mathematics as a universal language

It has often been pointed out that despite the great differences between cultures and natural languages on Earth, mathematics is the same the world over. In fact, scientists are inclined to believe that mathematics and the mathematical rules which underpin nature are universal, so that all intelligent races in space have at least this much in common. Since the fundamental properties of numbers are the same everywhere, these can be used as the basis of interstellar messages. Binary numbers and prime numbers, in particular, being so fundamental, are considered to be of great importance in SETI. They underpinned the Arecibo Message and provided the initial clues to the decipherment of the alien signals in Carl Sagan's Contact and Fred Hoyle and John Elliot's A for Andromeda.