The Classification of Finite Simple Groups (CFSG) is a highlight of 20th-century mathematics, both with respect to its mathematical content and to the complex process of proving the result. It is also known as " the enormous theorem", and it offers an excellent opportunity to focus on more general developments in the history of 20th-century mathematics, such as changing perceptions of what a mathematical proof is, the character and the many contexts of mathematics as an intergenerational and international collaborative enterprise, and the impact of Cold War research policies on CFSG/pure mathematics. We will discuss the history of the CFSG from the perspective of what we tentatively call "Big mathematics" and go into details on why we think this perspective gives new insights.