Oh dear - one of the problems with asking questions about things you barely know about is that the questions come out wrong and you can get dumped on. I hope this didn't put you off.
I feel this question is related to later ones so I figured I'd revisit it... some of what I will say will be repeats of what the others have said.
Stu21 said:
If Einstein taught us the space time is one and the same thing,
... well, the idea is commonly associated with him in popular science publications
then how did he mathematically prove that.
He didn't - he used the mathematical description of the idea to produce results that agreed well with experiments. You can mathematically prove all kinds of things that are not true in nature. This is why physics is an empirical science.
How did he put dimensions into his E=mc2 formula.
You mean the 4 space-time dimensions ... you can see from the formula that he didn't. But the links to the derivations the others have provided (above) should help you understand that.
The mass-energy relation is very famous but it is not the only relation concerning relativity.
The first 3 dimensions are strictly positions, positions in 3D require 3 numbers, and time is linear movement in one direction, the number being relative to whomever is making the measurement.
Technically the three position coordinates are also relative to whoever is doing the measuring so there is a similarity there. It is clear that we can express where and when something is by three position coordinates (x,y,z) wrt some origin (0,0,0) and one time coordinate t wrt whenever we started the stopwatch.
But it is clear that time, like this, is quite different - eg, the distance to a point (x,y) in space is \sqrt{x^2+y^2} but the distance to point (x,t)? You can't do: \sqrt{x^2+t^2} can you?
I have a feeling that this is what you are actually asking about.
In order to make time play well with the position coordinates, we have to measure time in units of length. That's not as silly as it sounds. We turn a time into a length by multiplying it with a speed ... unfortunately the speed of something is relative to the observer: if only there were some speed that was the same for all observers, then we could describe the space-time coordinates as (x,y,z,ct) - oh hey! :) Speed of light to the rescue!
Notice that the c in "ct" acts as a constant of proportionality relating one way of looking at something to another. It is as valid to think of time and distance as the same thing as it is to think of mass and energy as the same thing.
The trick with this sort of representation is you have to change the way a distance measurement is done ... the "distance" to an event in space-time is r=\sqrt{x^2+y^2+z^2-(ct)^2}
This should give you an idea of how time can get included as a dimension of space.
My notation is a bit sloppy - you should read more around the subject of space-time to get the conventions down properly. The idea here is to point you in a helpful direction to do your own searching, not to provide complete answers.
