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Pythagoras Theories Research Paper

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Updated: Nov 15th, 2018


Pythagoras holds the distinction of holding three titles in modern thought. People consider him a mathematician, a philosopher, and a mystic. What is interesting about him is that it is difficult to put dates and places around him, despite the fact that he was one of the greatest mathematicians that ever lived.

He did not believe in writing down his discoveries, and those that he wrote did not survive. His was an oral approach to learning. Pythagoras studied under some of the most influential teachers of his time, and travelled the continents, thereby amassing knowledge from all parts of the world.

By the time he established a school, he was indeed, a very learned man. The mystery in Pythagoras, especially for a modern day audience is the way he found a way to connect religion and mysticism, with the facts of science and mathematics. It is almost impossible to maintain a consistent reputation as a mystic and as a mathematician in today’s professional environment. The goal of this paper is to examine the life of Pythagoras to uncover some of the important issues that his work brought about.

Brief History of Pythagoras

Pythagoras was born in Samos, hence the title, Pythagoras the Samian. It is almost impossible to pin down the exact year of his birth with different accounts giving various dates covering almost a quarter of a century in the early years of the fifth century BC. His father’s name was Mnersarchus, however there are claims that he was the son of the Greek god Apollo.

His family was moderately wealthy hence; they could afford an education for him. His first teacher was Pherecydes, who died when Pythagoras was eighteen. After pherecydes died, Pythagoras moved to the island of Lesbos to further his education under the teacher Anaximander. Anaximander was a philosopher and an astronomer.

Later on, he studied under Thales, a well-known mathematician and philosopher. Pythagoras travelled to Sidon, where he learnt about the mysteries of Tyre and Biblos, before going to Egypt under the teacher Thales where he spent twenty-two years. While there, he perfected his understanding of astronomy, mathematics, and philosophy. Pythagoras ended up in Babylon after the Cambyses captured Egypt.

While there, he studied with the Magi, and learnt about the Chaldean mysteries. After his Babylonian Stint, Pythagoras went through Persia into India, from where he left as a teacher after staying there for more than a decade. From India, Pythagoras travelled back to Europe and settled in Crotona. He then moved to his home town of Samos and established a school. It was while in this school that he came up with some of his most enduring teachings.

The Pythagoreans

Pythagoras established a religious order called the Pythagoreans. In this order, numbers were sacred and their basic belief was that everything in the universe had a mathematical relationship (Mandell 4). In this sense, they believed that mathematics was the absolute reality.

While this society became very influential in the area of mathematics, it remained secretive and did not publish its important findings. This is the main reason why there are no records in existence of the works of Pythagoras. The society had its own social norms. The most prominent of these was that it did not advocate for the consumption of animal-based food. This came about because of their belief in reincarnation.

While it was a very secretive group, they were unusually accommodative of women as compared to the general rules that governed social relations at the time. A woman in the group had the same rights and social position as a man. There are claims that the group practiced celibacy among its top leaders. However, Pythagoras himself married and had children, who ran the school after his death.

This type of secretive group seems to have inspired the foundation of the freemason movement, and in addition, it seems to have inspired the development of Plato’s republic. The Pythagorean order lasted for about one century after its founding and later on disappeared all together. At some point, due to political issues, the buildings of the school were lost to arsonists, with the claim that Pythagoras died in that fire. This is not the only claim to Pythagoras death.

Religious Beliefs

The Pythagoreans believed in reincarnation. This influenced their decision to avoid eating animal products. It is difficult to miss the correlation between this belief and Hinduism. Since Pythagoras spent a lot of time in India, it is possible that he built this belief while in that environment. In one of the later writings about Pythagoras, he believed that he was in his fourth reincarnation as a human being (Klauber 7).

Originally, he was the son of Apollo, the Greek god. The Pythagoreans believed that the soul was eternal and that it moved from one living thing to another upon death. In this sense, it was possible to reincarnate as an animal. This belief in animals possessing a soul formed the basis of their vegetarian lifestyle. There was an incident where Pythagoras claimed he identified the barking of a dog as the pleas of a former friend of his.

Pythagoras Theorem

The best-known theory in mathematics named after Pythagoras is the Pythagoras Theorem. This theorem claims that there is a fixed ratio for all right-angled triangles defined by the formula, a2+b2=c2. In this case, “a” and “b” are the length and the width of a triangle, which meet at a right angle, while “c” is the hypotenuse of the triangle. This theorem was in use by the Egyptians many centuries before hence its discovery cannot have been by Pythagoras.

However, it appears that the Pythagoreans were the first to prove it. It is not easy to tell whether it was Pythagoras’ work or whether it was the work of one of his students. It was customary at that time to credit the discovery of students to their teachers. This case also points further to the fact that Pythagoras benefitted a lot from the knowledge of the civilizations that he went to study.

