On September 27, 1905, the physics journal Annalen der Physik received a three-page paper by Albert Einstein, titled Does the Inertia of a Body Depend Upon Its Energy Content. The answer, in the form the paper gives it, is that if a body gives off energy in the form of radiation, its mass diminishes by that energy divided by the square of the speed of light. The relation is E=mc2, though he did not write it in that form in 1905.
He was 26, living in Bern, and working as a technical expert third class at the Swiss Patent Office, examining patent applications, mostly about electromechanical devices for synchronising clocks. He had finished his doctorate at Zurich in April 1905. What he published that year is four papers, in the Annalen's volume 17, and they are the reason 1905 is called the miracle year.
The first, received in March, was on the photoelectric effect, proposing that light consists of quanta. The second and third, in May, were on Brownian motion, which settled the argument about whether atoms were real, and on special relativity, which set out the two postulates and their consequences for time and length. The fourth, in September, was this one, and it is a footnote to the relativity paper.
The argument is short. Einstein considered a body emitting two equal pulses of light in opposite directions, and compared the situation as seen from the body's own frame and from a frame in which the body is moving. Because the velocity of light is the same in both frames, the momentum carried away by the light is different in the two, and for momentum to be conserved the body's kinetic energy must change, which means its mass must change.
Its meaning took decades. The paper says that mass and energy are equivalent, and that a small amount of mass corresponds to an enormous amount of energy, because c2 is about 9 times 10 to the 16. Nobody could test it. Rutherford showed in 1919 that nuclear reactions release enormous energy, and the first direct confirmation came in 1932, when Cockcroft and Walton measured the energy released in splitting lithium and found it matched.
The applications came in 1938, when Hahn and Meitner found fission, and in 1945. Einstein himself had signed the letter to Roosevelt in August 1939 that led to the American bomb programme, and he did not work on it. He never received a Nobel Prize for relativity: the 1921 prize, awarded in 1922, was for the discovery of the law of the photoelectric effect.