When I did Project Euler, I couldn't come up with elegant solution that was derived from high enough abstraction using math, leaving me using brute force method

When I did Project Euler, I couldn't come up with elegant solution that was derived from high enough abstraction using math, leaving me using brute force method that was not really efficient. I was fascinated by how people come up with elegant math solution for the challenges in Project Euler. I am not sure how I can achieve such elegance, proving my math is insufficient for what can be done.