1. Topic selection: Choose a challenging math problem or a new math field to explore.

2. Theoretical basis: Before starting the exploration, we need to understand the relevant mathematical theories and knowledge, so as to provide the basis for the follow-up exploration.

3. Breaking through traditional thinking: In the process of inquiry, we need to find methods different from traditional thinking, so as to create new thinking modes and ways to solve problems.

4. Creative thinking: Mathematical brain hole requires creative thinking, looking for new ways and methods of thinking, integrating different mathematical knowledge and theories, and opening up new fields of mathematics.

5. Stream-of-consciousness writing: When writing mathematical brain holes, you can use the skills of stream-of-consciousness writing to freely express your thoughts and thinking process, so as to better show your creative thinking.

6. Multi-faceted exploration: When exploring mathematical brain holes, we need to explore from multiple angles and find different solutions and ways of thinking in order to open up a broader field of mathematics.

7. Reasonably organize the article: When writing a math brain hole, you need to reasonably organize the structure and logic of the article and organically link all the parts, so as to better show your thinking process and creative thinking.