Usually if you want to prove something you have to either
a) Show a single case (or more) that contradicts said proposition
b) Show that case is true by exhaustion (assuming proposition encompasses a finite range of states)
c) Prove the general case logically
With regards to the above you can also do the following:
d) Assume that said proposition is false and arrive at a contradiction
In the realm of science the easiest thing to do is to cleverly do a). b) often won't prove something but it will instill confidence that something may indeed be true. c) is pretty much impossible at least at the stage of human intellect now.
Another thing to remember is that the scientific method is actually relatively young. Not long ago people use to burn witches at the stake, thought that the Earth (and sometimes themselves) were at the centre of the universe, and that the Earth was flat.
Deny it or not, we still possesses the same kind of thinking that we did back in the days of witch hunts, but thankfully not to the same degree.
There's a book by a Physics Professor at Tulane university (if he is still there) called the Physics of Immortality which is an exposition of how modern physics supports the ideas of immortality. I'm not a physicist though so I can't comment on its authenticity or soundness of argument.
I have however read a series of books called Conversations with God and there was something very interesting in that book. As a quick background to the series, there is a guy called Neale Walsch who claimed to have god communicate with him where he wrote down things unconsciously that God was telling him.
For the moment let's suspend our disbelief and listen to what he has to say and not "shoot the messenger" immediately.
There was something that he mentioned about what God actually is. Basically he said that God is an entity that divides itself eternally and comes into existence to experience itself.
What was actually interesting to me as someone who studies mathematics was what he said about the process behind the experience:
He said that in order to experience something, you need to experience something as well as its complement. So its like in set theory you have an experience and its complement within some universal set.
A conjecture based on what he said can be that God is essentially this being that is aware of the universe of all experience in which they (it?) choose to experience all that is based on the specific experience and its complement.
The argument he gave for the complement is basically the same idea as a fish not knowing they are in water until someone scoops them up and puts them on land.
Now whether the guy went through a religious experience, made it up creatively or not in his head, or is trying to cash in on vulnerable people is one thing. But some of the ideas in his series of books including this one in my mind is incredible and for the moment I will suspend my disbelief but at the same time not turn myself over to him (ie idolize)
