tetraktys

The tetraktys is a mystical concept in Pythagorean philosophy that emphasizes the significance of numbers. It represents the sum of the first four integers (1 + 2 + 3 + 4 = 10), which was considered the most perfect number. This numerical arrangement, often visualized as a triangle, held cosmic importance and was linked to the harmony of the cosmos.12

Pythagoreans believed that "things are number" or resemble number, suggesting that reality is fundamentally mathematical. This idea influenced their understanding of music, where basic intervals like the octave, fifth, and fourth correspond to simple numerical ratios. They also applied numerical symbolism to abstract concepts and geometrical figures, seeing numbers as the underlying structure of the universe.134