0, 1, 2, 3

Numbers and their operations or Arithmetic have emerged out of the need to count and record. So Numbers can be regarded as the starting point of Mathematics from a historical point of view at the least. This point of view puts Number Theory at the foundation of Mathematics. Lets call this step as One.

Mathematical Logic and Set Theory are closely related yet separate fields. They have always been there in Mathematics but it took time to establish them as distinct fields. Lets call this step as Two.

When One and Two are defined like this, Three becomes obvious; Analysis, Algebra and Geometry. Written as a stack;

(Number Theory, 

(Mathematical Logic, Set Theory), 

(Analysis, Algebra, Geometry))

This implies an obvious question; What would be the ground that is Zero? It exists in every mathematical field in different forms and as '0' in Number Theory and null set '{}' in Set Theory. It took time to invent the number Zero and it has not been obvious that it simplifies Arithmetic. Even the ancient Greeks and Romans failed to invent or discover it. I will leave the naming of this field Zero out for the moment.

This (0, 1, 2, 3) classification of Mathematics rings an interesting bell; Hurwitz's (1, 2, 4, 8) theorem.