How does verifying work. How is the mathematical puzzle created?

I’m mostly wondering what data is being used in order to create the mathematical puzzle that miners need to solve. What is that puzzle based on? Could the puzzle f.e. also be created by computing data from science projects like BOINC (https://boinc.berkeley.edu/) or am I misunderstanding this fully? (Got introduced to crypto 3 days ago)
Thanks for engaging 🙂