The numbers-doctrine of the Pythagoreens
Aristoteles sums up the basic views of the Pythagoreens this way:
"As the pythagoreens realized that he characteristics of harmonies are determined by numbers and as to them it seemed, that all the other things reproduce numbers and numbers are the first thing in nature, they believed that the elements of numbers were also the elements of things. Consequently the whole sky was harmony and number."

The elements of cognition and of being are contained in the first four numbers:

1 One means the absolute beginning and origin, on which all numbers are based; One means the unity in itself, the Unchangeable. The one starts the series of numbers without losing value; One is the symbol of God
2 With two everything starts that is different from one, it's the symbol of difference, diversity and none-identity One and two behave like opposites: light and darkness etc.
3 The connection of one and two makes three as the symbol of synthesis, totality, connection (1 + 2 = 3) and established entirety
4 Four is the holy root of the world,
the primeval sign of proportion: a:b = c:d.
There are four seasons, four basic substances, four saps of the body
5 As in geometry five regular solid bodies were found (tetraeder, cube, octaeder, dodecaeder, icosaeder, ... the five platonic solid bodies), they also gave the five a special importance.

links:
The five platonic solid bodies and their meanings.
(according to Johannes Keppler, Weltharmonik, 1619)
1. octaeder (= air)
2. tetraeder (= fire)
3. dodecaeder(= sky, the entire world)
4. hexaeder (= earth)
5. iocsaeder (= water)

The "tetractys", the sum of the first four numbers: 1 + 2 + 3 + 4 = 10 not only makes the basic number of our system of numbers, it also contains according to the view of the Pythagoreens the basis of the world (that the reason why it was called the "vow of the Pythagoreens")

The graph of ten as figurated (triangle) number again shows this connection (to the whole Greek mathematics there was a close connection between abstract theory of numbers and geometric experience):

in addition it was thought that one was assigned to the point,
two to the line,
three to the area,
and the four to bodies (especially pyramids).

world's secret (picture)