Science has grey areas; for example have you ever had the feeling that you are being watched? And you find out that you were, science cannot explain that feeling we have when we are being watched, almost like a six sense. If you think science has an explanation for this, it doesn't.
As for religion, let me change the question to can religion prove science? Hell no, they failed right on the first chapter of Genesis, if you consider the creation account to an allegory then you face the problem that original sin never existed, but you don’t have that problem if you convert to Judaism, circumcision anyone?. There is no point of thinking that the bible is its own stand-alone complex as it touches on history and miracles, and things that don’t add up. Many Muslims think that their holy books are correct, it’s just that science has not caught up to it, hey who knows maybe the earth really is flat after all lol.
In all science does not have all the answers but it's all we have, we can believe on what we know, religion on the other hand is quite the opposite, it’s a leap of faith, may the force be with you.