Einstein's equation doesn't have a "proof" because it's not a mathematical theorem.  It's a physical *theory* that is overwhelmingly supported by experimental data.

To understand Einstein's motivation for developing the theory of relativity, as well as [mass-energy equivalence][1], Wikipedia has an excellent article on the [history of relativity][2].


  [1]: http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence#History
  [2]: http://en.wikipedia.org/wiki/History_of_special_relativity