Pythagoras: One of the Greatest Minds of His Time
Pythagoras was one of the greatest minds and philosophers of his time and his unquestionable influence can be felt even today in mathematics. It is believed that he was the first man who referred to himself as a “philosopher.” He was the founder of Pythagoreanism, a religious and political movement that appeared mainly in the big cities of Magna Grecia (today southern Italy).
The city of Croton was his base, and the great philosopher dedicated his life to the spiritual and moral awakening and reformation of people from all social classes and sexes. This means Pythagoras was one of the most open-minded thinkers of his era.
Pythagoras advocating vegetarianism. ( Public Domain )
The Young Pythagoras
Many historians say that Pythagoras was born on the Greek island of Samos in 585 BC - even though the exact date remains uncertain. His parents named him Pythagoras after Pythia, the oracle of Delphi.
Like Socrates, Pythagoras didn’t leave behind any texts and this is the main reason we don’t know many details about his life. Some information about Pythagoras’s philosophy and teachings were told by other historical figures from antiquity, such as Plato, Aristotle, Heraclitus, Herodotus, and Isocrates. However, the main sources for his biographical information are Diogenes Laërtius, Iamblichus, and Porphyry.
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A great deal of information about Pythagoras’ youth comes from Diogenes Laërtius and his book Lives and Opinions of Eminent Philosophers :
“And as he was a young man, and devoted to learning, he quitted his country, and got initiated into all the Grecian and barbarian sacred mysteries. Accordingly, he went to Egypt, on which occasion Polycrates gave him a letter of introduction to Amasis; and he learnt the Egyptian language, as Antipho tells us, in his treatise on those men who have been conspicuous for virtue, and he associated with the Chaldaeans and with the Magi.
Afterwards he went to Crete, and in company with Epimenides, he descended into the Idaean cave, (and in Egypt too, he entered into the holiest parts of their temples), and learned all the most secret mysteries that relate to their Gods. Then he returned back again to Samos, and finding his country reduced under the absolute dominion of Polycrates, he set sail, and fled to Crotona in Italy. And there, having given laws to the Italians, he gained a very high reputation, together with his scholars, who were about three hundred in number, and governed the republic in a most excellent manner; so that the constitution was very nearly an aristocracy.”
Illustration said to depict a younger Pythagoras teaching women. ( Public Domain )
Despite his adventurous life as a young man, it’s his teachings, theories, and contributions to science and mathematics that are most important for us today. Pythagoras had very specific goals to achieve through his teachings and he passionately tried to impart his knowledge to his students so they could better understand the laws of nature. His supporters and students, known as Pythagoreans, believed that the essence of everything in life could be found in numbers and mathematics.
Aristotle verifies this in Metaphysics, books 1 through 5, where he mentions among other things:
“The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things.”
Pythagoreans celebrate sunrise. (1869) By Fyodor Bronnikov. ( Public Domain )
Pythagoras was also a great inventor and is credited with a series of innovations such as the Pythagorean Theorem, which cemented his legacy. His theory is described mathematically as α2 = β2 + γ2 and says that: “In a right- angled triangle the square of the long side is equal to the sum of the squares of the other two sides.”
The theorem which now bears his name may have been invented in India by Baudhayana around 800 BC - but only as an empirical observation. All official historical sources concur that Pythagoras is the one who proved and analyzed the theorem on a scientific basis by using theoretical geometry, logical evidence, a ruler, and a compass as his tools.
Illustration of the Pythagorean theorem . ( CC BY SA 3.0 )
Pythagoras’s name is also connected with the Tetractys, which is considered by many historians to be the essence of his teaching and the sacred symbol of his followers. It consists of the numbers 1 through 10 arranged in four rows: one in the first row, two in the second, three in the third, and four in the fourth.
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The Tetractys is a triangular figure consisting of ten points arranged in four rows: one, two, three, and four points in each row. It was very important to the Pythagoreans. ( Public Domain )
The Greedy Cup
Another of Pythagoras’s inventions, one that unfortunately remains widely unknown, is the Pythagorean Cup, also known as the Greedy Cup. Local traditions in Samos say that he made the cup for drinking wine in moderation. Inside, there was a line that defined the maximum level of wine the cup could be filled with. A trickle above that line and the cup automatically emptied its contents from a hidden hole in its base.
Cross section of a Pythagorean cup being filled: at B, the cup may be drunk from, but at C, the siphon effect causes the cup to drain . ( Nevit Dilmen /CC BY SA 3.0 )
Some also called it the “Justice Cup” since they believed that Pythagoras, who wasn’t much of a drinker, wanted to show his students and followers the negative effects of greediness in one’s life. When the limit is exceeded (hubris), you won’t only lose what passes that limit, but also what you had previously acquired (nemesis).
Simply by applying a hydraulic principle, Pythagoras teaches you to accept moderation and to enjoy the things you already have in life without asking for more - things you don’t really need, but seek out for selfish reasons.
Cut-through illustration of a Pythagorean cup . ( Fair Use )
An Uncertain Death
Like the date of his birth, sources vary on the cause of his death as well. Diogenes Laërtius wrote that Pythagoras and his students were victims of a bloody massacre by the local Croton authorities who feared the immense influence of Pythagoras’s teachings on the local society. Dicaearchus however, claims Pythagoras died from starvation after not eating for over forty days.
Pythagoras emerging from the underworld. (1662) By Salvator Rosa. ( Public Domain )
Despite not knowing for sure how this great philosopher, mathematician, and inventor died, his name and theories have lived on to this day. His magnificent teachings have been studied throughout the centuries and will be remembered for centuries to come.
Top Image: Raphael, School of Athens, fresco, 1509-1511, depicting Pythagoras ( Steven Zucker / flickr )
Ancient-Symbols.com (2014) Tetractys. Available at: http://www.ancient-symbols.com/symbols-directory/tetractys.html
The Stanford Encyclopedia of Philosophy (2014) Pythagoreanism. Available at: https://plato.stanford.edu/entries/pythagoreanism/
Puiu, T. (2015) The Pythagorean cup – the vessel that spills its content if you’re too greedy . Available at: http://www.zmescience.com/science/physics/the-pythagorean-greedy-cup-423545/
Pythagoras’s Effect On Our World Today (2009). Available at: http://www.slideshare.net/992751/pythagorass-effect-on-our-world-today-presentation
I could've used one of those cups in my fraternity.