Pythagoras – So much more than just a triangle man.

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Sophi

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Was Pythagoras a philosopher or mathematician?

Philosophibytes level 2Pythagoras was both a philosopher and a mathematician. He is best known for his contributions to mathematics, particularly the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is fundamental in geometry and has numerous applications. However, Pythagoras was also the founder of the Pythagorean school of philosophy, which had a profound influence on the development of Western philosophy. The Pythagoreans believed that numbers were the essence of all things and that they governed the universe. They sought to uncover the mathematical and numerical principles underlying nature, and their philosophical ideas extended beyond mathematics to encompass metaphysics, ethics, and cosmology. Pythagoras and his followers made significant contributions to various fields, including mathematics, music theory, astronomy, and philosophy. Their work laid the foundation for the development of rational inquiry and mathematical reasoning.

When and where did he live?

PythagorasPythagoras is believed to have lived from around 570 BCE to 495 BCE. He was born on the island of Samos, which was then a part of the Greek world. Samos was a prosperous and influential city-state in the eastern Aegean Sea. Pythagoras later moved to the city of Croton (modern-day Crotone) in southern Italy, where he established his school and gained prominence as a philosopher and teacher. The Pythagorean school in Croton became a center of intellectual and philosophical activity, attracting many followers and students. It’s worth noting that some details about Pythagoras’ life and teachings are shrouded in myth and legend, and there are differing accounts and interpretations of his life and work. Nonetheless, he is widely recognized as one of the most important figures in the history of mathematics and philosophy.

So, what were some of his philosophical teachings?

Pythagoras’ philosophical teachings were wide-ranging and encompassed various aspects of metaphysics, ethics, and cosmology. However, due to the limited availability of primary sources and the secretive nature of the Pythagorean school, it can be challenging to discern his precise teachings. Nonetheless, here are some key philosophical ideas associated with Pythagoras and the Pythagorean school:

1. Dualism: Pythagoras and his followers believed in the existence of two fundamental principles or realities: the limited (or finite) and the unlimited (or infinite). These principles were seen as the foundation of all things and represented opposing cosmic forces.

2. Transmigration of Souls: The Pythagoreans believed in the concept of metempsychosis or the transmigration of souls. They held that the soul is immortal and undergoes a cycle of rebirths in different bodies. This belief in reincarnation was tied to notions of purification and spiritual progression.

3. Numerology and Harmony of the Spheres: Pythagoras emphasized the significance of numbers and their relationship to the fundamental structure of the universe. He believed that numbers represented the key to understanding the cosmos and that they governed both the physical and spiritual realms. The Pythagoreans also explored the concept of the “harmony of the spheres,” which suggested that the celestial bodies move according to mathematical ratios, producing a harmonious cosmic music.

4. Ethical Teachings: Pythagoras emphasized the importance of moral and ethical conduct. His teachings promoted virtues such as temperance, justice, and self-control. The Pythagoreans advocated for a balanced and harmonious life, emphasising the pursuit of wisdom and the cultivation of virtue.

5. Asceticism and Vegetarianism: The Pythagoreans followed a strict way of life that included ascetic practices, such as abstaining from meat consumption and adhering to a vegetarian diet. They believed in the inherent sacredness of all living beings and advocated for compassion towards animals. These teachings, along with the emphasis on mathematics, influenced later philosophers such as Plato and had a lasting impact on Western philosophical thought. However, due to the secretive nature of the Pythagorean school and the lack of extensive written records, some aspects of their teachings remain speculative or subject to interpretation.

What was he most famous for in Mathematics?

512px Pythagoras Theorem

Pythagoras is most famous for the discovery of the Pythagorean theorem, which is a fundamental concept in geometry. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Mathematically, this can be expressed as: a² + b² = c² Where ‘a’ and ‘b’ are the lengths of the two shorter sides (the legs) of the right triangle, and ‘c’ is the length of the hypotenuse. The Pythagorean theorem has numerous applications in geometry and trigonometry, allowing for the calculation of unknown side lengths or angles in right triangles. It forms the foundation for the study of right triangles and plays a crucial role in various areas of mathematics, engineering, physics, and other sciences. Pythagoras’ discovery of the Pythagorean theorem revolutionized the understanding of geometric relationships and laid the groundwork for further developments in mathematics. His theorem remains one of the most important and widely known mathematical results to this day.

How were Pythagoras’s Philosophy and Mathematics teaching recorded in history?
The philosophical and mathematical teachings of Pythagoras were primarily passed down through an oral tradition within the Pythagorean school. Pythagoras himself did not write down his teachings, and his followers were known to keep the knowledge within the school and restrict its dissemination.
However, some of Pythagoras’ teachings and mathematical discoveries were recorded by later Pythagoreans and other ancient scholars. The Pythagoreans believed in the secrecy and exclusivity of their knowledge, which led to a limited amount of written material being available to the public. As a result, much of what we know about Pythagorean philosophy and mathematics comes from secondary sources and accounts by later philosophers and historians. One influential figure who wrote about Pythagorean philosophy was the ancient Greek philosopher and mathematician, Plato. In his dialogues, Plato often references Pythagorean ideas and incorporates them into his own philosophical system. Plato’s works helped to popularize and preserve Pythagorean teachings. Other ancient philosophers and historians, such as Aristotle, Diogenes Laertius, and Iamblichus, also wrote about Pythagoras and the Pythagorean school. They provided insights into Pythagorean philosophy, mathematical discoveries, and the broader influence of the school. It’s important to note that due to the passage of time, the reliability and accuracy of these ancient sources can vary, and there are often differing accounts and interpretations of Pythagorean teachings. The secretive nature of the Pythagorean school also contributed to the scarcity of primary sources. Nonetheless, these writings have played a crucial role in preserving and transmitting the legacy of Pythagoras and his teachings throughout history.
Pythagoras’s death – what actually happened?

The details of his death are somewhat shrouded in myth and legend, with several accounts existing, but the exact circumstances and reasons are not definitively known.

It’s commonly believed his death involves a conflict that arose in Croton, where he had established a school. This conflict led to an attack on his followers, and Pythagoras was either killed in the attack or managed to escape and later died of starvation in Metapontum. The reasons for the conflict vary in different accounts, but they often suggest tensions between Pythagoras’s followers and the broader community or political factions in Croton.

Another story suggests that Pythagoras was murdered because of his beliefs or practices, which might have been considered controversial or threatening to certain groups.

What’s the story about a field of beans?

The story involving Pythagoras and a field of beans is one of the more peculiar legends associated with his life and death. According to this legend, Pythagoras had a profound aversion to beans (fava beans, in particular). There are various interpretations as to why he might have had such an aversion:

  1. Metaphysical or Religious Beliefs: Some sources suggest that Pythagoras believed beans were impure or had a connection with the underworld. This belief might have been based on the appearance of the beans, which were thought to resemble human genitals or the gates of Hades. Others say he thought beans contained the souls of the dead.
  2. Dietary or Health Reasons: Another theory is that Pythagoras advised against eating beans due to dietary or health reasons, possibly because they were believed to cause digestive issues or interfere with a clear state of mind.

As for how this relates to his death, one of the legends states that Pythagoras was being pursued by enemies and came across a bean field. His aversion to beans was so strong that he chose not to run through the field, which would have been the easiest escape route. This hesitation or refusal to enter the bean field ultimately led to his capture and death.

It’s important to remember that much of what is known about Pythagoras comes from accounts written many years after his death, and many of these stories have a mythical or legendary quality to them. The truth behind his aversion to beans and how it might have contributed to his death is therefore unclear and likely to remain a topic of speculation rather than historical fact.

Written/edited by Sophi and Steff


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