I am looking for a reference or short explanation of a proof by E. Brieskorn.

In his famous work "Singularities of complex hypersurfaces" Milnor proves that the (nowadays called) Milnor Number (in the sense of the local degree) of a polynomial $f\in\mathbb{C}{[X_1,X_2,...,X_{n+1}]}$ with an isolated singular point at the origin coincides with the $n$-th Betti number of the fibers of the corresponding Milnor fibration.

Himself remarks that Brieskorn "[...] has recently given a simple proof[...]" of this Theorem "[...] which is quite different from the one [...]" he presents and I'm looking exactly for this Proof. Milnor might mean Brieskorn's dissertation as I was told, but I do not have any access to this work. So I wonder if someone else published an at least related version of this proof.

Is it about perturbing the singularity to non-degenerate singularities?