Full Idea
The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms.
Gist of Idea
Set-theory gives a unified and an explicit basis for mathematics
Source
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
A Reaction
I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape.