Pythagoras was an ancient Greek philosopher born in Samos (an island near Miletus, the famed “birthplace of Greek philosophy”) in 570 BC. He was famous throughout Greece as the leader of a religious community (the Pythagoreans), for his belief that the soul is immortal and in the possibility of reincarnation, as well as for maintaining that numbers are the fundamental principle of the world. He was a charismatic figure who combined mathematics, mysticism, science and religion together to create a way of life with a devoted following. Today, he is best known for his theory about the hypotenuse of a triangle ( a2 + b2 = c2), what is known as the Pythagorean theorem.

In Samos, Pythagoras studied the astronomy of Anaximander as well as the geometry of Thales, until leaving at the age of 40 when the tyrant Polycrates came to power. He traveled to Egypt and Babylonia, learning the belief of the immortality of the soul as well as the secret teachings and rituals of the Egyptian priests. He settled in Croton, a city in Southern Italy, where he would found his own religious community based on what he had learned.

Pythagoras’s belief in the immortality of the soul and the possibility of reincarnation was a huge break from tradition. The Greeks believed in the tradition of the 8th century poet Homer who believed that after you die, you go on to live an unfriendly, shadowy existence in the underworld (Tartarus). In contarst, Pythagoras optimistically believed that the soul does not go to the underworld, but instead is reincarnated in another life form (an animal or human). Based on this belief, it would be possible to have a good life after you die. With this belief along with his charisma, Pythagoras was able to both attract a devoted following as well as establish an influential position for himself in the political life of his new city.

Because of his belief in reincarnation, Pythagoras also maintained that what you do in this life will determine what happens to you after you die. As such, he created a way of life for himself and his followers that would allow the soul to be purified so that it could have the best reincarnation, and ideally would be able to break from the cycle of reincarnation altogether by uniting with the divine. This way of life brought about another important break from tradition. Instead of honoring the Gods with prayers and gifts, now the focus was on purifying oneself in order to influence what will happen to you when you die.

The way of life Pythagoras created involved a great deal of discipline and adherence to many rituals. For example, initiates had to complete a 5-year period of silence before being admitted into the select group of followers. Once inside, the akousmatikoi (“listeners”) had to keep silent about what they learned. The Pythagoreans were admired for their silence and self-control, which contrasted sharply with the Greek tradition of public speaking. The community was very loyal to one another, performing may rituals as well as not doing many things that were considered taboo. For example, they performed sacrifices but were not to sacrifice a white cock. They would enter the temple barefoot, and there were restrictions on what you could wear and what you could eat, most famously the restriction on eating beans. The respect for animal life included vegetarianism. Many of these rituals (the acusmata, “heard things”) had also been performed in other places in the ancient world, and in particular in the Greek mystery religion known as Orphism.

Pythagoreas believed ritual alone was not enough to guarantee the best possible reincarnation. Along with his inner circle of his followers, the mathematikoi, they sought to understand the nature of reality. Pythagoras understood the soul to be made up of several parts that were in harmony (harmonia) with one another. Unfortunately, this harmony is negatively affected by the body. For this reason, since the soul is different than the body, instead being made up of the divine substance of the world, by coming to an understanding of the world one is able to purify the soul in preparation for its next life.

Pythagoras’s understanding of the world was rooted in his interest in numbers and belief that all things participate in simple, yet profound mathematical relationships. Pythagoras recognized that the concordant intervals of the music scale (octave, fifth and fourth) correspond to ratios of whole numbers, specifically 2:1, 3:2, and 4:3. He therefore saw mathematics and the relationship between numbers as the basis for harmony in the world. Just as music was harmonious, so was the soul, and so too was the entire world. He believed the planets were in harmony too, what is known as “the music of the spheres.”

Along with his followers, Pythagoras revered numbers as things in and of themselves. The Greeks used arithmetic in trade, for example: 2 ships + 2 ships = 4 ships. But what Pythagoras did is he recognized mathematical relationships like this outside of a practical context. He thought about them abstractly: 2 + 2 = 4. He therefore viewed numbers as things. The pythagoreans would investigate the properties of numbers (“number theory”) such as even and odd, triangular, and prime numbers. Pythagoras even gave numbers personalities, considering them masculine or feminine, perfect or imperfect, and beautiful or ugly. The first 4 whole numbers: 1, 2, 3, 4 (tetraktys, coming from the concords sung by the Sirens of Greek mythology) were favored as well as most prominently the number 10 since 1 + 2 + 3 + 4 = 10. Pythagoras is also credited for recognizing the existence of irrational numbers (ex: the square root of 2).

Pythagoras’s understanding of the world (cosmology) believed everything participates in numerical relationships. He saw all of reality, the One, as being comprised of odd and even. His teacher Anaximander believed the fundamental principle of the world was what he called the apeiron (meaning “unlimited”). Pythagoras believed that in addition to the unlimited there is also the limited, and it’s the limiting of the unlimited that helps us understand the world. Odd and even, limited and unlimited, as well as other pairs (10 in total) allow us to account for how all the things of the world relate. Medicine, for example, was an understanding of how the opposites hot and cold affect the body.

Unlike his teacher, Pythagoras did not believe the earth was the center of the universe. He held that the center is the most respected place, and therefore the sun should be there and not the earth since fire is purer than earth. While we know Pythagoras was correct, the earth was still believed to be the center of the universe until the Copernican revolution of the 16th century.

Pythagoras’s teachings have been very influential on later developments in philosophy. He influenced Plato’s understanding of the soul as distinct from the body and his understanding of the soul’s ability to unite with the divine, his understanding of a ““tight organized community of like-minded thinkers” that Plato describes in the Republic, his tri-partite division of the soul in the Phaedo, the cosmological mythologies included at the end of the Gorgias, Republic and Phaedo as well as in the Timaeus, as well his emphasis on math and the use of abstract thinking as a basis for thinking philosophically, scientifically, and morally.

Additionally, Pythagoras’s followers continued for a 100 years after his death, as well as would inspire a neo-pythagorean movement and deeply influence the neoplatonic movement. Him and his community would also inspire future esoteric traditions that emphasized the study of mathematics including the Roiscurians and Freemasons. Pythagoras demonstrated the unity between myth and philosophy, religion and science, and mysticism and mathematics possible in his time.