Einstein's theorem is in the last sentence of the following quote (bold) [1]:

"If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity

*v*along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by

*1/2 tv*(up to magnitudes of fourth and higher order),

^{2}/c^{2}*t*being the time occupied in the journey from A to B. It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and

**also when the points A and B coincide**."

This theorem is better known as the twin paradox. Einstein did not stop at a preliminary remark and wrote

in more detail:

"If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting

*t*seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be

*1/2tv*second slow. Thence we conclude that a balance-clock at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."

^{2}/c^{2}Each observer determines that all clocks in motion relative to that observer run slower than that observer’s own clock. If the moving observer returns to point A, he will notice the following: the clock at point A is slower than his own clock. but this clock shows that more time has passed since his departure than his own clock. For moving observers this conjucture makes no sense. If a clock is slower than its own clock, it should also show less time. Therefore, the clock in point A should be synchronized according to the rules of relativity ... but how?

[1] ON THE ELECTRODYNAMICS OF MOVING BODIES By A. EINSTEIN June 30, 1905.