The classification of finite simple groups -- whether it be viewed as finished, or as a work in progress -- is (or will be) without doubt an enormous achievement. It clearly sheds a great deal of light on the structure of finite groups. However, as with the classification of simple Lie algebras, one might expect this to have a significant impact outside of the immediate subject. So what are some of the known, or expected, applications to the classification outside of finite group theory?
NB: This major edit is an attempt to extract what I'm guessing is the essence of the question. -D.A.
Extra edit by Will Jagy. First, quoting a comment below: $$ $$ To anybody who is considering casting the 5th and final vote to close: Please wait at least a day or so before doing so! Whether or not this question should be closed, there's not a great reason to get too hasty here. Kevin Lin.
Next, some rather negative comments you might be able to view below concern the initial version of the question, which one might be able to see by viewing the edit history.
To anyone who has doubts about the proof, please see http://ams.org/notices/200407/fea-aschbacher.pdf and do not debate that particular matter here.