If you are a high-school student who is interested in joining either a software engineering project or to sneak into mathematics research I may have sth for you. (So far I only mentored students from Orange County, CA, but thanks to zoom it is easy to collaborate anywhere in the world.)
Btw, if you are wondering, yes, the math side and the software-engineering side are closely related, but that takes more time to explain.
If you want to learn how to make your own proofs in mathematics from a programming point of view the best starting point is the Lean Number Game and then the Lean Intro to Logic. If that appeals to you, get in touch and I can help you out with tips and background.
If you want to learn more traditional pen and paper mathematics, you can start on the exercises on Stone Duality. So far I only had one high-school student who got through this, so don’t hesitate to ask for help. It is worth the effort, there is much to learn here.
If you do both the math-as-programming and the pen-and-paper math, you will see that while closely related, there is a big gap between the two. To bridge this gap using machine learning tools (such as large language models) is a cutting edge research topic.
My interests in software engineering are currently evolving quickly. A recent summary I gave to my students in my Algorithm Analysis course is available here. I am interested in setting up software engineering projects that explore these questions.