Sometimes a mathematical result is initially proved with a very long and convoluted argument, but later after the proof and truth is well-understood, a better, simpler proof of the same result will become apparent.
Are there any examples of problems which had huge first-proofs, but later insight yielded extremely short and elegant proofs?
Irrationality of $\pi$
The proof given by Lambert is long but Niven's proof is just a paragraph long.