PYTHAGORAS: BIOGRAPHY, PHILOSOPHY AND CONTRIBUTIONS - SCIENCE - 2024

Pythagoras of Samos (570 BC - 490 BC) was a pre-Socratic philosopher, considered the father of mathematics and the founder of Pythagoreanism, a philosophical movement. He contributed significantly to the development of the mathematical principles of his time, of arithmetic, geometry, cosmology, and music theory.

The doctrine of Pythagoras is a combination of mysticism and mathematics. The Pythagoreans were equally interested in religion and science, which were indivisible and were part of the same way of life. They were concerned with unraveling the mysteries of the universe and the destiny of the soul at the same time.

It should be noted that no original Pythagorean text has been preserved. Everything we know about him comes from secondary and sometimes contradictory historical sources.

In addition, the members of the society he founded, professing infinite admiration for their teacher, took on the task of attributing all the discoveries they made to him, as if it were a great collective entity.

Biography

The information on the life of Pythagoras is not very extensive, and the sources that are preserved do not have data that is verifiable.

Therefore, the information available about his career is based on elements extended orally, or through books written by great biographers of the time, such as the philosopher Iamblichus and the Greek historian Diogenes Laercio.

In relation to his birth, it is believed that Pythagoras was born on the island of Samos in the years around 569 BC.

Family

The data on who his parents were were obtained from the biographies made by the philosopher Porfirio and by Iamblico. Mnesarco was the name of the father of Pythagoras, who worked as a merchant in the Lebanese city Tire.

There is an anecdote told by Porfirio in which he indicates that Mnesarco had an important role at a time when a severe famine had struck the island of Samos.

Mnesarco arrived carrying a large quantity of seeds, which was beneficial and even saving for the people of Samos. As a result of this action, it is said that Mnesarco obtained the citizenship of this Greek island.

The mother's name was Pythais, and according to data found, it can be said that she was originally from Samos, the place where Pythagoras was born. As for her brothers, some sources indicate that she had two and others establish that she had three.

The first years of Pythagoras' life were characterized by being framed in many trips, as his father took him with him to the different destinations he visited thanks to his work as a merchant.

There is little information about their appearance and character at an early age. However, several sources have agreed to describe that Pythagoras had a large mole located on her thigh.

Education

Various sources suggest that Pythagoras was instructed from an early age. Among the learning that he is estimated to have obtained from a young age, the ability to recite texts by the Greek writer Homer, the ability to play the lyre and the skill in writing poetry stand out.

It has also been estimated that Pythagoras' father took him at some point to Tire, where he had the possibility of being educated by wise men from Syria, as well as by men from Chaldea, a name that the region located in the middle Mesopotamia obtained at that time..

There is other information that Mnesarco may have taken his son to Italy, with the same objective of giving him access to a good education.

According to the records found, Pythagoras had three teachers: Thales of Miletus, Anaximander and Pherecides of Siros. Among these three, Feréquides is the personage who is associated with Pythagoras in the most direct and usual way, since even historical texts usually refer to him as the teacher of Pythagoras.

Influence of his first teachers

Thales of Miletus was the first teacher that Pythagoras approached. Historical records estimate that the latter went to Miletus to visit Thales when he was between 18 and 20 years old. By this time Thales was quite advanced in age.

Despite this age difference, Thales managed to interest young Pythagoras in matters related to astronomy and mathematics, which aroused great curiosity in him and made a deep impression on him that marked his life.

It was precisely Thales who recommended to Pythagoras that he travel to Egypt, where he could deepen even more about all the teachings that the former was imparting to him.

Anaximander, who was a disciple of Thales, also had a presence in this context. In fact, Anaximander was the one who continued with Thales' school once he died.

When Pythagoras coincided with Anaximander, he was dedicated to giving talks on cosmology and geometry, topics that interested Pythagoras a lot.

Travels

The recommendation of his teacher Thales to travel to Egypt to continue deepening and strengthening his training was followed by Pythagoras, who also visited other countries such as Phenicia, India, Arabia and Babylon.

Some historical sources reflect that Pythagoras was a man who liked the fact of accessing the information from the source directly. That is why he insisted on traveling to all these countries and finding the roots of the teachings he was learning.

At the time this happened there was a friendly relationship between Samos and Egypt, promoted by the head of the Greek island, Polycrates of Samos.

