Let $P$ be a mathematical statement or a mathematical problem. I am looking for a couple of nice examples for $P$ that satisfy the following criteria:
Given two (or more) mathematical points of view on $P$, we find that one of them views makes $P$ easy to solve/prove and the other one makes $P$ hard to solve/prove.
$P$ should (at least from the easier point of view) be understandable by someone who studied maths obtained the basics and has a quiet good understanding of mathematical problems.
It shouldn't take to much text to formulate, since I don't have that much time and space to present it.
It would be nice if the problem is prominent and it is ok if the problem is not pure math but must have a clear link to maths.
Any ideas? A short explanation of the problem from the different angels is welcome and appreciated.
Edit: I forgot to mention that by different point of view I meant somethink like looking at $P$ from an algebraic point of view and from an analytical point of view and maybe from a topological point of view. I want to point out the awesome properties of maths to transform a hard problem to another theory where the problem is easily solvable.