Quite good article at exchristian.net, which kicks off by making an important distinction that most people unfamiliar with atheism overlook. In a nutshell: Contrary to popular belief, very few atheists are certain (in the mathematical sense) that God does not exist; rather, we believe that the very notion of there being a God is implausible. Since it is unsustainable to hold implausible beliefs, we are atheists. It really is that simple.
Most of the time people have this impression that atheists are absolutely certain about the non-existence of God since they claim to know that God does not exist, however this impression is misleading. While there are atheists who claim to be absolutely certain that God does not exist, not all atheists are like this. Most atheists are not committed to the view that the non-existence of God is some kind of axiomatic or self-evident truth… What most atheists would agree is that the belief in the existence of God is implausible, hence unreasonable belief. Most atheists do not feel compelled to produce and reproduce absolute proof that God does not exist; it would be self-defeating and futile to even try. This is because most things in life cannot be shown to be true by absolute proof, especially in science.