War conflict

This harmonious atmosphere changed around 525 BC, when the then Persian king named Cambyses II carried out invasive actions in Egypt.

Pythagoras was in Egypt at this time, and some sources indicate that he was taken as a prisoner by Persian authorities and transferred to Babylon.

This occurred after the Battle of Pelusium, an encounter that was decisive for the Persians to seize Egypt.

While in Babylon, Pythagoras had access to different teachings. On the one hand, it is believed that it began in some sacred rites, and on the other, in Babylon it was able to delve into the teachings and mathematical approach that the Babylonians had developed long ago.

Cambyses II died in 522 BC, which may have been one of the reasons why Pythagoras regained his freedom. However, there is no concrete information that explains the reason for his release, if at all. In any case, after regaining his freedom, Pythagoras traveled to Samos.

Lessons learned

It is not known exactly how long it was before Pythagoras finally arrived in Crotona, but it is known that he lived through a series of events and situations from which he learned many elements that he then put into practice in his time in Italy.

For example, some information establishes that the sacred rites that Pythagoras learned were obtained as a result of his visit to various temples, as well as from his conversations with priests of different characteristics and with different approaches.

One of Pythagoras' maxims was to refuse to wear fabrics made from animal skins, as well as to promote vegetarianism as a way of life.

Likewise, both purity and secrecy were very marked aspects in his life and were penetrating his being in this time prior to his settlement in Crotona.

Influence of priests

In the same way, it is important to clarify that the fact that all this knowledge and ways of seeing life have been generated by the priests whom he visited is not proven.

Since there are not many records of the life of Pythagoras, it is very difficult to verify that indeed they were the greatest influence of this character at that time in his life.

There are even historians who believe that the mere fact of having been exposed to the reality of his time was enough for Pythagoras to develop this vision of life in himself.

First settlement

Shortly after returning to Somas after his time in captivity, Pythagoras traveled to Crete, where he devoted himself to studying the legal system of that city. After his short stay in Crete, he returned to Somas.

There Pythagoras created the school that was named Semicircle. According to historical accounts by Diogenes, this school focused on the discussion of political issues.

In addition, there was a private space for Pythagoras' reflections, which was located in a cave located on the outskirts of Somas. It is said that in this space he reflected more deeply on mathematics and its various uses.

Definitive settlement

In approximately 518 BC Pythagoras traveled to Crotona, in southern Italy, where he settled.

The city of Crotona became his teaching center, the place where he developed the so-called Pythagorean way of life.

There are two main versions that explain why Pythagoras chose Croton. One of these, exposed by the historiographer Diogenes, establishes that the main motive was to get away from Polycrates and his yoke.

Regarding this version, others point out that it makes more sense that Pythagoras tried to develop his approach on the island of Somas, but that there he did not have the acceptance he hoped for.

Likewise, both the Somas authorities and the citizens themselves demanded that Pythagoras be a participant in the political and public spheres, reasons that could have made him prefer to settle in another location.

Pythagorean school

In Crotona Pythagoras had many adherents and followers, who called themselves the matematikoi. These were members of the society that he created and they were characterized by living together, being vegetarians and having no private personal property.

It can be considered that the matematikoi were privileged, in that they had access to the teachings of Pythagoras. However, in order to receive these lessons they had to comply with fairly strict rules.

In addition to the matematikoi there was also an external group, called the accusmatists. These did not live with the former all the time, but lived in their houses and had their properties. They attended school during the day and it was not mandatory for them to be vegetarians.

Death of Pheecides and war

Years passed and the Pythagorean school continued to carry out its work. In 513 BC Pythagoras traveled to Delos, since his most emblematic teacher, Ferécides de Siros, was going through his last years of life.

Pythagoras stayed there for a few months, accompanying his teacher until his death. It was at that moment that he returned to Croton.

Some time later, during 510 BC, the city of Crotona attacked its neighboring city Sibaris. Crotona was the winner in this meeting and some authorities of Sibaris suspected that both Pythagoras and his society participated in some way.

Attack on school

Towards the year 508 BC the Pythagorean school suffered an attack by the noble Cilón, who turned out to be a native of Croton itself.

Cilón was a wealthy man with a certain despotic character who asked to enter the Pythagorean society. The latter did not allow him to society, given the personality he had.

