Proof of the Irrationality of the Square Root of Two in Babylonian   Geometry Problem Tablets
  One of the greatest achievements of Greek mathematics is the proof that the square root of 2 is irrational. It has not been thought that the Babylonians appreciated the concept of irrationality and certainly that they did not prove that the square root of two is irrational. Here we show that two Babylonian geometry problem tablets contain a simple proof of the irrationality of the square root of two. It is not known, as yet, if the Babylonians appreciated that these tablets indeed contained this proof. 
Benjamin M. Altschuler, Eric L. Altschuler
math.HO