Other mathematical relationships credited to the Pythagoreans include the fact that the first four numbers add up to ten. This relationship held special significance to this sect. In fact, they made a triangle based on it. The triangle held a central place in worship and they even took oaths in its name.

The triangle, known as a Tetractys or Pythagorean triangle is also the mystic triad. One of its modern appearances is in the Bishop’s coat of arms. There are Jewish Tetractys too, which incorporate the four letter of the Tetragrammaton that is the four letters of the name of Yahweh, in scriptures.

Other findings articulated by or credited to the Pythagoreans include the grouping of number into perfect numbers, odd numbers, and even umbers. Perfect numbers, according to the Pythagoreans, were those whose multiples added up to the number itself. The first perfect number is six. The multiples of six are one, two, and three. The sum of these multiples is six. Between one and ten thousand, there are four perfect numbers, six, twenty-eight, four hundred and ninety six, and the last one is eight thousand, one hundred and twenty eight.


While Pythagoras did a lot of work in mathematics, his influence seems greater in the area of philosophy. He had as many admirers as there were critics, with some agreeing with certain things and disagreeing with others.

His work influenced later thinkers such as Plato. Plato’s republic seemed to borrow many ideas from the Pythagorean organization as a model of how a society should work. Plato is one of the most influential philosophers; hence, by following the work of Pythagoras, it means that Pythagoras is the most influential philosopher of all time.


In the area of astronomy, there are significant contributions that the Pythagoreans made to the field. They seem to have been among the earliest scholars to discover that the world was actually round. This came about after observing the shadow of the earth on the moon during an eclipse. The basic belief that there was a mathematical relationship between everything in the universe made the Pythagoreans postulate that the planets revolved following a particular cyclic pattern.

While they did not provide final proof of this, they laid the foundation for later thinkers and astronomers to develop the modern concepts we now carry because of their work. Pythagoras is also responsible for observing that Venus in the morning is the same as Venus in the evening. Earlier, people thought that the two were distinct stars.


Pythagoras also had profound influence in the world of music. He related the sounds of three hammers pounding on an anvil in a blacksmiths shop to a mathematical pattern. Upon further investigation, he came up with musical notes based on a ratio of two to one. This work made it possible to develop some later day instruments and was especially useful in the renaissance period.

Important Observations about the Life of Pythagoras

The life of Pythagoras was an exceptional one. He had the rare opportunity of travelling and spending considerable time with some of the most influential thinkers of all time. He learnt the ways and the views of many societies, in Europe, Africa, and Asia. This gave him an overwhelming advantage over any other scholar in that day and time.

From his life, it is clear that the things one experiences and the teachers one sits under have a way of shaping the direction of professional living that a person settles for. Pythagoras acumen in mathematics and the sciences came about because he participated as a student of the best mathematicians of his time.

His religious beliefs, especially his belief in reincarnation must have been the result of his interaction with the Hindu faith in India. His idea that everything in the universe had a relationship betrays a Buddhist experience. The use of the elements of fire, earth, water, and wind as symbols of philosophy further proves this claim.

There are some important indicators that he was an independent thinker (Johns 42). The two important ones were his independent observations about the shape of the earth, and the place of women among the Pythagoreans. At that time, it was universal knowledge that the earth was flat hence there was no basis for thinking that it had any other shape.

The fact that the Pythagoreans entertained the thought means that Pythagoras was not satisfied with the things he knew. He sought to advance his knowledge. This also shows in the development of new views regarding mathematics and the interesting associations among numbers made bare by the Pythagoreans.

His views on women stand out because of the practice at the time that gave women second-class status. While the Greek society generally had more space for women compared to other cultures, it was still a very paternal society. It is not clear where Pythagoras got the idea that he could develop a society where women enjoyed similar status to men.

This in itself is very remarkable. However, he still had categories of students, with some enjoying greater privileges than other, remotely similar to the Hindu caste system. The difference though is that a student could grow from one stage to another.


There is nothing much today to show for the primary work of Pythagoras. In modern day science and mathematics, he could have fit within the ranks of professors, however, in his time; it seems he was more influential as a religious leader, a sage, or an ancient wise man. His beliefs, especially about reincarnation would require private observance if he lived today. However, his work in mathematics and philosophy would find a place in many institutions of higher learning.

Works Cited

Johns, Christopher. Becoming a Reflective Practione, Oxford: Blackwell-Wiley, 2009.Print.

Klauber, Martin I. “Continuity and Discontinuity in Post-Reformation Reformed Theology: An Evaluation of the Muller Thesis.” Journal of Evangelical Theological Society 33.4 (1990): 467-475.Print.

Mandell, Deena. “Use of Self: Contexts and Dimensions.” Mandell, Deena. Towards a Use of Self as Respectful Relations of Recognition, Toronto: Canadian Scholar’s Press, 2007. 1-20.Print.

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