Of course I can prove a negative, but never with 100% certainty, but with reasonable certainty. For instance, if you say there is an elephant in your garage, and I look for the evidences and find none, it is very reasonable to say that there is no elephant, because of the total lack of evidence. 99% of the things you do not believe is because of the lack of evidence for it.

And modern science is not a religion, because it cannot adopt dogmas, but only proven (reasonable) truths.