In 18th century, Euler solved a pretty hard problem that even Leibniz cannot solve it, either. This problem made him become very famous and confident. This problem shows . It is a wonderful theory, and we can use it to get more interesting results.
It is true that Basel problem has to do with Riemann function, because Basel problem is in order to find . About 100 years later, Riemann used one equation to build a bridge between functions and prime numbers. The equation is . Here is Euler's proof.