Mathematics starts with very simple rules ( called axioms ), from which more and more complex mathematical structures are developed.
The axioms for the set of natural numbers, were defined by Peano:
There exists a set N of natural numbers, which is defined by the following axioms:
- There exists a first number 1 in N
- any element n of N has a successor n+1
From these axioms follows:
- 1 has a successor 1+1 = 2
And from axiom 2 follows also, that there exist infinite many natural numbers.
- These axioms are very simple, but the structure of the set of natural numbers and the relations between them get very complicated.
- In Mathematics a whole theory, called Number Theory, is engaged, to study these relationships.
We can observe the same in physics:
- There exists only a small set of concepts and physical equations, with which most of the physical world can be described, not yet all physical phenomena, but phyiscs is still under development.
Similar it is in biolgy:
- With the concept of a cell, DNA and the postulates of evolution, quite a lot about living beings can be described.
And there exists the peculiar fact, that we can describe a lot of nature, using mathematics.
- All that supports the assumption, that there exist simple rules and some simple structures, from which all our universe and all living beings evolved over time.