Einstein's derivation of E=mc^2 is not hard at all to follow. It is just a 3 steps high school math exercise which everyone fond of quoting this formular should first close exermine it. That is to say this derivation should be as famous as the equation itself. Infact you should examine it yourself and arrive at your own conclusion as to whether or not it is correct.

I will show you that Einstein's derivation is erroneous. It is not possible to derive E=mc^2 using Special Relativity (SR). It should be obvious because SR is a theory solely of objects moving close to the speed of light. So you cannot use this theory to derive state of matter at complete rest! You cannot understand the physics of stationary objects by thinking solely of dynamic objects while insisting that the physics of the latter is different from those of the former! Theoretical physicists admits that no one has ever correctly derived E=mc^2 solely from SR and that perhaps it is not possibly to derive it this way. Nevertheless they lie to the public that E=mc^2 is a product of SR! Here I will rub it in, without any political correctness. It is not that E=mc^2 is not derivable from SR. It is CONTRADICTORY to SR, and I will show it to you before your face!

In SR, due to 'time dilation', we know that frequency, f, transforms as f'/f=γ where γ=sqrt(1/(1-(v^2/c^2)) is called 'lorentz's factor'. That is to say if 'time pass slow', then 'things vibrate slow' as well, so that the frequency transforms in a way closely similar to how time transforms. Einstein uses his photo electric law, E=hf to suggest that light energy too transforms the same way as frequency, that is to say E'/E=γ. The Taylor expansion (or binomial expansion) of lorenz's factor is given by γ=1+v^2/2c^2+,....But you don't even need to understand the maths behind 'Taylor expansion' to understand my argument. The math, nevertheless is not hard to understand. For now, just accept that γ=1+v^2/2c^2+,...This is not disputed by anyone.

Einstein considered a stationary object with intrinsic energy, H0. It emits light simultaneously in two opposite directions. Each light carries an energy of E/2. So E is the total energy. Having emited energy E, H0 reduces by that amount and becomes H1. So H1-H0=E. Then Einstein thinks of another observer moving towards the object at speed v along a direction perpendicular to the emitted light. Because of time dilation and the fact that energy is related to frequency by E=hf, the moving observer sees a different energy E' while the stationary one sees E. In addition to that, the moving observer sees the object as though moving at v. So in his calculation of the total energy of the object before it emits the light, he includes the kinetic energy, 1/2m0v^2 and 1/2m1v^2 after the object emits the light. So he assumes that the emission of the light of energy E changes the mass from m0 to m1 (he assumes what we thought he was going to proove!) The following is the clearer calculation:

 Note:

1.In the first line, Einstein envisions what the stationary observer will see. He 'sees' the intrinsic energy change as the object emits energy E

2.In the second line, he insists that this is what the observer moving at v will see. He will see that the total energy in the system will include the object's kinetic energy and that emiting the light energy will reduce the object's mass.

3.In the third line, he rearanges the equation and then in the 4rth line,  replace E in the left as indicated in the first line. He also replace E' with its lorentz's transform after taylor expanding.

This reasoning is problematic because if some intrinsic energy, H gets converted to light energy, and the thus converted energy alters as seen in a moving frame, then so must H alter as seen from that moving frame. To see the error more clearly, let the stationary body emits the whole of H, which is theoretically possible. Perharps the best way to see this is to let H be the very light itself trapped in a box. You can think of two rays of light bouncing horizontally back and forth off perfectly reflecting walls. Then suddenly, the two rays escapes in opposite directions as the relativists envisions. It is not reasonable say that the light that has emanated off the box has different energy, E' as seen by the moving observer but the same light trapped in the box has the same energy H as seen by the same moving observer!

 Note that here, we repeat the same calculation but envisioning a case where the whole of intrinsic energy gets converted to light. This is to make the error easier to notice! The following is the correct way of 'deriving it'

Note the second line where H must also Lorentz Transform. If H is equal to E, then if E is transformed in the moving frame, then H must be similarly transformed!

But we can even turn Einstein's thinking right on its own head. Accordind to Einstein's disciples, H must be the 'mass' that is getting converted to energy. So we can replace it with mc^2:

So the problem is now even clearer! If the stationary object will convert its entire mass to energy, then we can surely replace H=mc^2 and we now see that by using the same same H in the moving frame, Einstein's unwittingly fails to factor in the relativistic transformation of m! According to the same relativity, the moving observer can never see the 'rest mass' of the stationary object. He must see the 'relativistic mass'. When we factor in the transformation of 'mass', we find the the assumtion that H=mc^2 leads to a contradiction. So it is a reductio ad absurd. So we have shown that E=mc^2 actually contradicts SR!