first propose an author-centered knowledge graph construction method and inspiration source sampling algorithms to construct external knowledge base. Then, we propose a hybrid retrieval mechanism that is composed of both RAG and GraphRAG to retrieve content with both depth and breadth knowledge. It forms a hybrid context. Thirdly, we propose a Prompt optimization strategy incorporating reinforcement learning principles to automatically guide LLMs optimizing the results based on the hybrid context. To evaluate the proposed approaches, we constructed an evaluation dataset based on arXiv (2018-2023). This paper also develops a comprehensive evaluation method including empirical automatic assessment in multiple-choice question task, LLM-based scoring, human evaluation, and semantic space visualization analysis. The generated ideas are evaluated from the following five dimensions: novelty, feasibility, clarity, relevance, and significance. We conducted experiments on different LLMs including GPT-4o, DeepSeek-V3, Qwen3-8B, and Gemini 2.5. Experimental results show that GYWI significantly outperforms mainstream LLMs in multiple metrics such as novelty, reliability, and relevance.