An Apology of Pythagorean Mathematics

The paper emphasizes the role of ancient mathematics in the philosophical considerations in Pythagorean school and contains a reconstruction of some basic mathematical ideas giving reason for the explanation of many early-Pythagorean fragments. Some contributions to the discovery of incommensurability within Pythagorean school are presented. Their importance for mathematics cannot be overestimated. Then the course of mathematically oriented inquiries is set against some purely philological studies.