Brief steps about research that you need to know

You need to understand how complex your chosen subject is, for example, it will be much harder to learn topology than number theory or combinatorics as a high school student. My journey began with Martin Gardner’s Mathematical Circus which I found during 9th grade summer. The cyclic number 142 857 captivated me.
You need to read literature specifically focused on your topic, as well as several articles that represent the current state of research and review articles that provide a general overview for beginners. After exhausting Gardner’s book, I realized one source wasn’t enough to understand the hidden beauty of numbers. I expanded to works by Ian Stewart, Alex Bellos and Eugenia Cheng.
In my opinion, the most difficult part is finding a mentor. It took me over 3 months of writing emails and attending lectures and open classes by professors at various universities. Start with your school teachers. After over a hundred rejections, I connected with my mentor – I found him through a university professor, whom I found through my math teacher.

You need to narrow your focus to something concrete and manageable. My initial fascination with cyclic numbers was too broad. With my mentor’s guidance, I narrowed my focus to Kaprekar’s function and established my own.
Develop a clear plan for your methodology, timeline and necessary resources. Break down your timeline into specific phases: background research (3‑4 weeks), preliminary testing (4‑6 weeks), core research phase (8‑10 weeks), analysis (4 weeks) and paper writing (6‑8 weeks). Identify your requirements early to avoid delays.
Identify what tools you’ll need and develop proficiency in them. For my research, I needed to strengthen my mathematical foundation, computer science and LaTeX skills. I created small test cases to verify each property I discovered. The time spent building your knowledge base will make your actual research much more productive.

For more information about Research and all of the necessary steps as a beginner, I made an article with the 650magazine, which you can check out here.