What is specified complexity? I've read several summaries of William Dembski's concept of specified complexity, including one by Dembski himself, and I've got to confess I have no idea what he is talking about.

Is it an attempt to prove God's existence mathematically?
It's an attempt to show that the universe, and all it contains, is too orderly to have originated by chance with no intelligent guiding force.  It simply implies an intelligent Creator, not necessarily the God of the Bible. 

In short, it's an argument for creationism, without naming the Creator explicitly, which is what Intelligent Design is.

It's not so much an attempt to prove his existence mathematically, it is, (depending on which side of the fence you sit on) more of:


using mathematics to imply His existence


or


use mathematics to show how His existence is implied by the evidence around us.