Where can I find Einstein's proof of the existence of atoms? as the question states, where i can i find einstein's proof of the existence of atoms, and also, what math pre-requisites do i need to understand it deeply enough to be able to replicate it.
 A: The original paper is written in german and is called "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen". It was published by Einstein in 1905 in Annalen der Physik.
The translation of the title is "On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat". There is a full english translation of the paper avaiable here.
There is also an interesting wikipedia article about that paper.

In 1905, Albert Einstein proved the reality of these molecules and
  their motions by producing the first statistical physics analysis of
  Brownian motion. French physicist Jean Perrin used Einstein's
  results to experimentally determine the mass, and the dimensions, of
  atoms, thereby conclusively verifying Dalton's atomic theory.
Before this paper, atoms were recognized as a useful concept, but
  physicists and chemists hotly debated whether atoms were real
  entities. Einstein's statistical discussion of atomic behavior gave
  experimentalists a way to count atoms with an ordinary microscope.
  Wilhelm Ostwald, one of the leaders of the anti-atom school, later
  told Arnold Sommerfeld that he had been converted to a belief in atoms
  by Einstein's complete explanation of Brownian motion.
The paper also provided the best way up to that time of estimating
  Avogadro's Number—the corrected value from Einstein's paper was
  accurate to one significant figure.