Then, Cilón met with several friends, with whom they attacked not only the headquarters of the school, but also carried out a persecution of all members of Pythagorean society.

This harassment was so serious that the attackers' intention was to eliminate all followers of Pythagoras, including the same character.

Then, as a result of this attack, Pythagoras was forced to flee to Metaponto, in Italy, where he died.

As with other data related to the life of Pythagoras, there is no confirmed information to attest that this was the case.

In fact, other versions indicate that there was an attack carried out by Cilón, but they establish that it was not so serious, reason why Pythagoras could have returned to Crotona after having gone to Metaponto. According to these versions, the Pythagorean society lasted for many years after this attack.

Death

On the exact date of the death of Pythagoras there is also no specific verifiable information. Some authors establish that he died in the year 532 BC, but the information about the attack that Pythagorean society experienced in Crotona does not agree with this year.

On the other hand, other historical sources indicate that Pythagoras could have died rather around the year 480 before Christ, taking into account that he gave teachings to Empedocles, whose years of study were around this date.

In the time of Marco Tulio Cicero, the tomb of Pythagoras was presented in the city of Metaponto.

Philosophy

Pythagorean school

Pythagorean Society

The school founded by Pythagoras was religious and philosophical. More than 300 people became part of the group of the matematikoi, who led an ascetic life, were vegetarians and received the teachings directly through Pythagoras.

In addition to the matematikoi, there were also the accusmatics, who lived externally, without having to follow the strict laws that the matematikoi followed. These laws were as follows:

-Recognize that, in its deepest essence, reality is mathematical in nature.

-Understand that philosophy is a practice that can purify the spirit.

-Understand that the soul is capable of "rising", in order to gain that which is divine.

-Recognize that there are some symbols whose origin and essence are mystical.

-Accept that absolutely all members of society must be loyal to each other and must practice secrecy.

Secrecy

As a consequence of the secrecy of this society, it is not possible to know exactly which of the findings were made directly by Pythagoras and which were discovered by the members themselves.

Furthermore, according to the customs of Pythagorean society, all the discoveries that were carried out were attributed to Pythagoras.

It cannot be said with total certainty that all the findings had this philosopher as their author, especially since they involve areas as diverse as astronomy, mathematics and medicine, among other natural sciences.

However, it can be admitted that many of the discoveries were made by Pythagoras.

After 500 BC the Pythagorean society spread much more throughout the territory, even becoming a society with political interests. Later, society was divided based on different political approaches.

Forty years later, in 460 BC, the Pythagoreans were persecuted and annihilated. Its members were oppressed, as well as its headquarters and schools were looted and burned.

A particular case is popular in which more than fifty Pythagoreans living in Croton were ruthlessly annihilated. The few members who survived did so because they fled to other cities.

Thought

One of the main notions on which the philosophy of Pythagoras was based had to do with the destiny of the soul after death, since this philosopher offered a more optimistic vision.

In addition, another basic characteristic of his thinking was framed in the lifestyle he professed, which was disciplined and quite rigorous.

Although Pythagoras was an illustrious mathematician and many of his findings in this area were fundamental to human life, the area that made him most popular in the time in which he lived was religious.

In fact, that is the reason why the Pythagorean way of life is spoken of, because that was the approach that most stood out from Pythagoras and his teachings: it was about some precepts linked especially to reincarnation, immortality, various religious rituals and a disciplined and rigorous life.

Approach to society

The activities carried out by the Pythagoreans differed from those carried out by contemplative organizations, since the purpose of these was not to isolate themselves from society.

Instead, they rather sought to promote a new vision to approach this society, based on self-control and the constant search for balance and harmony. In the end, the goal of the Pythagoreans was to find a way to elevate character and cultivate a calm spirit.

In addition to this essential element, the teachings of Pythagoras generated specific reflections in different fields of action; This is why it is considered that this school encompassed so many elements and that its influence was very strong.

Findings of the Pythagorean school

Below we will describe the most important findings that the Pythagorean school was able to discover, taking into account the most developed fields of action:

Numbers

For the Pythagoreans, numbers were the basis for any effective approach to the real and true, to knowledge as such.

Reincarnation

There is evidence that supports that Pythagoras believed in reincarnation, since he considered that the soul was immortal and moved from one being to another.

Music

Pythagoras is also credited with discovering the relationships of the arithmetic domain that exist on the musical scale.

