Six-minute summary: Pythagoras

Hello readers! This week we’re exploring the life of Pythagoras, an Ancient Greek philosopher best known for a theory regarding right-angled triangles. His impact on modern science is undeniable. Centuries after his death, he inspired eminent scientists such as Kepler and Newton to discover fundamental laws of physics, and even now, he has the power to inspire dread in the hearts of GCSE maths students whenever they are faced with a question involving ladders leaning against walls.

A somewhat suspicious selection of sources

Our knowledge of Pythagoras relies on some dubious documents. Most accounts of his life were written centuries after his death, by which point he had become a mythical figure capable of miracles.

The earliest sources are poems from Pythagoras’ contemporaries in the 5^th century BC, written after he died. These aren’t flattering accounts by any means: one depicts him as mad, and the other describes him as a charlatan. The first mention of his mathematical theories come from Philolaus of Croton in the late 5^th century, and many historians believe that it was Philolaus himself who came up with them.

By the 4^th century BC, Pythagoras was becoming more of a mythical figure. There are three surviving biographies of Pythagoras from Ancient Greece, and each one is more fantastical than the last – possibly in response to the rise of Christianity. However, even with the power of triangles on his side, the miracles of Pythagoras couldn’t compete with the miracles of Jesus.

Origins

Pythagoras was probably born around 570 BC on the island of Samos. We know nothing of his childhood, but the island was a centre of trade in the Aegean, with plenty of goods and ideas coming in from North Africa and the Near East. As a young man, he is said to have studied in all sorts of places in order to develop his genius. He reportedly went to Egypt and to the Near East, and some writers claim that he was taught by magi in Persia and sages in India. Other sources suggest that the Phoenicians taught him arithmetic and that the Chaldeans taught him astronomy, and that he learnt from Celts and Iberians, too.

Does this diverse education sounds impossible? Well, think again. One source claims that Pythagoras had a magic arrow that let him fly long distances, while another claims that he was seen in two places at once. Still not convinced? We’re talking about a guy who predicted an earthquake after tasting the water from a well. A guy who had a thigh made of gold, according to Aristotle (who, lest we forget, invented logic). Pythagoras was more than just a man. He was once bitten by a deadly snake, only to bite it back and kill it. He once convinced a rampaging bear to stop killing people. One time, as he walked up to a river, people heard the river greet him by name. And rivers don’t just greet anybody.

The Croton cult

In 530 BC, at around the age of 40, Pythagoras moved to Croton. This was a Greek colony in southern Italy (on the ball of the foot), and nobody is quite sure what prompted him to relocate. He might have disagreed with the tyrannical ruler of Samos, or he might have been overburdened with public duties, or he might have been held in such high esteem by his fellow citizens that he felt compelled to leave (oh, the high price of success). In any case, once he arrived, he made the logical next step of setting up a cult.

Pythagoras had all the attributes of a successful cult leader. All sources agree that he was charismatic, and Herodotus reported that he taught his followers how to attain immortality. One of Pythagoras’ contemporaries was more sceptical, accusing him of “artful knavery” – but he still ended up with plenty of followers.

Plato and Isocrates both describe the “school” that Pythagoras founded in Croton. Members shared all their possessions and excluded outsiders. They viewed music as a purification of the soul, and practised therapeutic dancing. Every day, the members took morning walks. It’s all decidedly sinister.

To become a member, people had to spend five years in total silence. Those who disobeyed the rules were expelled, and the remaining members put up tombstones for them as if they had died. The rules themselves were very strange. They included never wearing woollen clothing, never poking fires with swords, and never, absolutely NEVER eating fava beans. Some accounts say that members were vegetarians, while others say that Pythagoras prescribed diets of meat to his athletes – but whatever was on the menu, it certainly wasn’t fava beans.

Some modern historians argue that Pythagoras accepted women as philosophers, because 17 out of 235 notable members were women. Given the uncertainty of the historic sources, I think this conclusion says more about the standards of modern historians than it does about Pythagoras.

