Concerning the proof that $\zeta(3)$ is irrational, Van der Poorten famously noted that

"*Apéry's incredible proof appears to be a mixture of miracles and mysteries*".

Indeed, many ideas introduced in Apéry's proof such as $\zeta(3)=\frac{5}{2} \sum_{k=1}^{\infty}{\frac{ (-1)^{k-1}} {\binom {2k}{k}k^{3}}}$ and the recurrence $n^3u_n + (n-1)^3 u_{n-2} = (34n^3-51n^2+27n-5)u_{n-1}, n\geq2$ amazed contemporary mathematicians (although the fast-converging series was already derived several years earlier by Hjortnaes).

What are other examples of "miraculous" proofs, whose ingredients amazed mathematicians of their time? In particular, proofs such that:

- a large portion of the Theorems involved in the proof represent entirely new ideas,
- these Theorems are applicable to a wide area of mathematics,
- the general atmosphere among contemporary mathematicians was a mixture of surprise and awe ("
*where did this come from?*").