Pythagoras of Samos

Year 10 Philosophy

Gabriella Ladu

The School of Athens. Pythagoras is seen in the bottom left-hand corner in a red robe writing in a book Source_1:

Section 1: Timeline of Pythagoras’ life

Section 2: Pythagoras’ Teachings

Pythagoras was considered to be the father of mathematics, but he also had important philosophical theories that we still use to this day. Pythagoras had many different theories in many different areas of study; music, mathematics, astrology, science, and cosmology; Pythagoras relates all of his theories back to his ideology that the foundations of life are built on the concepts of mathematics.

School of Pythagoras and Pythagoreanism

Pythagoras and the Pythagoreans Source_2:

In the 6th century BC, Pythagoras founded a school in Croton, Italy that was based on the ideology that the universe and all life functions were made from mathematics and numbers. The School of Pythagoras was as much a cult or religion as it was a school of mathematics. They lived by customs similar to the modern monastic way of life. Abiding by a strict code of conduct, the Pythagoreans lived with little to no personal possessions.

The Pythagoreans were categorized into two main schools of thought;
Mathematikoi: Learners and practitioners of Pythagoras’ mathematical and scientific theories
Akoustamakoi: Listeners and believers of Pythagoras’ more religious and spiritual thinkings.
The Mathematikoi were closely associated with a Pythagorean way of thinking, whilst the Akoustamakoi were disregarded as members of the Pythagorean society. The Mathematikoi became closely attached to the Platonic way of thinking and meshed Plato’s ideas with Pythagoras’.

The Pythagoreans were heavily restrained by vegetarianism because of Pythagoras theory of the transmigration of souls. The transmigration of souls is when the soul of a body passes through to another body; animal, human, or an inanimate object. This theory grounded many of the strange customs that were part of the Pythagorean cult. The Pythagoreans were not allowed to harm any living life form other than humans, in fear of hurting the soul of a friend or ancestor that they once knew. Pythagoras had once stopped an animal from being beaten and killed because he heard the cry of a dead friend. This leads him to his theory of metempsychosis otherwise known as the transmigration of souls.

Pythagoras had learned from his teacher, Anaximander, that the essence of a substance is described as ‘Apeiron’ which is an undefined infinite. The Apeiron, as believed by Pythagoras, inhaled the void from the outside filling the void with vacuous bubbles that split the universe into many interconnected parts separated by the void. Pythagoras proves again in this theory that numbers and mathematics constitute the true nature of things.

One strange custom that no one really understands is Pythagoras’ fear of beans. Pythagoras had banned the consumption of beans within his Pythagorean cult. Pythagoras believed that beans took away a part of your soul. It is assumed that Pythagoras died as a result of this fear or protection of beans. A few accounts of his death state that Pythagoras was running from a man who burnt his house but stopped in front of a field of beans. Pythagoras had let the man slit his throat so that he did not have to step on a single bean.

Mathematical Theories

Pythagoras’ central beliefs were that the essence of being is found in numbers and that this essence can be calculated through the study of mathematics. From Aristotle, we learn that Pythagoras believed everything that existed had a number so that aggregate of all things in the world is based on a system of numbers. The principles of Number form the principles of all things, and those things consist of an unlimited and limited element by which its being or essence is being constituted. In the Aristotelian Phraseology, we find that Pythagoras believed the indeterminate basis of being is the unlimited element in the principles of all things. The limited element is the principle in which the indeterminate reduces to a definite being. Both of these elements constitute the essence of any determinate object. This concept is also the basis of Aristotle’s Phraseologies, The Matter and The Form.

He believed that good health was based on the perfect balance of elements that an imbalance is what makes people unhealthy.

The number system is ultimately the universe system in the eyes of the Pythagoreans. Pythagoras numerical system was based on the sum of numbers one to four with the belief that odd numbers of masculine and even numbers were feminine.

A representation of Pythagoras’ Tetractys Source_5:

Tetractys is a sacred symbol of the Pythagoreans. The arrangement of the Tetractys symbolises the organisation of the universe and the cosmos. To the Pythagoreans, the number 10 was a number of the highest order and is of such divinity that it should be worshipped. The Pythagoreans had a specific prayer or ‘oath’ that they would swear by the number ten, “by that pure, holy, four-lettered name on high … to our mortal race did bring the Tetractys.” The Tetractys Pythagoras Mathematical theories to the theories and customs of his own religion.

The Pythagoreans would worship numbers as if they were Holy Beings. The number 7 was the number of wisdom and the number 8 was the number of justice. To the Pythagoreans, every part of math was holy, and when they discovered new theorems, they would sacrifice an ox to the Greek Gods.

