Postulates and axioms have been used as a means of knowledge since ancient times. The well-known ancient Greek thinkers Aristotle, Plato, Euclid, and others used this cognitive tool. As an example, we all know – Euclid’s postulates. Although mathematicians consider him the pioneer of mathematics, one of the most famous mathematicians, nevertheless, it is more appropriate to consider Euclid as a Greek philosopher, who presented the most important postulates and axioms in his book "Elements". The prevailing opinion is that in essence it is exactly enough to prove all mathematical statements. Even though that the most perfect axiomatics is classical Euclidian geometry, there is an alternative here, i.e., modern non-Euclidean geometry.