On Pythagorean Numbers

Speusippus, a Greek philosopher and head of the Academy after Plato, wrote On Pythagorean Numbers. This work explored the significance of numbers, particularly the number 10, and their "perfections". Like other Pythagoreans, Speusippus emphasized numbers and numerical combinations, deemphasizing abstract ideas.12

Pythagoreanism posits that "things are number" or resemble number, meaning they are measurable and proportional. This philosophy also involved a doctrine of opposites, such as limit versus unlimited, and odd versus even, which they believed fit together to create cosmic order. The number 10, formed by 1+2+3+4 (the tetraktys), held particular cosmic significance. The Pythagoreans also associated numbers with abstract concepts like justice and marriage. Their work laid groundwork for later mathematical theories, including those concerning polygonal and irrational numbers.23456