# What are some proofs for which dramatically shorter alternatives were later published?

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?

• It would make more sense to ask for proofs that have not been simplified over the years. – franz lemmermeyer Jan 5 '17 at 11:46

Irrationality of $\pi$