Music was of great importance to the Pythagoreans, who considered that it had medicinal properties in terms of generating harmony and well-being.

Math

Among the areas most studied by the Pythagoreans, mathematics stands out. Of course, the approach they practiced differs from what is normally taught in academies, since their main interest was not to find solutions to mathematical problems.

Instead, the Pythagoreans sought to dedicate themselves exclusively to reflecting on the principles of this science based on number.

As the Pythagoreans put it, all elements are, in essence, numbers. For this reason it was possible that they found the number within everything that surrounds the human being, including the universe, music and, in general, all things.

Contributions

Pythagoras theorem

The most famous contribution that Pythagoras has bequeathed is his famous theorem for calculating the squares of the sides of a right triangle.

The Pythagorean theorem was proven in the 6th century BC by the Greek philosopher and mathematician Pythagoras, but it is estimated that it may have been prior to its existence, or proved under another name.

The main importance of this theorem is that it allows us to find an unknown value if we know the other two. This feature allows it to be used in various disciplines and have different uses.

A series of complementary principles emerge from it, such as the ratio of the internal angles of a triangle. Also, it is one of the mathematical propositions that has more checks through many methods.

Other of the most relevant findings made by the Pythagoreans in the field of mathematics are the following:

-Analysis and reflection on geometric, harmonic and arithmetic means.

-Structuring of figures once a specific area is known.

-Demonstration of the existence of five regular polyhedra.

-Proof that a triangle drawn inside a semicircle corresponds to a right triangle.

-Find the so-called polygonal numbers, those whose number of points can form the figure to which they correspond.

Gender equality

Although there are some controversies about the role of women in the Pythagorean School, it is undeniable that the female sex had an important representation.

It is stated that at least thirty women were part of it as students and teachers, highlighting Aesara of Lucania and Teano of Crotona (Pythagoras' wife).

They could not practice politics, they were only allowed to participate in mathematical and philosophical activities.

Pythagoras' philosophy was dualistic and saw the woman as an indivisible complement to the masculine.

The Pythagorean diet

One of the most significant goals of the Pythagorean doctrine was the attainment of purity. To this end, they professed an ascetic life that was characterized by having no personal possessions and a strict vegetarianism where the eating of meat was strictly prohibited.

The Pythagoreans believed in the transmigration of souls or reincarnation and did not tolerate harm to any living being.

As a curious fact, another of the precepts of the Pythagorean diet that has not been satisfactorily deciphered is Pythagoras' vehement rejection of any type of beans.

The cup of Pythagoras

Legend has it that Pythagoras created a cup that promoted fairness and punished greed. It is nothing more than a container that is completely emptied if you try to fill beyond a certain level that is marked.

The device is called the fair cup or Pythagorean cup and on Samos, his home island, it can be purchased at any souvenir shop.

It consists of a hollow cylinder in the center of the glass that, thanks to the principle that Pascal would enunciate centuries later, generates a siphon effect that empties the content.

Although we cannot verify the fidelity of the story, it serves to exemplify the Pythagorean idea that mathematics is everywhere, even in everyday objects.

Musical scale

Another story with everyday objects, places the mathematician passing through a smithy. Between the noise of the blows, the metal managed to perceive a certain harmony.

Upon entering the premises and investigating the origin of the sounds, Pythagoras discovered that the weight of the hammers were proportional intervals and that the relationship of these intervals to each other was what generated dissonance or consonance.

That observation will define the seven basic tones of the diatonic scale used in music today.

Another story attributes the construction of a monochord, a string instrument that produces the same fundamental tones by varying the length of the single string.

Sphericity of the earth

For the Pythagoreans, music transcended any field, like any mathematical principle. For this reason, they thought that regular intervals also governed celestial mechanics.

Then arises the theory of music or harmony of the spheres, where each of the celestial bodies moves in the frequency of each musical note.

This reasoning made them affirm that the earth also had a spherical shape, perhaps with more poetic than scientific inclination to equip it with the other planetary spheres.

Numbers and things

One of the greatest contributions of Pythagoras to Western thought was the systematization of abstract ideas. The Pythagoreans are the first to consider numbers as things in themselves and that they form all other things in the universe.

This numerical prominence meant the initial impulse to explain the world from constant and demonstrable phenomena, where problems were not solved but principles were sought.

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