Pythagorean philosophy

Although many discoveries are attributed to Pythagoras, modern historians can only trace one of his ideas back to him directly: the concept of metempsychosis. This is the belief that every soul is immortal, so that when we die, our soul transfers to a new body. According to one account, Pythagoras claimed to remember four of his past lives, one of which was a hero in the Trojan War, and one of which was a beautiful courtesan. Maybe this was why he was so accepting of women?

Another belief that we can attribute to Pythagoras with a fair amount of confidence is the “harmony of the spheres” – the idea that the planets move by mathematical equations corresponding to musical notes, resulting in a beautiful symphony inaudible to human ears. Many artists have made versions of this “music of the spheres”, including Coldplay, who wilfully disregarded the “inaudible” aspect.

Pythagoras has another musical theorem attached to his name: the more tangible concept of Pythagorean Tuning. This is where the intervals between notes on an instrument are separated by the ratio 3:2, the perfect fifth. This is the easiest way to tune an instrument by ear, and it sounds much nicer than other forms of tuning until you try to change key (which makes it poorly suited to modern music). However, this style of tuning is first documented in Ancient Mesopotamia, and Pythagoras was by no means the first to come up with it. Indeed, this is the natural way for the human ear to tune an instrument, so most people probably saw no need to write it down.

The most famous idea carrying Pythagoras’ name is Pythagoras’ Theorem, but this is now widely believed to have little to do with him. The Babylonians and Indians had used it for centuries before him, and there is little evidence that he taught it to his followers. The first mention of it comes from Philolaus, who was a member of the Pythagorean cult decades after Pythagoras died.

A religion of numbers

Philolaus recorded that the Pythagoreans treated numbers as mystical symbols. They thought one was the origin of all things, two was all matter, and three was the “ideal number” because it had a beginning, middle and end, and could form the sacred symbol of a triangle. They believed that odd numbers were male, and even numbers were female. Four signified the four seasons, and five represented marriage, because it was the sum of two and three. Seven was sacred because it was the number of known planets, and ten was regarded as the “perfect number” because ten points can form a tetractys – a symbol of great mystical importance.

However, we don’t know if Pythagoras himself ever obsessed over numbers in this manner. There is a good chance that all the stuff about numbers and triangles was started by Philolaus, as he tried to leave his mark on the cult.

Death of Pythagoras

Pythagoras lived a relatively long life, surviving into his seventies before tragedy struck. The nature of this tragedy is up for debate, although all the sources agree that he didn’t die of natural causes. Most stories claim that the Pythagoreans rejected a democratic constitution, and so the people of Croton rose against them. A building was set on fire and many people died, but this is where sources differ. Some claim that Pythagoras died in the fire, while others say he escaped, and others say he wasn’t there in the first place.

Of the sources that say he escaped the fire, one of them claims that he and a handful of followers fled to the neighbouring colony of Metapontum, only to starve to death while hiding in a temple. Another source claims that the followers died to help their leader escape, and Pythagoras was so upset about this that he killed himself. Finally, there is an account of Pythagoras fleeing from the mob only to be chased into a field of beans. His fear of the fava bean was so great that he refused to set foot there, and so he was brutally murdered.

Lasting influence

Before I started reading about Pythagoras, I assumed he was a mathematician. However, it seems that he had little to do with maths or numbers, and even his philosophy was a bit sketchy. In truth, we know little about him. He became a mythical figure, and the fictitious image we have of him managed to inspire some great scientists. Copernicus cites Pythagoras as one of the most important influences on his heliocentric model of the solar system, and Kepler believed so strongly in the music of the spheres that he derived the laws of planetary motion. Newton even attributed the discovery of the Law of Universal Gravitation to Pythagoras, and he was renowned for failing to cite his sources.

In summary…

Even by the standards of Ancient Greece, it seems unlikely that Pythagoras was a mathematician. From all the differing accounts of his life, we can only conclude that he was something of a character – and, by the looks of it, a successful cult leader. His impact on science has been profound, but possibly undeserved. Still, I hope his six-minute summary was an enlightening diversion from your day!