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By studying the sources of the origin of mathematics, we inevitably come to Pythagoras and his doctrine, named the Pythagoreanism (see Wikipedia article Pythagoreanism, the Free Encyclopedia). As mentioned in Wikipedia, the Pythagoreanism originated in the 6th century BC and was based on teachings and beliefs of Pythagoras and his followers called the Pythagoreans. Pythagoras established the first Pythagorean community in Croton, Italy. The Early Pythagoreans espoused a rigorous life and strict rules on diet, clothing and behavior.

According to tradition, Pythagoreans were divided into two separate schools of thought: the mathematikoi (mathematicians) and the akousmatikoi (listeners). The listeners had developed the religious and ritual aspects of Pythagoreanism; the mathematicians studied the four Pythagorean MATHEMs: arithmetic, geometry, spherics, and harmonics. These MATHEMs, according to Pythagoras, were the main composite parts of mathematics. Unfortunately, the Pythagorean MATHEM of the harmonics was lost in mathematics during the process of its historical development.