Hilbert famously said

> 
> The art of doing mathematics consists in finding that special case which contains all the germs of generality.
> 
> 
> 

Can you give an example of a situation in mathematics where this quote applies? I don't remember many situations like this where finding the special case was really the essential core of the argument. I wonder why Hilbert gives such a significance to finding the special case -- in my opinion the creativity mostly lies somewhere else. But since it is Hilbert, there must me something to this quote, and I want to understand it.

Question can possibly be community wiki.

I just saw [Examples for Hilbert's Quote](https://math.stackexchange.com/questions/1806153/examples-for-hilberts-quote/1806167#1806167) but the answers there do not seem satisfactory: they (at least to me) don't indicate why finding special cases containing all generality is *that* important that Hilbert puts so much significance to it.