One of Pythagoras most famous followers, Hippasus, is credited to the discovery of the first irrational number. Hippasus had found that the square root of 2 was irrational or never-ending. Pythagoras had always believed that any number or integer could be expressed as a fraction or ratio, but Hippasus had proven his teacher wrong. A boat outing with the Pythagoreans had lead to a gruesome death. Legend states that whilst Hippasus was discussing irrational numbers, Pythagoras attacked him until he fell overboard. Pythagoras then held Hippasus under the water until he stopped moving. This story was spread like a parable amongst the Pythagoreans, warning them that if they stepped out of line, they would have the same fate as their fellow follower.

Pythagorean Theorem as represented by circles Source_6:

Pythagorean Theorem is what we recognise Pythagoras and his students for discovering. This theory states that in any right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Section 3: Translation of Original Writings

Life of Pythagoras: Transmigration, Diogenes Laertius

Herclides Ponticus says that he was accustomed to speak of himself in this manner: that he had formerly been Aethalides, and had been accounted the son of Mercury; and that Mercury had desired him to select any gift he pleased except immortality. Accordingly he had requested that, whether living or dead, he might preserve the memory of what had happened to him. While, therefore, he was alive, he recollected everything; and when he was dead, he retained the same memory. At a subsequent period he passed into Euphorbus, and was wounded by Menelaus. While he was Euphorbus, he used to say that he had formerly been Aethalides, and that he had received as a gift from Mercury, the perpetual transmigration of his soul; so that it was constantly transmitting and passing into whatever plants or animals it pleased; and he had also received the gift of knowing and recollecting all that his soul had suffered in hell, and what sufferings are too endured by the rest of the souls.

But after Euphorbus died, he said that his soul had passed into Hermotimus; and when he wished to convince people of this, he went to the territory of the Branchidas, and going into the temple of Apollo, he showed his sheild, which Menelaus had dedicated there as an offering. For he said that he, when he sailed from Troy, had offered up his shield which was already getting worn-out, to Apollo, and that nothing remained but the ivory face which was on it. He said that when Hermotimus died he had become Pyrruhs, a fisherman of Delos; and that he still recollected everything, how he had formerly been Aethalides, then Euphorbus, then Hermotimus, and then Pyrruhs. When Pyrruhs died he, became Pythagoras, and he still recollected the cirmumstances I have been mentioning.

Herclides Ponticus explained Pythagoras’ theory of the Transmigration of Souls through his recollection of the previous lives that his soul has come from. Herclides was once Aethalides, the son of Mercury the Greek God, and that Aethalides could choose any gift he wanted from Mercury except for immortality. His gift was for his soul to remember all that it has been through, living and dead. Aethalides soul had then passed into Euphorbus, who was then badly beaten by Menelaus. Euphorbus had remembered he was once Aethalides and that Mercury’s gift was the transmigration of souls, and the recollection of the sufferings of his soul in hell and the sufferings of all the other beings that it has been a part of.

Once Euphorbus died, his soul was passed to Hermotimus. Hermotimus had tried to convince people of the concept of the transmigration of souls and traveled to Branchids, to identify a shield to Apollo by Menelaus which was during the time of Euphorbus lifetime. Herclides then went on to explain that Hermotimus had become Pyrrhus who was a fisherman of Delos. Once again, Pyrrhus had remembered that he was Aethelides and the gift from his father Mercury and that he then became Euphorbus, then Hermotimus, and then himself. Pyrrhus then became Pythagoras, whose theories matched with the stories of the people that he had previously been.

This particular piece of writing represents the fondness of Pythagoras by Herclides Ponticus. Pythagoras had his theory of the transmigration of souls which is explored through the original writings of Diogenes Laertius. This article is valuable to a modern reader as they develop a better understanding of the concept of the transmigration of souls through a story like recount of the lifetime of one soul.

Bibliography (2019). Pythagoras > By Individual Philosopher > Philosophy. [online] Available at: [Accessed 27 Mar. 2019].

Laertius, D., 2019. Life of Pythagoras: Transmigration. [online] Available at: <> [Accessed 27 Mar. 2019].

Anon, 2019. Pythagoreanism — By Movement / School — The Basics of Philosophy. [online] Available at: <> [Accessed 27 Mar. 2019].

Anon, 2019. Pythagoreanism. [online] Encyclopedia Britannica. Available at: <> [Accessed 27 Mar. 2019].

Anon, 2019. 10 Strange Facts About Pythagoras: Mathematician And Cult Leader. [online] Listverse. Available at: <> [Accessed 27 Mar. 2019].

Anon, 2019. Pythagoras. [online] Available at: <> [Accessed 27 Mar. 2019].



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