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Pythagoras
c. 570 BCE–c. 490 BCE · Mathematician and Philosopher
An ancient Greek philosopher whose name became linked with the theorem about right-angled triangles and whose followers connected mathematics, music and philosophy.
“Number is the ruler of forms and ideas, and the cause of gods and demons.”
Why is this scientist famous?
Pythagoras is famous for the theorem that bears his name: in a right-angled triangle, a² + b² = c². The mathematical relationship was known in earlier cultures, and historians cannot prove that Pythagoras himself discovered or first proved it. His school nevertheless became highly influential in the history of mathematics, music, philosophy and the idea that patterns in nature can be understood using numbers.
Pythagoras's story
The Mysterious Sage
Pythagoras was born around 570 BCE on the Greek island of Samos. Very little about his life can be known with certainty because he left no surviving writings and detailed accounts of him were written much later. Ancient traditions say that he travelled, possibly including a visit to Egypt, but many detailed stories about his journeys cannot be verified.
The Brotherhood
Around 530 BCE, Pythagoras settled in Croton, a Greek city in southern Italy, where he established a community whose members studied philosophy, mathematics, music and ways of living. The group became known as the Pythagoreans. Later sources include women among Pythagorean followers, although we cannot know exactly how the community was organised. Many colourful stories about Pythagoras — including claims that he had supernatural powers — belong to later legend rather than reliable biography.
All is Number
The Pythagorean tradition became strongly associated with the idea that numbers and numerical relationships could help explain the natural world. Pythagoreans studied connections between musical harmony and numerical ratios. Exactly which discoveries were made personally by Pythagoras and which came from later members of his school is often impossible to determine.
The Theorem
The theorem now called Pythagoras's theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². The relationship was known in earlier mathematical traditions, including in ancient Babylon. Later Greek tradition connected the theorem with Pythagoras and his school, but historians cannot establish that Pythagoras himself was the first person to prove it.
Irrational Numbers and the Pythagoreans
Greek mathematicians eventually showed that some lengths, such as √2, cannot be written as ratios of whole numbers. This discovery challenged an important part of early Greek thinking about numbers. Later legends connected the discovery with a Pythagorean named Hippasus and even claimed that he was punished for revealing it, but historians do not treat the dramatic drowning story as established fact.
Legacy and Death
Pythagoras probably died around the beginning of the fifth century BCE. Even the circumstances of his death are uncertain. His followers continued to influence Greek mathematics and philosophy, and later Pythagorean ideas influenced thinkers including Plato. His lasting importance lies not in every discovery later attributed to him, but in the powerful tradition connecting mathematics, philosophy and the search for patterns in nature.
What did they discover?
Pythagoras's Theorem
The principle that in any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²). The relationship was known in earlier mathematical traditions, including in ancient Babylon. Later Greek tradition connected it with Pythagoras and his school, but historians cannot establish that Pythagoras himself was the first to prove it.
The Mathematics of Music
The Pythagorean tradition associated musical harmonies with simple numerical ratios of string lengths — the octave (2:1), the perfect fifth (3:2), and the perfect fourth (4:3). Exactly which discoveries were made personally by Pythagoras and which came from later members of his school is often impossible to determine.
Irrational Numbers
Greek mathematicians eventually showed that some lengths, such as √2, cannot be written as ratios of whole numbers. Later legends connected this discovery with a Pythagorean named Hippasus, but historians do not treat the dramatic drowning story as established fact.
The Pythagorean Brotherhood
Pythagoras founded a philosophical community in Croton that studied mathematics, music and philosophy. Later sources include women among Pythagorean followers. Pythagorean ideas influenced later Greek philosophy, including the work of Plato.
Number Theory Foundations
Later Greek writers associated the Pythagorean tradition with the study of properties and patterns of whole numbers. The surviving evidence rarely allows individual results to be assigned securely to Pythagoras himself.
Amazing facts
Pythagoras left no known writings. A few brief references come from his own era, while detailed accounts were written much later and mix history with legend.
He founded a philosophical community in Croton that later sources say included women among its followers.
Later legends claimed that Pythagoras had supernatural powers, including a golden thigh and the ability to be in two places at once, but historians do not treat these stories as reliable biography.
The Babylonians knew the relationship a² + b² = c² for over 1,000 years before Pythagoras. Historians cannot prove that Pythagoras himself discovered or first proved the theorem.
A later legend connected the discovery of irrational numbers with a Pythagorean named Hippasus and claimed he was drowned at sea for revealing the secret, but historians do not treat this story as established fact.
The Pythagorean tradition believed in transmigration of souls — that after death, a person's soul could be reborn in another body.
Pythagorean thinkers connected musical harmonies with simple numerical ratios, helping establish a lasting tradition of using mathematics to understand patterns in nature.
The word "mathematics" comes from the Greek word mathema, meaning learning or knowledge.
Later Pythagorean ideas influenced Plato and other Greek philosophers.
Timeline
Born on the Greek island of Samos, around 570 BCE
Settled in Croton in southern Italy and established the community later known as the Pythagoreans, around 530 BCE
Pythagorean ideas about mathematics, music and philosophy became influential in the Greek world, late 6th–early 5th century BCE
Died, probably in Metapontum in southern Italy; the exact date and circumstances are uncertain
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