  We present a simple information theoretical proof of the Fueter-P\'olya
Conjecture: there is no polynomial pairing function that defines a bijection
between the set of natural numbers N and its product set N^2 of degree higher
than 2. We introduce the concept of information efficiency of a function as the
balance between the information in the input and the output. We show that 1)
Any function defining a computable bijection between an infinite set and the
set of natural numbers is information efficient, 2) the Cantor functions
satisfy this condition, 3) any hypothetical higher order function defining such
a bijection also will be information efficient, i.e. it stays asymtotically
close to the Cantor functions and thus cannot be a higher order function.
